1#C This is a Fermat prime calculator, rigged to self-destruct and stop 2#C growing if any Fermat primes over 65537 turn up. Since the 3#C existence of such primes is an unsolved problem in mathematics, 4#C it is unknown if this pattern grows to infinite population. 5#C 6#C The tubs in a row represent the known Fermat primes, starting 7#C with 5. The other three represent 17, 257, and 65537. A tub gets 8#C destroyed whenever a Fermat prime is found. In the unlikely event 9#C that an additional Fermat prime exists, the pond will eventually be 10#C destroyed, followed by the puffers and breeders. 11#C 12#C A number N is tested at about generation 120N - 550, so the tubs 13#C will be destroyed at about generations: 50; 1,490; 30,290; and 14#C 7,863,890. 15#C 16#C The next-smallest Fermat number that is not known to be composite 17#C is 2^2^31+1. Therefore, the pond (and the breeders) will survive at 18#C least 10^640,000,000 generations. So don't expect to see anything 19#C interesting happen by watching this pattern. Remove the tubs if you 20#C want to see the destruction. 21#C 22#C The careful observer may notice that actually every number of the 23#C form 2^N+1 is tested for primality, while Fermat numbers are of the 24#C form 2^(2^N)+1. However, numbers of the form M^N+1 can never be 25#C prime unless N is a power of 2, so the only primes of the form 26#C 2^N+1 are in fact the Fermat primes. 27#C 28#C The "Primer" and "Caber Tosser" patterns used here are by Dean 29#C Hickerson. The beehive puffer is by Hartmut Holzwart. 30#C 31#C Jason Summers, 7 Jan 2000 32x = 838, y = 736, rule = B3/S23 3346b3o12b3o$46bobbo10bobbo$46bo16bo$46bo3bo8bo3bo$46bo6b4o6bo$47bobobo 34bboobbobobo$51bo6bo$51bo6bo$50boboobboobo$50bo3boo3bo$51bo6bo$51boo4b 35oo$54boo$49bo3bobbo3bo$53bobbo$50b4obb4o$52boobboo$53b4o$52bo4bo$$52bo 36boobo$51bo6bo$51bo6bo$53b4o$49boobobooboboo$48bobboobooboobbo$47boobb 378obboo$47bo3bobboobbo3bo$46boo5bobbo5boo$46boo3b3obb3o3boo$47bobboobo 38bboboobbo$48boobob4oboboo$53bobbo$48bo12bo82b3o15b3o$48bo4bobbo4bo81bo 393bo13bo3bo$50boo6boo82boo4bo11bo4boo$44bo5b3o4b3o81bobobooboo3b3o3boob 40oobobo$43b3o8boo84boobo4boboob3oboobo4boboo$43boboo4bobobbobo75bo4bo4b 41o3bo4bobo4bo3bo4bo$44b3obboboo4boobo69boob3o15bo5bo$39b3obb3obbo10bo 4267boobo3boobboo7boo9boo7boo$38bobbo4bo77b5o4bobboo$41bo9bo6bo61booboob 43obobo5bobbo$41bo4b3o4b4o7b3o15b3o33boobo3bo3bo8bo$38bobo4b3o15bo3bo13b 44o3bo28b5o4bo$45b3o14boo4bo11bo4boo23booboobobobo3bo$48bo5boo5boboboob 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