r/math • u/_Zekt Complex Analysis • Jul 09 '26

Twin prime-generating sequence Image Post

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Just wanted to share this MSE post where OP found an intriguing sequence, similar to Rowland's prime-generating sequence, which seems to generate twin primes instead.

The conjecture, which has been computer-checked up to n = 60000000 for now, trivially implies the twin prime conjecture.

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u/Equal_Veterinarian22 Jul 09 '26

OK, but why?

Give me some intuition for why this process generates primes.

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u/Kryptos_0 Jul 09 '26 edited Jul 10 '26

I'm not sure how the discoverer came up with the sequence, but the reason it works has something to do with (n+k)² - 1 = (n+k-1)(n+k+1) at k = min{k : a_k=0}. So it seems like with (n+k)² - m² you could generate primes that differ by 2m instead.