query: How to prove that $n$ is a prime if $2^n-1$ is a prime
positive_passages.docid: 154475
positive_passages.text: Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
negative_passages.docid: 131385
negative_passages.text: How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
negative_passages.docid: 118452
negative_passages.text: how to prove $\mathbb Z_n$ has divisors of zero if and only if $n$ is not prime
negative_passages.docid: 42885
negative_passages.text: Fermat primes relation to $2^n+1$
negative_passages.docid: 100984
negative_passages.text: Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
negative_passages.docid: 75685
negative_passages.text: Prove that there is prime number and natural so $n\times q$ digits are $1$.
negative_passages.docid: 147101
negative_passages.text: Show that if $p>5$ is prime, then $240 \mid (p^4-1)$
negative_passages.docid: 5043
negative_passages.text: Show that $2^n>1+n\sqrt{2^{n-1}}$
negative_passages.docid: 24403
negative_passages.text: Prove that $ n < 2^{n}$ for all natural numbers $n$.
negative_passages.docid: 136077
negative_passages.text: Prove that $x-1$ is a factor of $x^n-1$
negative_passages.docid: 152299
negative_passages.text: Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
negative_passages.docid: 5841
negative_passages.text: Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
negative_passages.docid: 33866
negative_passages.text: Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
negative_passages.docid: 8710
negative_passages.text: Bounds for $n$-th prime
negative_passages.docid: 6700
negative_passages.text: An Olympiad problem in prime numbers :can we proof that "n" is prime in this case "
negative_passages.docid: 63702
negative_passages.text: There is a prime between $n$ and $n^2$, without Bertrand
negative_passages.docid: 59036
negative_passages.text: If $a^{n}-1$ is prime then $a=2$ and $n$ is prime?