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Results tagged with prime-numbers
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user 1384
Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.
17
votes
1
answer
1k
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When are there infinitely many primes in a sequence generated by a simple recurrence relation?
tl;dr summary: am I right in thinking that we expect $2^n-1$ to be prime infinitely often, but $2^n+1$ to be prime only finitely often? What's the general story here?
An applied mathematician asked m …
- 41.4k
6
votes
Are there primes p, q such that p^4+1 = 2q^2 ?
I don't know if there is a simple proof, but I know one which is easy to do because it lets a computer do all the work (but the work is perhaps complicated): you simply ask a computer to solve Y^2=2X^ …
- 41.4k
17
votes
Accepted
Why is 2 so odd?
My take on this issue is that p=2 isn't really strange---all small primes are strange, it's just that the smaller you are, the earlier you become troublesome. Look at recent R=T results in the theory …
34
votes
Accepted
Integers not represented by $ 2 x^2 + x y + 3 y^2 + z^3 - z $
EDIT: Hendrik Lenstra emailed me a proof of Conjecture 2. I'll append it below. So Jagy's question is now solved.
OK so I think that Jagy wants to make the following conjecture:
CONJECTURE 1: an i …
- 41.4k
8
votes
Accepted
Families of number fields of prime discriminant
Klueners Malle online might be just the thing you're looking for. Make your own lists! And here's some they made themselves, if you run out of ideas.
- 41.4k
29
votes
6
answers
5k
views
Infinitely many primes of the form $2^n+c$ as $n$ varies?
At the time of writing, question 5191 is closed with the accusation of homework. But I don't have a clue about what is going on in that question (other than part 3) [Edit: Anton's comments at 5191 cla …
- 41.4k