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This is just a weaker version of the twin prime conjecture. You’re asking for primes that differ by 2^k instead of 2. Last I heard the best result was from Polymath 8a.

http://michaelnielsen.org/polymath1/index.php?title=Bounded_...

Edit: Actually I was wrong, differing by a binary digit is much stronger than a difference of 2^k. But that’s a starting point.



Neat. Thanks for tying it in to something real. Makes sense now that you phrase it that way. Not something I've ever looked into much.


Actually I replied without thinking too much, sorry... Your question is (probably a fair bit) stronger than the one I related to. Edited.


Big side note, but what you just exhibited is one of my favorite things about this community: admitting being wrong.

It wasn’t really until the workplace where I encountered level-headed people that would just shrug their shoulders and say “You are right. I was wrong” and then move on.

It’s so simple, but is amazingly powerful.


To take it a little further, what I was even more specifically interested in was a sequence of primes following the principle of a gray code [1] where each subsequent prime would differ from the previous prime by precisely one bit.

So basically, what is the longest sequence of primes you could find following that pattern?

[1] https://en.wikipedia.org/wiki/Gray_code


I think you were right the first time.


Nah, 3 (0b11) and 5 (0b101) differ by 2^1 but differ by two binary digits. Or 7 (0b111) and 11 (0b1011). But as I said it’s a starting point.




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