#CXRLE Pos=-637,-460 #C Four versions of a Game of Life prime number sieve. #C #C -- 1st quadrant (upper right): #C Original sieve by Dean Hickerson, 1 November 1991 #C Produces a stream of lightweight spaceships representing prime #C numbers. N is prime if a LWSS is above the "super beehive" #C at 120N ticks. LWSS reflector added in the center to turn the #C prime LWSS stream upward and line it up with the output of the #C faster 2nd-quadrant sieve -- no matches after the first pair... #C See also Calcyman-primer.zip, which simulates this pattern in a #C 10-state rule, using a starting configuration of only two cells. #C -- 2nd quadrant (upper left): #C New sieve #1 by Jason Summers, 15 October 2005 #C The original sieve pattern uses only every other glider relay. The #C gliders from half of the relays never strike a LWSS. By adjusting #C the spacing between the two halves, every relay can be used, #C which doubles the speed at which numbers are tested for primality. #C The only other change is to replace the backward p40 LWSS rake #C (in which only every third LWSS was used) with a p60 rake. #C All LWSSs are now used, so we can dispense with the pentadecathlon #C that deletes the unused ones. #C N is prime if an LWSS is directly above the "super beehive" #C after 60N ticks. For consistency with the 1st-quadrant sieve, #C the original base pattern has been run 3 ticks to get this version, #C and the super beehive was adjusted accordingly. #C -- 3rd quadrant (lower left): #C New sieve #2 by Jason Summers, 15 October 2005 #C In this pattern the vertical row of guns has been replaced with a #C functionally equivalent pentadecathlon+queen-bee reflector. #C Also the relay representing the factor 3 has been removed; #C it would be used only once, for the number 9, so this is handled #C as a special case. Note that each relay is used only a finite #C number of times: 3 is used once (9); 5 is used twice (15, 25); #C 7 is used three times (21, 35, 49); etc. #C N is prime if an LWSS is below the "super beehive" after 60N ticks. #C -- 4th quadrant (lower right): #C New sieve #3 by Jason Summers, 15 October 2005 #C This prime number calculator contains no glider guns, but the #C initial pattern is considerably larger than those that do. #C For reflectors, two pairs of pentadecathlons are used, plus #C a repositioner consisting of two spaceships. The repositioner #C allows a LWSS to be deleted during its reaction. #C There are four variants of the 2-PD reflector, which made it much #C more likely that a relay with the right timing could be found. #C N is prime if an LWSS is below the "super beehive" after 60N ticks. x = 1494, y = 1020, rule = B3/S23 410b3o11b3o$409bo2bo10bo2bo$379b3o11b3o16bo4b3o6bo$379bo2bo10bo2bo15bo 4bo2bo5bo$379bo6b3o4bo15bobo5bob2o2bobo$379bo5bo2bo4bo$380bobo2b2obo5b obo2$411bo8bo$410b3o5bobo$385bo8bo14b2obo$385bobo5b3o13b3o4bo2bo$393bo b2o13b2o4b3o$386bo2bo4b3o20bo$387b3o4b2o$388bo2$426b3o$426bo2bo$377b3o 46bo$376bo2bo46bo$379bo47bobo$379bo25b3o3b3o$376bobo25bo2bo3bo2bo9bo$ 392b3o3b3o6bo3bo12bo$381bo9bo2bo3bo2bo5bo3bo9b3o$381bo12bo3bo5bobo5bob o6bo$382b3o9bo3bo$384bo6bobo5bobo6b3o$408b3o$395b3o10bobo5b3o$395b3o 11bo6bo12bo13bo$387b3o5bobo11bo7bo10b3o11b3o$362bo13bo12bo6bo30b2obo5b o4b2obo$361b3o11b3o10bo7bo30b3o5b3o3b3o$361bob2o4bo5bob2o28bo20b2o4bo 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