3 ms·
Semi-related, but reading this article and thinking about it made me wonder if there is any study at all of "gray code" primes, for lack of a better word. Basi
by war1025 7y ago
Semi-related, but reading this article and thinking about it made me wonder if there is any study at all of "gray code" primes, for lack of a better word.
Basically, prime numbers that differ by exactly one binary digit in their representation.
Probably nothing about that relationship that would be interesting enough to look into beyond just "I ran some calculations and found these numbers that fit the pattern"
- oefrha 7y agoThis 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_gaps_between_primes 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.
- war1025 7y agoNeat. 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.
- oefrha 7y agoActually I replied without thinking too much, sorry... Your question is (probably a fair bit) stronger than the one I related to. Edited.
- chairmanwow1 7y agoBig 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.
- war1025 7y agoTo 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 https://en.wikipedia.org/wiki/Gray_code
- cygaril 7y agoI think you were right the first time.
- oefrha 7y agoNah, 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.