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Results tagged with prime-numbers
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user 10670
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.
10
votes
The number of different prime factors of a special class of positive integers
No it's not true you have the following counterexample:
$$ \frac{2^5-1}{2-1} \times \frac{5^3-1}{5-1} = 31^2 $$
- 854
7
votes
1
answer
614
views
Is there an Infinite increasing sequence of primes with bounded second or larger differences?
The opposite question is if for any infinite increasing sequence of primes and any $k$ the sequence of the $k$-th order differences of the elements of the sequence is unbounded.
But if the question i …
- 854
6
votes
Prime counting - any fast alternatives to the Lagarias-Miller-Odlyzko combinatorial method o...
I don't know if this might interest you, but there is a nice formula due to Lifchitz which allows to compute the parity of $\pi(x)$ in $O(\sqrt{x}\log x)$: if $\Pi(x)$ represent the number of prime po …
- 854