Primer

Primer is a pattern that was constructed by Dean Hickerson on November 1, 1991 that produces a stream of lightweight spaceships representing prime numbers. N is prime if and only if a lightweight spaceship escapes to the left of the pentadecathlon at the bottom-left corner of the pattern at generation 120N+100.[1][2] It was the first pattern created that computes prime numbers, though others have since been constructed using the same ideas (see glider gunless primer).

Primer
<html><div class="rle"><div class="codebox"><div style="display:none;"><code></html>x = 440, y = 294, rule = B3/S23 412b2o$410b2ob2o13b2o$410b4o13b4o$411b2o14b2ob2o$93b3o11b3o319b2o$93bo 2bo10bo2bo$93bo6b3o4bo16b3o11b3o$93bo5bo2bo4bo15bo2bo10bo2bo$94bo4b2ob o5bo17bo4b3o6bo285b2o$126bo4bo2bo5bo284bo2bo$125bo5bob2o4bo285bo2b2o$ 424bo2b2o$99bo8bo315b4o$99bobo5b3o278bo7bo$107bob2o14bo8bo254bo7b2o$ 100bo2bo4b3o13b3o5bobo249bo4bo6b2o30b2o$101b3o4b2o13b2obo258b5o29b4o4b 4o$102bo20b3o4bo2bo280bo3bo3bo4b2ob2o$124b2o4b3o282bo6bo6b2o$131bo279b o3bo5bo$412b4o$91b3o313b3o$90bo2bo311b2ob2o26b2o$93bo46b3o264b3o17b4o 4b4o$93bo46bo2bo268b4o10bo3bo4b2ob2o$92bo47bo270bo3bo14bo6b2o$106b3o3b 3o25bo274bo13bo$105bo2bo3bo2bo25bo272bo18bo$108bo3bo6b3o3b3o253bo49bo$ 96b3o9bo3bo5bo2bo3bo2bo253b2o47bo2b2o$98bo8bo5bo7bo3bo255b2o47bo5bo$ 97bo12bo10bo3bo9b3o293bobo2b2o$110bo9bo5bo8bo295bo3b2o$109bobo11bo12bo 296b3o$101b3o19bo$76bo13bo12bo18bobo$75b3o11b3o10bo27b3o303b2o$75bob2o 4bo5bob2o37bo12bo13bo277b4o$76b3o3b3o5b3o38bo10b3o11b3o245bo13b2o15b2o b2o$76b2o3b2o2bo4b2o49b2obo5bo4b2obo244bo13b4o16b2o$81bo3bo24b3o28b3o 5b3o3b3o245b3o11b2ob2o$81bob2o57b2o4bo2b2o3b2o261b2o$81b2o38b3o24bo3bo $149b2obo213bo$75b3o73b2o214b2o42b2o$74bo2bo288b2o41b2ob2o$77bo78b3o 250b4o$77bo78bo2bo246bo3b2o$76bo79bo248b2o$156bo249bo3b2o$102b3o52bo 251b4o$102bo2bo303b2ob2o$102bo26b3o279b2o$92bo9bo25bo2bo227bo$91b3o8bo 28bo226bo$55b3o11b3o19bob2o8bo27bo9bo216b3o36b4o$54bo2bo10bo2bo20b3o 36bo8b3o253bo3bo$57bo4b3o6bo20b2o36bo8b2obo239b2o16bo$57bo4bo2bo5bo67b 3o209bo21b4o4b4o14bo$56bo4bo8bo69b2o21bo13bo9b2o163b2o18bo3bo4b2ob2o$ 97bo5bo58b3o11b3o7b4o161b2o23bo6b2o$96b3o3b3o57bob2o4bo5bob2o6b2ob2o 184bo$62b2o31b2obo3bob2o4b2o18bo5bo26b3o3b3o5b3o8b2o189bo$62bo7bo24b3o 5b3o4bobo16b3o3b3o25b2o3b2o2bo4b2o198bo$69b3o24b2o5b2o6b2o9b2o4b2obo3b ob2o29bo3bo28bo175bo2b2o$68b2obo49bobo4b3o5b3o29bob2o30bo173bo5bo$68b 3o29bo20b2o6b2o5b2o30b2o28bo3bo174bobo2b2o$69b2o28b3o97b4o174bo3b2o$ 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View static image
Pattern type Miscellaneous
Number of cells 2953
Bounding box 440×294
Discovered by Dean Hickerson
Year of discovery 1991

It works by using gliders to emulate a prime number sieve. Lightweight spaceships that move westward are deleted by gliders that represent positive integers if the lightweight spaceship represents a multiple of that number.

The stream of spaceships representing prime numbers

Videos
<iframe src='//www.youtube.com/embed/68nEX5CEmZE?' width='300' height='169' frameborder='0' allowfullscreen='true'></iframe>
Primer outputting the prime numbers from 2 through 37
gollark: This is mostly just because of NIm's very immature libraries.
gollark: Weird.
gollark: I don't mean I found that and ignored it, I mean I never noticed such a thing occurring.
gollark: The redis session thing uses the random session ID generator.
gollark: I ignored that because the minoteaur session storage thing just generates 64-bit snowflakes for session IDs, which is probably not a horrible security risk much.

See also

References
  1. PRIMES.LIF from Alan Hensel's lifep.zip pattern collection. Accessed on July 28, 2009.
  2. four-primers.rle.gz from Golly's built-in pattern catalogue. Accessed on July 28, 2009.
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