1# 2# number.py : Number-theoretic functions 3# 4# Part of the Python Cryptography Toolkit 5# 6# Written by Andrew M. Kuchling, Barry A. Warsaw, and others 7# 8# =================================================================== 9# The contents of this file are dedicated to the public domain. To 10# the extent that dedication to the public domain is not available, 11# everyone is granted a worldwide, perpetual, royalty-free, 12# non-exclusive license to exercise all rights associated with the 13# contents of this file for any purpose whatsoever. 14# No rights are reserved. 15# 16# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 17# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF 18# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND 19# NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS 20# BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN 21# ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN 22# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 23# SOFTWARE. 24# =================================================================== 25# 26 27__revision__ = "$Id$" 28 29from Crypto.pct_warnings import GetRandomNumber_DeprecationWarning, PowmInsecureWarning 30from warnings import warn as _warn 31import math 32import sys 33from Crypto.Util.py3compat import * 34 35bignum = long 36try: 37 from Crypto.PublicKey import _fastmath 38except ImportError: 39 # For production, we are going to let import issues due to gmp/mpir shared 40 # libraries not loading slide silently and use slowmath. If you'd rather 41 # see an exception raised if _fastmath exists but cannot be imported, 42 # uncomment the below 43 # 44 # from distutils.sysconfig import get_config_var 45 # import inspect, os 46 # _fm_path = os.path.normpath(os.path.dirname(os.path.abspath( 47 # inspect.getfile(inspect.currentframe()))) 48 # +"/../../PublicKey/_fastmath"+get_config_var("SO")) 49 # if os.path.exists(_fm_path): 50 # raise ImportError("While the _fastmath module exists, importing "+ 51 # "it failed. This may point to the gmp or mpir shared library "+ 52 # "not being in the path. _fastmath was found at "+_fm_path) 53 _fastmath = None 54 55# You need libgmp v5 or later to get mpz_powm_sec. Warn if it's not available. 56if _fastmath is not None and not _fastmath.HAVE_DECL_MPZ_POWM_SEC: 57 _warn("Not using mpz_powm_sec. You should rebuild using libgmp >= 5 to avoid timing attack vulnerability.", PowmInsecureWarning) 58 59# New functions 60from _number_new import * 61 62# Commented out and replaced with faster versions below 63## def long2str(n): 64## s='' 65## while n>0: 66## s=chr(n & 255)+s 67## n=n>>8 68## return s 69 70## import types 71## def str2long(s): 72## if type(s)!=types.StringType: return s # Integers will be left alone 73## return reduce(lambda x,y : x*256+ord(y), s, 0L) 74 75def size (N): 76 """size(N:long) : int 77 Returns the size of the number N in bits. 78 """ 79 bits = 0 80 while N >> bits: 81 bits += 1 82 return bits 83 84def getRandomNumber(N, randfunc=None): 85 """Deprecated. Use getRandomInteger or getRandomNBitInteger instead.""" 86 warnings.warn("Crypto.Util.number.getRandomNumber has confusing semantics"+ 87 "and has been deprecated. Use getRandomInteger or getRandomNBitInteger instead.", 88 GetRandomNumber_DeprecationWarning) 89 return getRandomNBitInteger(N, randfunc) 90 91def getRandomInteger(N, randfunc=None): 92 """getRandomInteger(N:int, randfunc:callable):long 93 Return a random number with at most N bits. 94 95 If randfunc is omitted, then Random.new().read is used. 96 97 This function is for internal use only and may be renamed or removed in 98 the future. 99 """ 100 if randfunc is None: 101 _import_Random() 102 randfunc = Random.new().read 103 104 S = randfunc(N>>3) 105 odd_bits = N % 8 106 if odd_bits != 0: 107 char = ord(randfunc(1)) >> (8-odd_bits) 108 S = bchr(char) + S 109 value = bytes_to_long(S) 110 return value 111 112def getRandomRange(a, b, randfunc=None): 113 """getRandomRange(a:int, b:int, randfunc:callable):long 114 Return a random number n so that a <= n < b. 115 116 If randfunc is omitted, then Random.new().read is used. 117 118 This function is for internal use only and may be renamed or removed in 119 the future. 120 """ 121 range_ = b - a - 1 122 bits = size(range_) 123 value = getRandomInteger(bits, randfunc) 124 while value > range_: 125 value = getRandomInteger(bits, randfunc) 126 return a + value 127 128def getRandomNBitInteger(N, randfunc=None): 129 """getRandomInteger(N:int, randfunc:callable):long 130 Return a random number with exactly N-bits, i.e. a random number 131 between 2**(N-1) and (2**N)-1. 132 133 If randfunc is omitted, then Random.new().read is used. 134 135 This function is for internal use only and may be renamed or removed in 136 the future. 137 """ 138 value = getRandomInteger (N-1, randfunc) 139 value |= 2L ** (N-1) # Ensure high bit is set 140 assert size(value) >= N 141 return value 142 143def GCD(x,y): 144 """GCD(x:long, y:long): long 145 Return the GCD of x and y. 146 """ 147 x = abs(x) ; y = abs(y) 148 while x > 0: 149 x, y = y % x, x 150 return y 151 152def inverse(u, v): 153 """inverse(u:long, v:long):long 154 Return the inverse of u mod v. 155 """ 156 u3, v3 = long(u), long(v) 157 u1, v1 = 1L, 0L 158 while v3 > 0: 159 q=divmod(u3, v3)[0] 160 u1, v1 = v1, u1 - v1*q 161 u3, v3 = v3, u3 - v3*q 162 while u1<0: 163 u1 = u1 + v 164 return u1 165 166# Given a number of bits to generate and a random generation function, 167# find a prime number of the appropriate size. 168 169def getPrime(N, randfunc=None): 170 """getPrime(N:int, randfunc:callable):long 171 Return a random N-bit prime number. 172 173 If randfunc is omitted, then Random.new().read is used. 174 """ 175 if randfunc is None: 176 _import_Random() 177 randfunc = Random.new().read 178 179 number=getRandomNBitInteger(N, randfunc) | 1 180 while (not isPrime(number, randfunc=randfunc)): 181 number=number+2 182 return number 183 184 185def _rabinMillerTest(n, rounds, randfunc=None): 186 """_rabinMillerTest(n:long, rounds:int, randfunc:callable):int 187 Tests if n is prime. 188 Returns 0 when n is definitly composite. 189 Returns 1 when n is probably prime. 190 Returns 2 when n is definitly prime. 191 192 If randfunc is omitted, then Random.new().read is used. 193 194 This function is for internal use only and may be renamed or removed in 195 the future. 196 """ 197 # check special cases (n==2, n even, n < 2) 198 if n < 3 or (n & 1) == 0: 199 return n == 2 200 # n might be very large so it might be beneficial to precalculate n-1 201 n_1 = n - 1 202 # determine m and b so that 2**b * m = n - 1 and b maximal 203 b = 0 204 m = n_1 205 while (m & 1) == 0: 206 b += 1 207 m >>= 1 208 209 tested = [] 210 # we need to do at most n-2 rounds. 211 for i in xrange (min (rounds, n-2)): 212 # randomly choose a < n and make sure it hasn't been tested yet 213 a = getRandomRange (2, n, randfunc) 214 while a in tested: 215 a = getRandomRange (2, n, randfunc) 216 tested.append (a) 217 # do the rabin-miller test 218 z = pow (a, m, n) # (a**m) % n 219 if z == 1 or z == n_1: 220 continue 221 composite = 1 222 for r in xrange (b): 223 z = (z * z) % n 224 if z == 1: 225 return 0 226 elif z == n_1: 227 composite = 0 228 break 229 if composite: 230 return 0 231 return 1 232 233def getStrongPrime(N, e=0, false_positive_prob=1e-6, randfunc=None): 234 """getStrongPrime(N:int, e:int, false_positive_prob:float, randfunc:callable):long 235 Return a random strong N-bit prime number. 236 In this context p is a strong prime if p-1 and p+1 have at 237 least one large prime factor. 238 N should be a multiple of 128 and > 512. 239 240 If e is provided the returned prime p-1 will be coprime to e 241 and thus suitable for RSA where e is the public exponent. 242 243 The optional false_positive_prob is the statistical probability 244 that true is returned even though it is not (pseudo-prime). 245 It defaults to 1e-6 (less than 1:1000000). 246 Note that the real probability of a false-positive is far less. This is 247 just the mathematically provable limit. 248 249 randfunc should take a single int parameter and return that 250 many random bytes as a string. 251 If randfunc is omitted, then Random.new().read is used. 252 """ 253 # This function was implemented following the 254 # instructions found in the paper: 255 # "FAST GENERATION OF RANDOM, STRONG RSA PRIMES" 256 # by Robert D. Silverman 257 # RSA Laboratories 258 # May 17, 1997 259 # which by the time of writing could be freely downloaded here: 260 # http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.17.2713&rep=rep1&type=pdf 261 262 # Use the accelerator if available 263 if _fastmath is not None: 264 return _fastmath.getStrongPrime(long(N), long(e), false_positive_prob, 265 randfunc) 266 267 if (N < 512) or ((N % 128) != 0): 268 raise ValueError ("bits must be multiple of 128 and > 512") 269 270 rabin_miller_rounds = int(math.ceil(-math.log(false_positive_prob)/math.log(4))) 271 272 # calculate range for X 273 # lower_bound = sqrt(2) * 2^{511 + 128*x} 274 # upper_bound = 2^{512 + 128*x} - 1 275 x = (N - 512) >> 7; 276 # We need to approximate the sqrt(2) in the lower_bound by an integer 277 # expression because floating point math overflows with these numbers 278 lower_bound = divmod(14142135623730950489L * (2L ** (511 + 128*x)), 279 10000000000000000000L)[0] 280 upper_bound = (1L << (512 + 128*x)) - 1 281 # Randomly choose X in calculated range 282 X = getRandomRange (lower_bound, upper_bound, randfunc) 283 284 # generate p1 and p2 285 p = [0, 0] 286 for i in (0, 1): 287 # randomly choose 101-bit y 288 y = getRandomNBitInteger (101, randfunc) 289 # initialize the field for sieving 290 field = [0] * 5 * len (sieve_base) 291 # sieve the field 292 for prime in sieve_base: 293 offset = y % prime 294 for j in xrange ((prime - offset) % prime, len (field), prime): 295 field[j] = 1 296 297 # look for suitable p[i] starting at y 298 result = 0 299 for j in range(len(field)): 300 composite = field[j] 301 # look for next canidate 302 if composite: 303 continue 304 tmp = y + j 305 result = _rabinMillerTest (tmp, rabin_miller_rounds) 306 if result > 0: 307 p[i] = tmp 308 break 309 if result == 0: 310 raise RuntimeError ("Couln't find prime in field. " 311 "Developer: Increase field_size") 312 313 # Calculate R 314 # R = (p2^{-1} mod p1) * p2 - (p1^{-1} mod p2) * p1 315 tmp1 = inverse (p[1], p[0]) * p[1] # (p2^-1 mod p1)*p2 316 tmp2 = inverse (p[0], p[1]) * p[0] # (p1^-1 mod p2)*p1 317 R = tmp1 - tmp2 # (p2^-1 mod p1)*p2 - (p1^-1 mod p2)*p1 318 319 # search for final prime number starting by Y0 320 # Y0 = X + (R - X mod p1p2) 321 increment = p[0] * p[1] 322 X = X + (R - (X % increment)) 323 while 1: 324 is_possible_prime = 1 325 # first check candidate against sieve_base 326 for prime in sieve_base: 327 if (X % prime) == 0: 328 is_possible_prime = 0 329 break 330 # if e is given make sure that e and X-1 are coprime 331 # this is not necessarily a strong prime criterion but useful when 332 # creating them for RSA where the p-1 and q-1 should be coprime to 333 # the public exponent e 334 if e and is_possible_prime: 335 if e & 1: 336 if GCD (e, X-1) != 1: 337 is_possible_prime = 0 338 else: 339 if GCD (e, divmod((X-1),2)[0]) != 1: 340 is_possible_prime = 0 341 342 # do some Rabin-Miller-Tests 343 if is_possible_prime: 344 result = _rabinMillerTest (X, rabin_miller_rounds) 345 if result > 0: 346 break 347 X += increment 348 # abort when X has more bits than requested 349 # TODO: maybe we shouldn't abort but rather start over. 350 if X >= 1L << N: 351 raise RuntimeError ("Couln't find prime in field. " 352 "Developer: Increase field_size") 353 return X 354 355def isPrime(N, false_positive_prob=1e-6, randfunc=None): 356 """isPrime(N:long, false_positive_prob:float, randfunc:callable):bool 357 Return true if N is prime. 358 359 The optional false_positive_prob is the statistical probability 360 that true is returned even though it is not (pseudo-prime). 361 It defaults to 1e-6 (less than 1:1000000). 362 Note that the real probability of a false-positive is far less. This is 363 just the mathematically provable limit. 364 365 If randfunc is omitted, then Random.new().read is used. 366 """ 367 if _fastmath is not None: 368 return _fastmath.isPrime(long(N), false_positive_prob, randfunc) 369 370 if N < 3 or N & 1 == 0: 371 return N == 2 372 for p in sieve_base: 373 if N == p: 374 return 1 375 if N % p == 0: 376 return 0 377 378 rounds = int(math.ceil(-math.log(false_positive_prob)/math.log(4))) 379 return _rabinMillerTest(N, rounds, randfunc) 380 381 382# Improved conversion functions contributed by Barry Warsaw, after 383# careful benchmarking 384 385import struct 386 387def long_to_bytes(n, blocksize=0): 388 """long_to_bytes(n:long, blocksize:int) : string 389 Convert a long integer to a byte string. 390 391 If optional blocksize is given and greater than zero, pad the front of the 392 byte string with binary zeros so that the length is a multiple of 393 blocksize. 394 """ 395 # after much testing, this algorithm was deemed to be the fastest 396 s = b('') 397 n = long(n) 398 pack = struct.pack 399 while n > 0: 400 s = pack('>I', n & 0xffffffffL) + s 401 n = n >> 32 402 # strip off leading zeros 403 for i in range(len(s)): 404 if s[i] != b('\000')[0]: 405 break 406 else: 407 # only happens when n == 0 408 s = b('\000') 409 i = 0 410 s = s[i:] 411 # add back some pad bytes. this could be done more efficiently w.r.t. the 412 # de-padding being done above, but sigh... 413 if blocksize > 0 and len(s) % blocksize: 414 s = (blocksize - len(s) % blocksize) * b('\000') + s 415 return s 416 417def bytes_to_long(s): 418 """bytes_to_long(string) : long 419 Convert a byte string to a long integer. 420 421 This is (essentially) the inverse of long_to_bytes(). 422 """ 423 acc = 0L 424 unpack = struct.unpack 425 length = len(s) 426 if length % 4: 427 extra = (4 - length % 4) 428 s = b('\000') * extra + s 429 length = length + extra 430 for i in range(0, length, 4): 431 acc = (acc << 32) + unpack('>I', s[i:i+4])[0] 432 return acc 433 434# For backwards compatibility... 435import warnings 436def long2str(n, blocksize=0): 437 warnings.warn("long2str() has been replaced by long_to_bytes()") 438 return long_to_bytes(n, blocksize) 439def str2long(s): 440 warnings.warn("str2long() has been replaced by bytes_to_long()") 441 return bytes_to_long(s) 442 443def _import_Random(): 444 # This is called in a function instead of at the module level in order to 445 # avoid problems with recursive imports 446 global Random, StrongRandom 447 from Crypto import Random 448 from Crypto.Random.random import StrongRandom 449 450 451 452# The first 10000 primes used for checking primality. 453# This should be enough to eliminate most of the odd 454# numbers before needing to do a Rabin-Miller test at all. 455sieve_base = ( 456 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 457 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 458 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 459 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 460 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 461 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 462 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 463 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 464 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 465 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 466 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 467 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 468 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 469 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 470 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 471 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 472 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 473 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 474 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 475 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 476 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 477 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 478 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 479 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 480 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 481 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 482 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 483 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 484 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 485 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 486 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 487 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 488 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 489 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 490 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 491 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 492 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 493 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 494 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 495 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 496 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 497 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 498 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 499 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 500 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 501 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 502 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 503 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 504 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 505 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 506 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 507 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 508 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 509 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 510 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 511 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 512 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 513 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 514 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 515 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 516 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 517 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 518 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 519 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 520 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 521 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 522 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 523 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 524 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 525 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 526 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 527 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 528 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 529 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 530 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 531 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 532 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 533 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 534 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 535 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 536 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 537 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 538 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 539 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 540 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 541 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 542 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 543 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 544 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 545 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 546 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 547 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 548 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 549 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 550 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 551 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 552 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 553 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 554 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 555 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 556 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 557 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 558 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 559 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 560 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 561 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 562 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 563 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 564 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 565 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 566 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 567 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 568 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 569 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 570 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 571 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 572 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 573 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 574 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 575 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 576 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 577 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 578 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 579 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 580 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 581 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 582 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 583 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 584 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 585 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 586 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 587 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 588 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 589 10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 590 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 591 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, 592 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 593 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 594 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 595 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 596 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 597 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 598 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 599 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 600 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 601 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 602 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 603 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 604 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 605 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 606 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 607 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 608 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 609 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 610 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 611 13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 612 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 613 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 614 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 615 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 616 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 617 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 618 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 619 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 620 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 621 13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 622 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 623 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 624 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14419, 625 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 626 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 627 14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 628 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 629 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 630 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 631 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 632 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 633 15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 634 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 635 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401, 636 15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493, 15497, 637 15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607, 638 15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667, 15671, 15679, 639 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773, 640 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 15881, 641 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971, 642 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 643 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 644 16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 645 16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 646 16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453, 16477, 16481, 647 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603, 648 16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 649 16693, 16699, 16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811, 650 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, 16901, 16903, 651 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993, 652 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, 653 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 654 17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 655 17321, 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 656 17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 657 17483, 17489, 17491, 17497, 17509, 17519, 17539, 17551, 17569, 17573, 658 17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657, 17659, 17669, 659 17681, 17683, 17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783, 660 17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863, 17881, 17891, 661 17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971, 662 17977, 17981, 17987, 17989, 18013, 18041, 18043, 18047, 18049, 18059, 663 18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143, 664 18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 18233, 665 18251, 18253, 18257, 18269, 18287, 18289, 18301, 18307, 18311, 18313, 666 18329, 18341, 18353, 18367, 18371, 18379, 18397, 18401, 18413, 18427, 667 18433, 18439, 18443, 18451, 18457, 18461, 18481, 18493, 18503, 18517, 668 18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593, 18617, 18637, 669 18661, 18671, 18679, 18691, 18701, 18713, 18719, 18731, 18743, 18749, 670 18757, 18773, 18787, 18793, 18797, 18803, 18839, 18859, 18869, 18899, 671 18911, 18913, 18917, 18919, 18947, 18959, 18973, 18979, 19001, 19009, 672 19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, 19087, 19121, 673 19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211, 19213, 19219, 674 19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301, 19309, 19319, 675 19333, 19373, 19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423, 676 19427, 19429, 19433, 19441, 19447, 19457, 19463, 19469, 19471, 19477, 677 19483, 19489, 19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571, 678 19577, 19583, 19597, 19603, 19609, 19661, 19681, 19687, 19697, 19699, 679 19709, 19717, 19727, 19739, 19751, 19753, 19759, 19763, 19777, 19793, 680 19801, 19813, 19819, 19841, 19843, 19853, 19861, 19867, 19889, 19891, 681 19913, 19919, 19927, 19937, 19949, 19961, 19963, 19973, 19979, 19991, 682 19993, 19997, 20011, 20021, 20023, 20029, 20047, 20051, 20063, 20071, 683 20089, 20101, 20107, 20113, 20117, 20123, 20129, 20143, 20147, 20149, 684 20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233, 20249, 20261, 685 20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357, 686 20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431, 20441, 20443, 687 20477, 20479, 20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551, 688 20563, 20593, 20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 689 20707, 20717, 20719, 20731, 20743, 20747, 20749, 20753, 20759, 20771, 690 20773, 20789, 20807, 20809, 20849, 20857, 20873, 20879, 20887, 20897, 691 20899, 20903, 20921, 20929, 20939, 20947, 20959, 20963, 20981, 20983, 692 21001, 21011, 21013, 21017, 21019, 21023, 21031, 21059, 21061, 21067, 693 21089, 21101, 21107, 21121, 21139, 21143, 21149, 21157, 21163, 21169, 694 21179, 21187, 21191, 21193, 21211, 21221, 21227, 21247, 21269, 21277, 695 21283, 21313, 21317, 21319, 21323, 21341, 21347, 21377, 21379, 21383, 696 21391, 21397, 21401, 21407, 21419, 21433, 21467, 21481, 21487, 21491, 697 21493, 21499, 21503, 21517, 21521, 21523, 21529, 21557, 21559, 21563, 698 21569, 21577, 21587, 21589, 21599, 21601, 21611, 21613, 21617, 21647, 699 21649, 21661, 21673, 21683, 21701, 21713, 21727, 21737, 21739, 21751, 700 21757, 21767, 21773, 21787, 21799, 21803, 21817, 21821, 21839, 21841, 701 21851, 21859, 21863, 21871, 21881, 21893, 21911, 21929, 21937, 21943, 702 21961, 21977, 21991, 21997, 22003, 22013, 22027, 22031, 22037, 22039, 703 22051, 22063, 22067, 22073, 22079, 22091, 22093, 22109, 22111, 22123, 704 22129, 22133, 22147, 22153, 22157, 22159, 22171, 22189, 22193, 22229, 705 22247, 22259, 22271, 22273, 22277, 22279, 22283, 22291, 22303, 22307, 706 22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409, 22433, 22441, 707 22447, 22453, 22469, 22481, 22483, 22501, 22511, 22531, 22541, 22543, 708 22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637, 22639, 22643, 709 22651, 22669, 22679, 22691, 22697, 22699, 22709, 22717, 22721, 22727, 710 22739, 22741, 22751, 22769, 22777, 22783, 22787, 22807, 22811, 22817, 711 22853, 22859, 22861, 22871, 22877, 22901, 22907, 22921, 22937, 22943, 712 22961, 22963, 22973, 22993, 23003, 23011, 23017, 23021, 23027, 23029, 713 23039, 23041, 23053, 23057, 23059, 23063, 23071, 23081, 23087, 23099, 714 23117, 23131, 23143, 23159, 23167, 23173, 23189, 23197, 23201, 23203, 715 23209, 23227, 23251, 23269, 23279, 23291, 23293, 23297, 23311, 23321, 716 23327, 23333, 23339, 23357, 23369, 23371, 23399, 23417, 23431, 23447, 717 23459, 23473, 23497, 23509, 23531, 23537, 23539, 23549, 23557, 23561, 718 23563, 23567, 23581, 23593, 23599, 23603, 23609, 23623, 23627, 23629, 719 23633, 23663, 23669, 23671, 23677, 23687, 23689, 23719, 23741, 23743, 720 23747, 23753, 23761, 23767, 23773, 23789, 23801, 23813, 23819, 23827, 721 23831, 23833, 23857, 23869, 23873, 23879, 23887, 23893, 23899, 23909, 722 23911, 23917, 23929, 23957, 23971, 23977, 23981, 23993, 24001, 24007, 723 24019, 24023, 24029, 24043, 24049, 24061, 24071, 24077, 24083, 24091, 724 24097, 24103, 24107, 24109, 24113, 24121, 24133, 24137, 24151, 24169, 725 24179, 24181, 24197, 24203, 24223, 24229, 24239, 24247, 24251, 24281, 726 24317, 24329, 24337, 24359, 24371, 24373, 24379, 24391, 24407, 24413, 727 24419, 24421, 24439, 24443, 24469, 24473, 24481, 24499, 24509, 24517, 728 24527, 24533, 24547, 24551, 24571, 24593, 24611, 24623, 24631, 24659, 729 24671, 24677, 24683, 24691, 24697, 24709, 24733, 24749, 24763, 24767, 730 24781, 24793, 24799, 24809, 24821, 24841, 24847, 24851, 24859, 24877, 731 24889, 24907, 24917, 24919, 24923, 24943, 24953, 24967, 24971, 24977, 732 24979, 24989, 25013, 25031, 25033, 25037, 25057, 25073, 25087, 25097, 733 25111, 25117, 25121, 25127, 25147, 25153, 25163, 25169, 25171, 25183, 734 25189, 25219, 25229, 25237, 25243, 25247, 25253, 25261, 25301, 25303, 735 25307, 25309, 25321, 25339, 25343, 25349, 25357, 25367, 25373, 25391, 736 25409, 25411, 25423, 25439, 25447, 25453, 25457, 25463, 25469, 25471, 737 25523, 25537, 25541, 25561, 25577, 25579, 25583, 25589, 25601, 25603, 738 25609, 25621, 25633, 25639, 25643, 25657, 25667, 25673, 25679, 25693, 739 25703, 25717, 25733, 25741, 25747, 25759, 25763, 25771, 25793, 25799, 740 25801, 25819, 25841, 25847, 25849, 25867, 25873, 25889, 25903, 25913, 741 25919, 25931, 25933, 25939, 25943, 25951, 25969, 25981, 25997, 25999, 742 26003, 26017, 26021, 26029, 26041, 26053, 26083, 26099, 26107, 26111, 743 26113, 26119, 26141, 26153, 26161, 26171, 26177, 26183, 26189, 26203, 744 26209, 26227, 26237, 26249, 26251, 26261, 26263, 26267, 26293, 26297, 745 26309, 26317, 26321, 26339, 26347, 26357, 26371, 26387, 26393, 26399, 746 26407, 26417, 26423, 26431, 26437, 26449, 26459, 26479, 26489, 26497, 747 26501, 26513, 26539, 26557, 26561, 26573, 26591, 26597, 26627, 26633, 748 26641, 26647, 26669, 26681, 26683, 26687, 26693, 26699, 26701, 26711, 749 26713, 26717, 26723, 26729, 26731, 26737, 26759, 26777, 26783, 26801, 750 26813, 26821, 26833, 26839, 26849, 26861, 26863, 26879, 26881, 26891, 751 26893, 26903, 26921, 26927, 26947, 26951, 26953, 26959, 26981, 26987, 752 26993, 27011, 27017, 27031, 27043, 27059, 27061, 27067, 27073, 27077, 753 27091, 27103, 27107, 27109, 27127, 27143, 27179, 27191, 27197, 27211, 754 27239, 27241, 27253, 27259, 27271, 27277, 27281, 27283, 27299, 27329, 755 27337, 27361, 27367, 27397, 27407, 27409, 27427, 27431, 27437, 27449, 756 27457, 27479, 27481, 27487, 27509, 27527, 27529, 27539, 27541, 27551, 757 27581, 27583, 27611, 27617, 27631, 27647, 27653, 27673, 27689, 27691, 758 27697, 27701, 27733, 27737, 27739, 27743, 27749, 27751, 27763, 27767, 759 27773, 27779, 27791, 27793, 27799, 27803, 27809, 27817, 27823, 27827, 760 27847, 27851, 27883, 27893, 27901, 27917, 27919, 27941, 27943, 27947, 761 27953, 27961, 27967, 27983, 27997, 28001, 28019, 28027, 28031, 28051, 762 28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111, 28123, 28151, 763 28163, 28181, 28183, 28201, 28211, 28219, 28229, 28277, 28279, 28283, 764 28289, 28297, 28307, 28309, 28319, 28349, 28351, 28387, 28393, 28403, 765 28409, 28411, 28429, 28433, 28439, 28447, 28463, 28477, 28493, 28499, 766 28513, 28517, 28537, 28541, 28547, 28549, 28559, 28571, 28573, 28579, 767 28591, 28597, 28603, 28607, 28619, 28621, 28627, 28631, 28643, 28649, 768 28657, 28661, 28663, 28669, 28687, 28697, 28703, 28711, 28723, 28729, 769 28751, 28753, 28759, 28771, 28789, 28793, 28807, 28813, 28817, 28837, 770 28843, 28859, 28867, 28871, 28879, 28901, 28909, 28921, 28927, 28933, 771 28949, 28961, 28979, 29009, 29017, 29021, 29023, 29027, 29033, 29059, 772 29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147, 29153, 29167, 773 29173, 29179, 29191, 29201, 29207, 29209, 29221, 29231, 29243, 29251, 774 29269, 29287, 29297, 29303, 29311, 29327, 29333, 29339, 29347, 29363, 775 29383, 29387, 29389, 29399, 29401, 29411, 29423, 29429, 29437, 29443, 776 29453, 29473, 29483, 29501, 29527, 29531, 29537, 29567, 29569, 29573, 777 29581, 29587, 29599, 29611, 29629, 29633, 29641, 29663, 29669, 29671, 778 29683, 29717, 29723, 29741, 29753, 29759, 29761, 29789, 29803, 29819, 779 29833, 29837, 29851, 29863, 29867, 29873, 29879, 29881, 29917, 29921, 780 29927, 29947, 29959, 29983, 29989, 30011, 30013, 30029, 30047, 30059, 781 30071, 30089, 30091, 30097, 30103, 30109, 30113, 30119, 30133, 30137, 782 30139, 30161, 30169, 30181, 30187, 30197, 30203, 30211, 30223, 30241, 783 30253, 30259, 30269, 30271, 30293, 30307, 30313, 30319, 30323, 30341, 784 30347, 30367, 30389, 30391, 30403, 30427, 30431, 30449, 30467, 30469, 785 30491, 30493, 30497, 30509, 30517, 30529, 30539, 30553, 30557, 30559, 786 30577, 30593, 30631, 30637, 30643, 30649, 30661, 30671, 30677, 30689, 787 30697, 30703, 30707, 30713, 30727, 30757, 30763, 30773, 30781, 30803, 788 30809, 30817, 30829, 30839, 30841, 30851, 30853, 30859, 30869, 30871, 789 30881, 30893, 30911, 30931, 30937, 30941, 30949, 30971, 30977, 30983, 790 31013, 31019, 31033, 31039, 31051, 31063, 31069, 31079, 31081, 31091, 791 31121, 31123, 31139, 31147, 31151, 31153, 31159, 31177, 31181, 31183, 792 31189, 31193, 31219, 31223, 31231, 31237, 31247, 31249, 31253, 31259, 793 31267, 31271, 31277, 31307, 31319, 31321, 31327, 31333, 31337, 31357, 794 31379, 31387, 31391, 31393, 31397, 31469, 31477, 31481, 31489, 31511, 795 31513, 31517, 31531, 31541, 31543, 31547, 31567, 31573, 31583, 31601, 796 31607, 31627, 31643, 31649, 31657, 31663, 31667, 31687, 31699, 31721, 797 31723, 31727, 31729, 31741, 31751, 31769, 31771, 31793, 31799, 31817, 798 31847, 31849, 31859, 31873, 31883, 31891, 31907, 31957, 31963, 31973, 799 31981, 31991, 32003, 32009, 32027, 32029, 32051, 32057, 32059, 32063, 800 32069, 32077, 32083, 32089, 32099, 32117, 32119, 32141, 32143, 32159, 801 32173, 32183, 32189, 32191, 32203, 32213, 32233, 32237, 32251, 32257, 802 32261, 32297, 32299, 32303, 32309, 32321, 32323, 32327, 32341, 32353, 803 32359, 32363, 32369, 32371, 32377, 32381, 32401, 32411, 32413, 32423, 804 32429, 32441, 32443, 32467, 32479, 32491, 32497, 32503, 32507, 32531, 805 32533, 32537, 32561, 32563, 32569, 32573, 32579, 32587, 32603, 32609, 806 32611, 32621, 32633, 32647, 32653, 32687, 32693, 32707, 32713, 32717, 807 32719, 32749, 32771, 32779, 32783, 32789, 32797, 32801, 32803, 32831, 808 32833, 32839, 32843, 32869, 32887, 32909, 32911, 32917, 32933, 32939, 809 32941, 32957, 32969, 32971, 32983, 32987, 32993, 32999, 33013, 33023, 810 33029, 33037, 33049, 33053, 33071, 33073, 33083, 33091, 33107, 33113, 811 33119, 33149, 33151, 33161, 33179, 33181, 33191, 33199, 33203, 33211, 812 33223, 33247, 33287, 33289, 33301, 33311, 33317, 33329, 33331, 33343, 813 33347, 33349, 33353, 33359, 33377, 33391, 33403, 33409, 33413, 33427, 814 33457, 33461, 33469, 33479, 33487, 33493, 33503, 33521, 33529, 33533, 815 33547, 33563, 33569, 33577, 33581, 33587, 33589, 33599, 33601, 33613, 816 33617, 33619, 33623, 33629, 33637, 33641, 33647, 33679, 33703, 33713, 817 33721, 33739, 33749, 33751, 33757, 33767, 33769, 33773, 33791, 33797, 818 33809, 33811, 33827, 33829, 33851, 33857, 33863, 33871, 33889, 33893, 819 33911, 33923, 33931, 33937, 33941, 33961, 33967, 33997, 34019, 34031, 820 34033, 34039, 34057, 34061, 34123, 34127, 34129, 34141, 34147, 34157, 821 34159, 34171, 34183, 34211, 34213, 34217, 34231, 34253, 34259, 34261, 822 34267, 34273, 34283, 34297, 34301, 34303, 34313, 34319, 34327, 34337, 823 34351, 34361, 34367, 34369, 34381, 34403, 34421, 34429, 34439, 34457, 824 34469, 34471, 34483, 34487, 34499, 34501, 34511, 34513, 34519, 34537, 825 34543, 34549, 34583, 34589, 34591, 34603, 34607, 34613, 34631, 34649, 826 34651, 34667, 34673, 34679, 34687, 34693, 34703, 34721, 34729, 34739, 827 34747, 34757, 34759, 34763, 34781, 34807, 34819, 34841, 34843, 34847, 828 34849, 34871, 34877, 34883, 34897, 34913, 34919, 34939, 34949, 34961, 829 34963, 34981, 35023, 35027, 35051, 35053, 35059, 35069, 35081, 35083, 830 35089, 35099, 35107, 35111, 35117, 35129, 35141, 35149, 35153, 35159, 831 35171, 35201, 35221, 35227, 35251, 35257, 35267, 35279, 35281, 35291, 832 35311, 35317, 35323, 35327, 35339, 35353, 35363, 35381, 35393, 35401, 833 35407, 35419, 35423, 35437, 35447, 35449, 35461, 35491, 35507, 35509, 834 35521, 35527, 35531, 35533, 35537, 35543, 35569, 35573, 35591, 35593, 835 35597, 35603, 35617, 35671, 35677, 35729, 35731, 35747, 35753, 35759, 836 35771, 35797, 35801, 35803, 35809, 35831, 35837, 35839, 35851, 35863, 837 35869, 35879, 35897, 35899, 35911, 35923, 35933, 35951, 35963, 35969, 838 35977, 35983, 35993, 35999, 36007, 36011, 36013, 36017, 36037, 36061, 839 36067, 36073, 36083, 36097, 36107, 36109, 36131, 36137, 36151, 36161, 840 36187, 36191, 36209, 36217, 36229, 36241, 36251, 36263, 36269, 36277, 841 36293, 36299, 36307, 36313, 36319, 36341, 36343, 36353, 36373, 36383, 842 36389, 36433, 36451, 36457, 36467, 36469, 36473, 36479, 36493, 36497, 843 36523, 36527, 36529, 36541, 36551, 36559, 36563, 36571, 36583, 36587, 844 36599, 36607, 36629, 36637, 36643, 36653, 36671, 36677, 36683, 36691, 845 36697, 36709, 36713, 36721, 36739, 36749, 36761, 36767, 36779, 36781, 846 36787, 36791, 36793, 36809, 36821, 36833, 36847, 36857, 36871, 36877, 847 36887, 36899, 36901, 36913, 36919, 36923, 36929, 36931, 36943, 36947, 848 36973, 36979, 36997, 37003, 37013, 37019, 37021, 37039, 37049, 37057, 849 37061, 37087, 37097, 37117, 37123, 37139, 37159, 37171, 37181, 37189, 850 37199, 37201, 37217, 37223, 37243, 37253, 37273, 37277, 37307, 37309, 851 37313, 37321, 37337, 37339, 37357, 37361, 37363, 37369, 37379, 37397, 852 37409, 37423, 37441, 37447, 37463, 37483, 37489, 37493, 37501, 37507, 853 37511, 37517, 37529, 37537, 37547, 37549, 37561, 37567, 37571, 37573, 854 37579, 37589, 37591, 37607, 37619, 37633, 37643, 37649, 37657, 37663, 855 37691, 37693, 37699, 37717, 37747, 37781, 37783, 37799, 37811, 37813, 856 37831, 37847, 37853, 37861, 37871, 37879, 37889, 37897, 37907, 37951, 857 37957, 37963, 37967, 37987, 37991, 37993, 37997, 38011, 38039, 38047, 858 38053, 38069, 38083, 38113, 38119, 38149, 38153, 38167, 38177, 38183, 859 38189, 38197, 38201, 38219, 38231, 38237, 38239, 38261, 38273, 38281, 860 38287, 38299, 38303, 38317, 38321, 38327, 38329, 38333, 38351, 38371, 861 38377, 38393, 38431, 38447, 38449, 38453, 38459, 38461, 38501, 38543, 862 38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611, 38629, 38639, 863 38651, 38653, 38669, 38671, 38677, 38693, 38699, 38707, 38711, 38713, 864 38723, 38729, 38737, 38747, 38749, 38767, 38783, 38791, 38803, 38821, 865 38833, 38839, 38851, 38861, 38867, 38873, 38891, 38903, 38917, 38921, 866 38923, 38933, 38953, 38959, 38971, 38977, 38993, 39019, 39023, 39041, 867 39043, 39047, 39079, 39089, 39097, 39103, 39107, 39113, 39119, 39133, 868 39139, 39157, 39161, 39163, 39181, 39191, 39199, 39209, 39217, 39227, 869 39229, 39233, 39239, 39241, 39251, 39293, 39301, 39313, 39317, 39323, 870 39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397, 39409, 39419, 871 39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511, 39521, 39541, 872 39551, 39563, 39569, 39581, 39607, 39619, 39623, 39631, 39659, 39667, 873 39671, 39679, 39703, 39709, 39719, 39727, 39733, 39749, 39761, 39769, 874 39779, 39791, 39799, 39821, 39827, 39829, 39839, 39841, 39847, 39857, 875 39863, 39869, 39877, 39883, 39887, 39901, 39929, 39937, 39953, 39971, 876 39979, 39983, 39989, 40009, 40013, 40031, 40037, 40039, 40063, 40087, 877 40093, 40099, 40111, 40123, 40127, 40129, 40151, 40153, 40163, 40169, 878 40177, 40189, 40193, 40213, 40231, 40237, 40241, 40253, 40277, 40283, 879 40289, 40343, 40351, 40357, 40361, 40387, 40423, 40427, 40429, 40433, 880 40459, 40471, 40483, 40487, 40493, 40499, 40507, 40519, 40529, 40531, 881 40543, 40559, 40577, 40583, 40591, 40597, 40609, 40627, 40637, 40639, 882 40693, 40697, 40699, 40709, 40739, 40751, 40759, 40763, 40771, 40787, 883 40801, 40813, 40819, 40823, 40829, 40841, 40847, 40849, 40853, 40867, 884 40879, 40883, 40897, 40903, 40927, 40933, 40939, 40949, 40961, 40973, 885 40993, 41011, 41017, 41023, 41039, 41047, 41051, 41057, 41077, 41081, 886 41113, 41117, 41131, 41141, 41143, 41149, 41161, 41177, 41179, 41183, 887 41189, 41201, 41203, 41213, 41221, 41227, 41231, 41233, 41243, 41257, 888 41263, 41269, 41281, 41299, 41333, 41341, 41351, 41357, 41381, 41387, 889 41389, 41399, 41411, 41413, 41443, 41453, 41467, 41479, 41491, 41507, 890 41513, 41519, 41521, 41539, 41543, 41549, 41579, 41593, 41597, 41603, 891 41609, 41611, 41617, 41621, 41627, 41641, 41647, 41651, 41659, 41669, 892 41681, 41687, 41719, 41729, 41737, 41759, 41761, 41771, 41777, 41801, 893 41809, 41813, 41843, 41849, 41851, 41863, 41879, 41887, 41893, 41897, 894 41903, 41911, 41927, 41941, 41947, 41953, 41957, 41959, 41969, 41981, 895 41983, 41999, 42013, 42017, 42019, 42023, 42043, 42061, 42071, 42073, 896 42083, 42089, 42101, 42131, 42139, 42157, 42169, 42179, 42181, 42187, 897 42193, 42197, 42209, 42221, 42223, 42227, 42239, 42257, 42281, 42283, 898 42293, 42299, 42307, 42323, 42331, 42337, 42349, 42359, 42373, 42379, 899 42391, 42397, 42403, 42407, 42409, 42433, 42437, 42443, 42451, 42457, 900 42461, 42463, 42467, 42473, 42487, 42491, 42499, 42509, 42533, 42557, 901 42569, 42571, 42577, 42589, 42611, 42641, 42643, 42649, 42667, 42677, 902 42683, 42689, 42697, 42701, 42703, 42709, 42719, 42727, 42737, 42743, 903 42751, 42767, 42773, 42787, 42793, 42797, 42821, 42829, 42839, 42841, 904 42853, 42859, 42863, 42899, 42901, 42923, 42929, 42937, 42943, 42953, 905 42961, 42967, 42979, 42989, 43003, 43013, 43019, 43037, 43049, 43051, 906 43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159, 43177, 43189, 907 43201, 43207, 43223, 43237, 43261, 43271, 43283, 43291, 43313, 43319, 908 43321, 43331, 43391, 43397, 43399, 43403, 43411, 43427, 43441, 43451, 909 43457, 43481, 43487, 43499, 43517, 43541, 43543, 43573, 43577, 43579, 910 43591, 43597, 43607, 43609, 43613, 43627, 43633, 43649, 43651, 43661, 911 43669, 43691, 43711, 43717, 43721, 43753, 43759, 43777, 43781, 43783, 912 43787, 43789, 43793, 43801, 43853, 43867, 43889, 43891, 43913, 43933, 913 43943, 43951, 43961, 43963, 43969, 43973, 43987, 43991, 43997, 44017, 914 44021, 44027, 44029, 44041, 44053, 44059, 44071, 44087, 44089, 44101, 915 44111, 44119, 44123, 44129, 44131, 44159, 44171, 44179, 44189, 44201, 916 44203, 44207, 44221, 44249, 44257, 44263, 44267, 44269, 44273, 44279, 917 44281, 44293, 44351, 44357, 44371, 44381, 44383, 44389, 44417, 44449, 918 44453, 44483, 44491, 44497, 44501, 44507, 44519, 44531, 44533, 44537, 919 44543, 44549, 44563, 44579, 44587, 44617, 44621, 44623, 44633, 44641, 920 44647, 44651, 44657, 44683, 44687, 44699, 44701, 44711, 44729, 44741, 921 44753, 44771, 44773, 44777, 44789, 44797, 44809, 44819, 44839, 44843, 922 44851, 44867, 44879, 44887, 44893, 44909, 44917, 44927, 44939, 44953, 923 44959, 44963, 44971, 44983, 44987, 45007, 45013, 45053, 45061, 45077, 924 45083, 45119, 45121, 45127, 45131, 45137, 45139, 45161, 45179, 45181, 925 45191, 45197, 45233, 45247, 45259, 45263, 45281, 45289, 45293, 45307, 926 45317, 45319, 45329, 45337, 45341, 45343, 45361, 45377, 45389, 45403, 927 45413, 45427, 45433, 45439, 45481, 45491, 45497, 45503, 45523, 45533, 928 45541, 45553, 45557, 45569, 45587, 45589, 45599, 45613, 45631, 45641, 929 45659, 45667, 45673, 45677, 45691, 45697, 45707, 45737, 45751, 45757, 930 45763, 45767, 45779, 45817, 45821, 45823, 45827, 45833, 45841, 45853, 931 45863, 45869, 45887, 45893, 45943, 45949, 45953, 45959, 45971, 45979, 932 45989, 46021, 46027, 46049, 46051, 46061, 46073, 46091, 46093, 46099, 933 46103, 46133, 46141, 46147, 46153, 46171, 46181, 46183, 46187, 46199, 934 46219, 46229, 46237, 46261, 46271, 46273, 46279, 46301, 46307, 46309, 935 46327, 46337, 46349, 46351, 46381, 46399, 46411, 46439, 46441, 46447, 936 46451, 46457, 46471, 46477, 46489, 46499, 46507, 46511, 46523, 46549, 937 46559, 46567, 46573, 46589, 46591, 46601, 46619, 46633, 46639, 46643, 938 46649, 46663, 46679, 46681, 46687, 46691, 46703, 46723, 46727, 46747, 939 46751, 46757, 46769, 46771, 46807, 46811, 46817, 46819, 46829, 46831, 940 46853, 46861, 46867, 46877, 46889, 46901, 46919, 46933, 46957, 46993, 941 46997, 47017, 47041, 47051, 47057, 47059, 47087, 47093, 47111, 47119, 942 47123, 47129, 47137, 47143, 47147, 47149, 47161, 47189, 47207, 47221, 943 47237, 47251, 47269, 47279, 47287, 47293, 47297, 47303, 47309, 47317, 944 47339, 47351, 47353, 47363, 47381, 47387, 47389, 47407, 47417, 47419, 945 47431, 47441, 47459, 47491, 47497, 47501, 47507, 47513, 47521, 47527, 946 47533, 47543, 47563, 47569, 47581, 47591, 47599, 47609, 47623, 47629, 947 47639, 47653, 47657, 47659, 47681, 47699, 47701, 47711, 47713, 47717, 948 47737, 47741, 47743, 47777, 47779, 47791, 47797, 47807, 47809, 47819, 949 47837, 47843, 47857, 47869, 47881, 47903, 47911, 47917, 47933, 47939, 950 47947, 47951, 47963, 47969, 47977, 47981, 48017, 48023, 48029, 48049, 951 48073, 48079, 48091, 48109, 48119, 48121, 48131, 48157, 48163, 48179, 952 48187, 48193, 48197, 48221, 48239, 48247, 48259, 48271, 48281, 48299, 953 48311, 48313, 48337, 48341, 48353, 48371, 48383, 48397, 48407, 48409, 954 48413, 48437, 48449, 48463, 48473, 48479, 48481, 48487, 48491, 48497, 955 48523, 48527, 48533, 48539, 48541, 48563, 48571, 48589, 48593, 48611, 956 48619, 48623, 48647, 48649, 48661, 48673, 48677, 48679, 48731, 48733, 957 48751, 48757, 48761, 48767, 48779, 48781, 48787, 48799, 48809, 48817, 958 48821, 48823, 48847, 48857, 48859, 48869, 48871, 48883, 48889, 48907, 959 48947, 48953, 48973, 48989, 48991, 49003, 49009, 49019, 49031, 49033, 960 49037, 49043, 49057, 49069, 49081, 49103, 49109, 49117, 49121, 49123, 961 49139, 49157, 49169, 49171, 49177, 49193, 49199, 49201, 49207, 49211, 962 49223, 49253, 49261, 49277, 49279, 49297, 49307, 49331, 49333, 49339, 963 49363, 49367, 49369, 49391, 49393, 49409, 49411, 49417, 49429, 49433, 964 49451, 49459, 49463, 49477, 49481, 49499, 49523, 49529, 49531, 49537, 965 49547, 49549, 49559, 49597, 49603, 49613, 49627, 49633, 49639, 49663, 966 49667, 49669, 49681, 49697, 49711, 49727, 49739, 49741, 49747, 49757, 967 49783, 49787, 49789, 49801, 49807, 49811, 49823, 49831, 49843, 49853, 968 49871, 49877, 49891, 49919, 49921, 49927, 49937, 49939, 49943, 49957, 969 49991, 49993, 49999, 50021, 50023, 50033, 50047, 50051, 50053, 50069, 970 50077, 50087, 50093, 50101, 50111, 50119, 50123, 50129, 50131, 50147, 971 50153, 50159, 50177, 50207, 50221, 50227, 50231, 50261, 50263, 50273, 972 50287, 50291, 50311, 50321, 50329, 50333, 50341, 50359, 50363, 50377, 973 50383, 50387, 50411, 50417, 50423, 50441, 50459, 50461, 50497, 50503, 974 50513, 50527, 50539, 50543, 50549, 50551, 50581, 50587, 50591, 50593, 975 50599, 50627, 50647, 50651, 50671, 50683, 50707, 50723, 50741, 50753, 976 50767, 50773, 50777, 50789, 50821, 50833, 50839, 50849, 50857, 50867, 977 50873, 50891, 50893, 50909, 50923, 50929, 50951, 50957, 50969, 50971, 978 50989, 50993, 51001, 51031, 51043, 51047, 51059, 51061, 51071, 51109, 979 51131, 51133, 51137, 51151, 51157, 51169, 51193, 51197, 51199, 51203, 980 51217, 51229, 51239, 51241, 51257, 51263, 51283, 51287, 51307, 51329, 981 51341, 51343, 51347, 51349, 51361, 51383, 51407, 51413, 51419, 51421, 982 51427, 51431, 51437, 51439, 51449, 51461, 51473, 51479, 51481, 51487, 983 51503, 51511, 51517, 51521, 51539, 51551, 51563, 51577, 51581, 51593, 984 51599, 51607, 51613, 51631, 51637, 51647, 51659, 51673, 51679, 51683, 985 51691, 51713, 51719, 51721, 51749, 51767, 51769, 51787, 51797, 51803, 986 51817, 51827, 51829, 51839, 51853, 51859, 51869, 51871, 51893, 51899, 987 51907, 51913, 51929, 51941, 51949, 51971, 51973, 51977, 51991, 52009, 988 52021, 52027, 52051, 52057, 52067, 52069, 52081, 52103, 52121, 52127, 989 52147, 52153, 52163, 52177, 52181, 52183, 52189, 52201, 52223, 52237, 990 52249, 52253, 52259, 52267, 52289, 52291, 52301, 52313, 52321, 52361, 991 52363, 52369, 52379, 52387, 52391, 52433, 52453, 52457, 52489, 52501, 992 52511, 52517, 52529, 52541, 52543, 52553, 52561, 52567, 52571, 52579, 993 52583, 52609, 52627, 52631, 52639, 52667, 52673, 52691, 52697, 52709, 994 52711, 52721, 52727, 52733, 52747, 52757, 52769, 52783, 52807, 52813, 995 52817, 52837, 52859, 52861, 52879, 52883, 52889, 52901, 52903, 52919, 996 52937, 52951, 52957, 52963, 52967, 52973, 52981, 52999, 53003, 53017, 997 53047, 53051, 53069, 53077, 53087, 53089, 53093, 53101, 53113, 53117, 998 53129, 53147, 53149, 53161, 53171, 53173, 53189, 53197, 53201, 53231, 999 53233, 53239, 53267, 53269, 53279, 53281, 53299, 53309, 53323, 53327, 1000 53353, 53359, 53377, 53381, 53401, 53407, 53411, 53419, 53437, 53441, 1001 53453, 53479, 53503, 53507, 53527, 53549, 53551, 53569, 53591, 53593, 1002 53597, 53609, 53611, 53617, 53623, 53629, 53633, 53639, 53653, 53657, 1003 53681, 53693, 53699, 53717, 53719, 53731, 53759, 53773, 53777, 53783, 1004 53791, 53813, 53819, 53831, 53849, 53857, 53861, 53881, 53887, 53891, 1005 53897, 53899, 53917, 53923, 53927, 53939, 53951, 53959, 53987, 53993, 1006 54001, 54011, 54013, 54037, 54049, 54059, 54083, 54091, 54101, 54121, 1007 54133, 54139, 54151, 54163, 54167, 54181, 54193, 54217, 54251, 54269, 1008 54277, 54287, 54293, 54311, 54319, 54323, 54331, 54347, 54361, 54367, 1009 54371, 54377, 54401, 54403, 54409, 54413, 54419, 54421, 54437, 54443, 1010 54449, 54469, 54493, 54497, 54499, 54503, 54517, 54521, 54539, 54541, 1011 54547, 54559, 54563, 54577, 54581, 54583, 54601, 54617, 54623, 54629, 1012 54631, 54647, 54667, 54673, 54679, 54709, 54713, 54721, 54727, 54751, 1013 54767, 54773, 54779, 54787, 54799, 54829, 54833, 54851, 54869, 54877, 1014 54881, 54907, 54917, 54919, 54941, 54949, 54959, 54973, 54979, 54983, 1015 55001, 55009, 55021, 55049, 55051, 55057, 55061, 55073, 55079, 55103, 1016 55109, 55117, 55127, 55147, 55163, 55171, 55201, 55207, 55213, 55217, 1017 55219, 55229, 55243, 55249, 55259, 55291, 55313, 55331, 55333, 55337, 1018 55339, 55343, 55351, 55373, 55381, 55399, 55411, 55439, 55441, 55457, 1019 55469, 55487, 55501, 55511, 55529, 55541, 55547, 55579, 55589, 55603, 1020 55609, 55619, 55621, 55631, 55633, 55639, 55661, 55663, 55667, 55673, 1021 55681, 55691, 55697, 55711, 55717, 55721, 55733, 55763, 55787, 55793, 1022 55799, 55807, 55813, 55817, 55819, 55823, 55829, 55837, 55843, 55849, 1023 55871, 55889, 55897, 55901, 55903, 55921, 55927, 55931, 55933, 55949, 1024 55967, 55987, 55997, 56003, 56009, 56039, 56041, 56053, 56081, 56087, 1025 56093, 56099, 56101, 56113, 56123, 56131, 56149, 56167, 56171, 56179, 1026 56197, 56207, 56209, 56237, 56239, 56249, 56263, 56267, 56269, 56299, 1027 56311, 56333, 56359, 56369, 56377, 56383, 56393, 56401, 56417, 56431, 1028 56437, 56443, 56453, 56467, 56473, 56477, 56479, 56489, 56501, 56503, 1029 56509, 56519, 56527, 56531, 56533, 56543, 56569, 56591, 56597, 56599, 1030 56611, 56629, 56633, 56659, 56663, 56671, 56681, 56687, 56701, 56711, 1031 56713, 56731, 56737, 56747, 56767, 56773, 56779, 56783, 56807, 56809, 1032 56813, 56821, 56827, 56843, 56857, 56873, 56891, 56893, 56897, 56909, 1033 56911, 56921, 56923, 56929, 56941, 56951, 56957, 56963, 56983, 56989, 1034 56993, 56999, 57037, 57041, 57047, 57059, 57073, 57077, 57089, 57097, 1035 57107, 57119, 57131, 57139, 57143, 57149, 57163, 57173, 57179, 57191, 1036 57193, 57203, 57221, 57223, 57241, 57251, 57259, 57269, 57271, 57283, 1037 57287, 57301, 57329, 57331, 57347, 57349, 57367, 57373, 57383, 57389, 1038 57397, 57413, 57427, 57457, 57467, 57487, 57493, 57503, 57527, 57529, 1039 57557, 57559, 57571, 57587, 57593, 57601, 57637, 57641, 57649, 57653, 1040 57667, 57679, 57689, 57697, 57709, 57713, 57719, 57727, 57731, 57737, 1041 57751, 57773, 57781, 57787, 57791, 57793, 57803, 57809, 57829, 57839, 1042 57847, 57853, 57859, 57881, 57899, 57901, 57917, 57923, 57943, 57947, 1043 57973, 57977, 57991, 58013, 58027, 58031, 58043, 58049, 58057, 58061, 1044 58067, 58073, 58099, 58109, 58111, 58129, 58147, 58151, 58153, 58169, 1045 58171, 58189, 58193, 58199, 58207, 58211, 58217, 58229, 58231, 58237, 1046 58243, 58271, 58309, 58313, 58321, 58337, 58363, 58367, 58369, 58379, 1047 58391, 58393, 58403, 58411, 58417, 58427, 58439, 58441, 58451, 58453, 1048 58477, 58481, 58511, 58537, 58543, 58549, 58567, 58573, 58579, 58601, 1049 58603, 58613, 58631, 58657, 58661, 58679, 58687, 58693, 58699, 58711, 1050 58727, 58733, 58741, 58757, 58763, 58771, 58787, 58789, 58831, 58889, 1051 58897, 58901, 58907, 58909, 58913, 58921, 58937, 58943, 58963, 58967, 1052 58979, 58991, 58997, 59009, 59011, 59021, 59023, 59029, 59051, 59053, 1053 59063, 59069, 59077, 59083, 59093, 59107, 59113, 59119, 59123, 59141, 1054 59149, 59159, 59167, 59183, 59197, 59207, 59209, 59219, 59221, 59233, 1055 59239, 59243, 59263, 59273, 59281, 59333, 59341, 59351, 59357, 59359, 1056 59369, 59377, 59387, 59393, 59399, 59407, 59417, 59419, 59441, 59443, 1057 59447, 59453, 59467, 59471, 59473, 59497, 59509, 59513, 59539, 59557, 1058 59561, 59567, 59581, 59611, 59617, 59621, 59627, 59629, 59651, 59659, 1059 59663, 59669, 59671, 59693, 59699, 59707, 59723, 59729, 59743, 59747, 1060 59753, 59771, 59779, 59791, 59797, 59809, 59833, 59863, 59879, 59887, 1061 59921, 59929, 59951, 59957, 59971, 59981, 59999, 60013, 60017, 60029, 1062 60037, 60041, 60077, 60083, 60089, 60091, 60101, 60103, 60107, 60127, 1063 60133, 60139, 60149, 60161, 60167, 60169, 60209, 60217, 60223, 60251, 1064 60257, 60259, 60271, 60289, 60293, 60317, 60331, 60337, 60343, 60353, 1065 60373, 60383, 60397, 60413, 60427, 60443, 60449, 60457, 60493, 60497, 1066 60509, 60521, 60527, 60539, 60589, 60601, 60607, 60611, 60617, 60623, 1067 60631, 60637, 60647, 60649, 60659, 60661, 60679, 60689, 60703, 60719, 1068 60727, 60733, 60737, 60757, 60761, 60763, 60773, 60779, 60793, 60811, 1069 60821, 60859, 60869, 60887, 60889, 60899, 60901, 60913, 60917, 60919, 1070 60923, 60937, 60943, 60953, 60961, 61001, 61007, 61027, 61031, 61043, 1071 61051, 61057, 61091, 61099, 61121, 61129, 61141, 61151, 61153, 61169, 1072 61211, 61223, 61231, 61253, 61261, 61283, 61291, 61297, 61331, 61333, 1073 61339, 61343, 61357, 61363, 61379, 61381, 61403, 61409, 61417, 61441, 1074 61463, 61469, 61471, 61483, 61487, 61493, 61507, 61511, 61519, 61543, 1075 61547, 61553, 61559, 61561, 61583, 61603, 61609, 61613, 61627, 61631, 1076 61637, 61643, 61651, 61657, 61667, 61673, 61681, 61687, 61703, 61717, 1077 61723, 61729, 61751, 61757, 61781, 61813, 61819, 61837, 61843, 61861, 1078 61871, 61879, 61909, 61927, 61933, 61949, 61961, 61967, 61979, 61981, 1079 61987, 61991, 62003, 62011, 62017, 62039, 62047, 62053, 62057, 62071, 1080 62081, 62099, 62119, 62129, 62131, 62137, 62141, 62143, 62171, 62189, 1081 62191, 62201, 62207, 62213, 62219, 62233, 62273, 62297, 62299, 62303, 1082 62311, 62323, 62327, 62347, 62351, 62383, 62401, 62417, 62423, 62459, 1083 62467, 62473, 62477, 62483, 62497, 62501, 62507, 62533, 62539, 62549, 1084 62563, 62581, 62591, 62597, 62603, 62617, 62627, 62633, 62639, 62653, 1085 62659, 62683, 62687, 62701, 62723, 62731, 62743, 62753, 62761, 62773, 1086 62791, 62801, 62819, 62827, 62851, 62861, 62869, 62873, 62897, 62903, 1087 62921, 62927, 62929, 62939, 62969, 62971, 62981, 62983, 62987, 62989, 1088 63029, 63031, 63059, 63067, 63073, 63079, 63097, 63103, 63113, 63127, 1089 63131, 63149, 63179, 63197, 63199, 63211, 63241, 63247, 63277, 63281, 1090 63299, 63311, 63313, 63317, 63331, 63337, 63347, 63353, 63361, 63367, 1091 63377, 63389, 63391, 63397, 63409, 63419, 63421, 63439, 63443, 63463, 1092 63467, 63473, 63487, 63493, 63499, 63521, 63527, 63533, 63541, 63559, 1093 63577, 63587, 63589, 63599, 63601, 63607, 63611, 63617, 63629, 63647, 1094 63649, 63659, 63667, 63671, 63689, 63691, 63697, 63703, 63709, 63719, 1095 63727, 63737, 63743, 63761, 63773, 63781, 63793, 63799, 63803, 63809, 1096 63823, 63839, 63841, 63853, 63857, 63863, 63901, 63907, 63913, 63929, 1097 63949, 63977, 63997, 64007, 64013, 64019, 64033, 64037, 64063, 64067, 1098 64081, 64091, 64109, 64123, 64151, 64153, 64157, 64171, 64187, 64189, 1099 64217, 64223, 64231, 64237, 64271, 64279, 64283, 64301, 64303, 64319, 1100 64327, 64333, 64373, 64381, 64399, 64403, 64433, 64439, 64451, 64453, 1101 64483, 64489, 64499, 64513, 64553, 64567, 64577, 64579, 64591, 64601, 1102 64609, 64613, 64621, 64627, 64633, 64661, 64663, 64667, 64679, 64693, 1103 64709, 64717, 64747, 64763, 64781, 64783, 64793, 64811, 64817, 64849, 1104 64853, 64871, 64877, 64879, 64891, 64901, 64919, 64921, 64927, 64937, 1105 64951, 64969, 64997, 65003, 65011, 65027, 65029, 65033, 65053, 65063, 1106 65071, 65089, 65099, 65101, 65111, 65119, 65123, 65129, 65141, 65147, 1107 65167, 65171, 65173, 65179, 65183, 65203, 65213, 65239, 65257, 65267, 1108 65269, 65287, 65293, 65309, 65323, 65327, 65353, 65357, 65371, 65381, 1109 65393, 65407, 65413, 65419, 65423, 65437, 65447, 65449, 65479, 65497, 1110 65519, 65521, 65537, 65539, 65543, 65551, 65557, 65563, 65579, 65581, 1111 65587, 65599, 65609, 65617, 65629, 65633, 65647, 65651, 65657, 65677, 1112 65687, 65699, 65701, 65707, 65713, 65717, 65719, 65729, 65731, 65761, 1113 65777, 65789, 65809, 65827, 65831, 65837, 65839, 65843, 65851, 65867, 1114 65881, 65899, 65921, 65927, 65929, 65951, 65957, 65963, 65981, 65983, 1115 65993, 66029, 66037, 66041, 66047, 66067, 66071, 66083, 66089, 66103, 1116 66107, 66109, 66137, 66161, 66169, 66173, 66179, 66191, 66221, 66239, 1117 66271, 66293, 66301, 66337, 66343, 66347, 66359, 66361, 66373, 66377, 1118 66383, 66403, 66413, 66431, 66449, 66457, 66463, 66467, 66491, 66499, 1119 66509, 66523, 66529, 66533, 66541, 66553, 66569, 66571, 66587, 66593, 1120 66601, 66617, 66629, 66643, 66653, 66683, 66697, 66701, 66713, 66721, 1121 66733, 66739, 66749, 66751, 66763, 66791, 66797, 66809, 66821, 66841, 1122 66851, 66853, 66863, 66877, 66883, 66889, 66919, 66923, 66931, 66943, 1123 66947, 66949, 66959, 66973, 66977, 67003, 67021, 67033, 67043, 67049, 1124 67057, 67061, 67073, 67079, 67103, 67121, 67129, 67139, 67141, 67153, 1125 67157, 67169, 67181, 67187, 67189, 67211, 67213, 67217, 67219, 67231, 1126 67247, 67261, 67271, 67273, 67289, 67307, 67339, 67343, 67349, 67369, 1127 67391, 67399, 67409, 67411, 67421, 67427, 67429, 67433, 67447, 67453, 1128 67477, 67481, 67489, 67493, 67499, 67511, 67523, 67531, 67537, 67547, 1129 67559, 67567, 67577, 67579, 67589, 67601, 67607, 67619, 67631, 67651, 1130 67679, 67699, 67709, 67723, 67733, 67741, 67751, 67757, 67759, 67763, 1131 67777, 67783, 67789, 67801, 67807, 67819, 67829, 67843, 67853, 67867, 1132 67883, 67891, 67901, 67927, 67931, 67933, 67939, 67943, 67957, 67961, 1133 67967, 67979, 67987, 67993, 68023, 68041, 68053, 68059, 68071, 68087, 1134 68099, 68111, 68113, 68141, 68147, 68161, 68171, 68207, 68209, 68213, 1135 68219, 68227, 68239, 68261, 68279, 68281, 68311, 68329, 68351, 68371, 1136 68389, 68399, 68437, 68443, 68447, 68449, 68473, 68477, 68483, 68489, 1137 68491, 68501, 68507, 68521, 68531, 68539, 68543, 68567, 68581, 68597, 1138 68611, 68633, 68639, 68659, 68669, 68683, 68687, 68699, 68711, 68713, 1139 68729, 68737, 68743, 68749, 68767, 68771, 68777, 68791, 68813, 68819, 1140 68821, 68863, 68879, 68881, 68891, 68897, 68899, 68903, 68909, 68917, 1141 68927, 68947, 68963, 68993, 69001, 69011, 69019, 69029, 69031, 69061, 1142 69067, 69073, 69109, 69119, 69127, 69143, 69149, 69151, 69163, 69191, 1143 69193, 69197, 69203, 69221, 69233, 69239, 69247, 69257, 69259, 69263, 1144 69313, 69317, 69337, 69341, 69371, 69379, 69383, 69389, 69401, 69403, 1145 69427, 69431, 69439, 69457, 69463, 69467, 69473, 69481, 69491, 69493, 1146 69497, 69499, 69539, 69557, 69593, 69623, 69653, 69661, 69677, 69691, 1147 69697, 69709, 69737, 69739, 69761, 69763, 69767, 69779, 69809, 69821, 1148 69827, 69829, 69833, 69847, 69857, 69859, 69877, 69899, 69911, 69929, 1149 69931, 69941, 69959, 69991, 69997, 70001, 70003, 70009, 70019, 70039, 1150 70051, 70061, 70067, 70079, 70099, 70111, 70117, 70121, 70123, 70139, 1151 70141, 70157, 70163, 70177, 70181, 70183, 70199, 70201, 70207, 70223, 1152 70229, 70237, 70241, 70249, 70271, 70289, 70297, 70309, 70313, 70321, 1153 70327, 70351, 70373, 70379, 70381, 70393, 70423, 70429, 70439, 70451, 1154 70457, 70459, 70481, 70487, 70489, 70501, 70507, 70529, 70537, 70549, 1155 70571, 70573, 70583, 70589, 70607, 70619, 70621, 70627, 70639, 70657, 1156 70663, 70667, 70687, 70709, 70717, 70729, 70753, 70769, 70783, 70793, 1157 70823, 70841, 70843, 70849, 70853, 70867, 70877, 70879, 70891, 70901, 1158 70913, 70919, 70921, 70937, 70949, 70951, 70957, 70969, 70979, 70981, 1159 70991, 70997, 70999, 71011, 71023, 71039, 71059, 71069, 71081, 71089, 1160 71119, 71129, 71143, 71147, 71153, 71161, 71167, 71171, 71191, 71209, 1161 71233, 71237, 71249, 71257, 71261, 71263, 71287, 71293, 71317, 71327, 1162 71329, 71333, 71339, 71341, 71347, 71353, 71359, 71363, 71387, 71389, 1163 71399, 71411, 71413, 71419, 71429, 71437, 71443, 71453, 71471, 71473, 1164 71479, 71483, 71503, 71527, 71537, 71549, 71551, 71563, 71569, 71593, 1165 71597, 71633, 71647, 71663, 71671, 71693, 71699, 71707, 71711, 71713, 1166 71719, 71741, 71761, 71777, 71789, 71807, 71809, 71821, 71837, 71843, 1167 71849, 71861, 71867, 71879, 71881, 71887, 71899, 71909, 71917, 71933, 1168 71941, 71947, 71963, 71971, 71983, 71987, 71993, 71999, 72019, 72031, 1169 72043, 72047, 72053, 72073, 72077, 72089, 72091, 72101, 72103, 72109, 1170 72139, 72161, 72167, 72169, 72173, 72211, 72221, 72223, 72227, 72229, 1171 72251, 72253, 72269, 72271, 72277, 72287, 72307, 72313, 72337, 72341, 1172 72353, 72367, 72379, 72383, 72421, 72431, 72461, 72467, 72469, 72481, 1173 72493, 72497, 72503, 72533, 72547, 72551, 72559, 72577, 72613, 72617, 1174 72623, 72643, 72647, 72649, 72661, 72671, 72673, 72679, 72689, 72701, 1175 72707, 72719, 72727, 72733, 72739, 72763, 72767, 72797, 72817, 72823, 1176 72859, 72869, 72871, 72883, 72889, 72893, 72901, 72907, 72911, 72923, 1177 72931, 72937, 72949, 72953, 72959, 72973, 72977, 72997, 73009, 73013, 1178 73019, 73037, 73039, 73043, 73061, 73063, 73079, 73091, 73121, 73127, 1179 73133, 73141, 73181, 73189, 73237, 73243, 73259, 73277, 73291, 73303, 1180 73309, 73327, 73331, 73351, 73361, 73363, 73369, 73379, 73387, 73417, 1181 73421, 73433, 73453, 73459, 73471, 73477, 73483, 73517, 73523, 73529, 1182 73547, 73553, 73561, 73571, 73583, 73589, 73597, 73607, 73609, 73613, 1183 73637, 73643, 73651, 73673, 73679, 73681, 73693, 73699, 73709, 73721, 1184 73727, 73751, 73757, 73771, 73783, 73819, 73823, 73847, 73849, 73859, 1185 73867, 73877, 73883, 73897, 73907, 73939, 73943, 73951, 73961, 73973, 1186 73999, 74017, 74021, 74027, 74047, 74051, 74071, 74077, 74093, 74099, 1187 74101, 74131, 74143, 74149, 74159, 74161, 74167, 74177, 74189, 74197, 1188 74201, 74203, 74209, 74219, 74231, 74257, 74279, 74287, 74293, 74297, 1189 74311, 74317, 74323, 74353, 74357, 74363, 74377, 74381, 74383, 74411, 1190 74413, 74419, 74441, 74449, 74453, 74471, 74489, 74507, 74509, 74521, 1191 74527, 74531, 74551, 74561, 74567, 74573, 74587, 74597, 74609, 74611, 1192 74623, 74653, 74687, 74699, 74707, 74713, 74717, 74719, 74729, 74731, 1193 74747, 74759, 74761, 74771, 74779, 74797, 74821, 74827, 74831, 74843, 1194 74857, 74861, 74869, 74873, 74887, 74891, 74897, 74903, 74923, 74929, 1195 74933, 74941, 74959, 75011, 75013, 75017, 75029, 75037, 75041, 75079, 1196 75083, 75109, 75133, 75149, 75161, 75167, 75169, 75181, 75193, 75209, 1197 75211, 75217, 75223, 75227, 75239, 75253, 75269, 75277, 75289, 75307, 1198 75323, 75329, 75337, 75347, 75353, 75367, 75377, 75389, 75391, 75401, 1199 75403, 75407, 75431, 75437, 75479, 75503, 75511, 75521, 75527, 75533, 1200 75539, 75541, 75553, 75557, 75571, 75577, 75583, 75611, 75617, 75619, 1201 75629, 75641, 75653, 75659, 75679, 75683, 75689, 75703, 75707, 75709, 1202 75721, 75731, 75743, 75767, 75773, 75781, 75787, 75793, 75797, 75821, 1203 75833, 75853, 75869, 75883, 75913, 75931, 75937, 75941, 75967, 75979, 1204 75983, 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102881, 102911, 102913, 102929, 102931, 1441102953, 102967, 102983, 103001, 103007, 103043, 103049, 103067, 103069, 103079, 1442103087, 103091, 103093, 103099, 103123, 103141, 103171, 103177, 103183, 103217, 1443103231, 103237, 103289, 103291, 103307, 103319, 103333, 103349, 103357, 103387, 1444103391, 103393, 103399, 103409, 103421, 103423, 103451, 103457, 103471, 103483, 1445103511, 103529, 103549, 103553, 103561, 103567, 103573, 103577, 103583, 103591, 1446103613, 103619, 103643, 103651, 103657, 103669, 103681, 103687, 103699, 103703, 1447103723, 103769, 103787, 103801, 103811, 103813, 103837, 103841, 103843, 103867, 1448103889, 103903, 103913, 103919, 103951, 103963, 103967, 103969, 103979, 103981, 1449103991, 103993, 103997, 104003, 104009, 104021, 104033, 104047, 104053, 104059, 1450104087, 104089, 104107, 104113, 104119, 104123, 104147, 104149, 104161, 104173, 1451104179, 104183, 104207, 104231, 104233, 104239, 104243, 104281, 104287, 104297, 1452104309, 104311, 104323, 104327, 104347, 104369, 104381, 104383, 104393, 104399, 1453104417, 104459, 104471, 104473, 104479, 104491, 104513, 104527, 104537, 104543, 1454104549, 104551, 104561, 104579, 104593, 104597, 104623, 104639, 104651, 104659, 1455104677, 104681, 104683, 104693, 104701, 104707, 104711, 104717, 104723, 104729, 1456) 1457