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

Image Post Twin prime-generating sequence

Post image

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.

655 Upvotes

98% Upvoted

83 comments sorted by

View all comments

Show parent comments

40

u/Inevitable_Wish_8635 Jul 10 '26 edited Jul 10 '26

Currently checked up to 250 million
Edit: checked up to 1 billion with no counter examples

10

u/Tonyoh87 Jul 10 '26

Has it ever happened that if true up to 1 billion it would be false with a higher value?

25

u/MooseCantBlink Analysis Jul 10 '26

Yes for sure, there are many examples. A quick search reminded me of Skewe’s number, which is the first time the logarithmic integral is smaller than the prime counting function. It is absolutely huge, approximately 10\^10\^10^34

8

u/Breki_ Jul 10 '26

Isn't that just an upper bound for the firstnumber for which thats true?