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Results tagged with prime-numbers
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user 6153
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.
18
votes
Accepted
The multiplicative order of 2 modulo primes
The answer is "yes" - the order mod p of 2 is almost always as large as the square root of p (actually you get epsilon less than this in the exponent). If you take r multiplicatively independent numbe …
- 12.6k
17
votes
prime powers between n and 2n
Actually there is a power of 2. It goes to show the power of binary arithmetic ... : write 2n in binary and write zeroes after the initial one.
- 12.6k
9
votes
Accepted
Can Gauss sums derandomize any heuristic arguments?
The thing is that it is well known that for the quadratic Gauss sums, expressed as an exponential sum rather than with Legendre symbols, the path is very much not a random walk when you plot it in the …
- 12.6k
7
votes
Accepted
Refinements of the Riemann hypothesis
Yes, your question is imprecise. If we knew exactly where the zeta zeroes were, we could answer any question about the primes that could be formulated by means of the explicit formulae. In crude terms …
- 12.6k
6
votes
Accepted
Sum of reciprocals of primes modulo which a polynomial has a root
This should follow from the Theorem of Frobenius mentioned on p. 7 (PDF numbering) of http://websites.math.leidenuniv.nl/algebra/chebotarev.pdf.
- 12.6k
6
votes
Accepted
Prime Number Theorem w/o Complex Analysis
http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf explains the classic proof in context (there is what amounts to a priority dispute).
- 12.6k
0
votes
An estimate of the sum related to primes
It looks to me like the intended method is to use the loglog divergence of the sum of the reciprocals of the primes on the first sum, and then presumably the Prime Number Theorem with error term on th …
- 12.6k