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Results tagged with prime-numbers
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user 120914
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.
4
votes
Accepted
What are the exceptional properties of Mersenne exponent for known largest prime?
Primes $p$ such that $2^p-1$ is prime are called Mersenne exponents. You can find many of their properties on the corresponding entry of the OEIS, namely A000043. Beyond their obvious connections with …
3
votes
Accepted
Behavior of biggest prime divisor of $n$ as $n$ grows large
The number of prime divisors of $n$ grows typically as $\log \log n$. Suppose $n$ has $k$ prime factors. Now $n/L(n)$ has only $k-1$ prime factors, so
$$
k-1 \approx \log \log \frac{n}{L(n)} = \log \l …
8
votes
1
answer
650
views
Arithmetic sequences and Artin's conjecture
(Sorry if this is a naive question; it is not my area!)
Consider the following strengthening of Artin's conjecture on primitive roots (and Dirichlet's theorem) for the case of $n=2$: every arithmetic …
25
votes
Why is integer factoring hard while determining whether an integer is prime easy?
Let me give a slightly different example. The Baumslag-Gersten group is a one-relator group with the presentation $\langle a, b \mid [a, a^b] = a\rangle$. This has a Dehn function which grows faster t …