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Results tagged with prime-numbers
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user 74676
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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If $\binom{2p}{p}$ is $(-1)^{p-1} \bmod 2p+1$ is then $2p+1$ prime?
Let $p$ be a positive integer; if $2p+1$ is prime then it is easily checked that
$$(2p+1)\mid\left(\binom{2p}{p}+(-1)^{p-1}\right);$$
conversely I conjecture that if the above divisibility assumption …
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