Prove $2^n - 1$ is NOT a prime number, when n is NOT a prime number also
136947
Simple Mersenne prime divisibility proofs
123033
Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$
144622
Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime
68328
Infinitely many $n$ such that $2^n-n$ is divisible by a prime
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
73515
Primes Number Theory
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
59036
If $a^{n}-1$ is prime then $a=2$ and $n$ is prime?
43939
Show that $3^{2n+1}-4^{n+1}+6^n$ is never prime for natural n except 1.
39915
Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number
140294
prove that $n >2$ and $n$ is a prime then $n$ is odd
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
37315
not both $2^n-1,2^n+1$ can be prime.
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
55266
Prove that $(n+1)^{n-1}<n^n$
42885
Fermat primes relation to $2^n+1$