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Results tagged with prime-numbers
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user 30445
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.
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Consecutive integers with no large prime factors
Yuta is correct, Størmer's method, or preferably, D.H. Lehmer's 1963 refinement of that method, applies to a finite set of primes. If the set contains $k$ primes, then you have $2^k-1$ Pell equations …
- 225
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For any prime $p$, is there $C$ such that if $x\ge C$, then all but one integer among $x+1, ...
I don't know how far Larry went in pursuing this problem, but this touches on a topic I've spent some time on, ie. Lehmer's method.
Let $S_j$ be the maximum $S$ for which the pair {$S, S+j$} is $p$-sm …
- 225