Prove that $8p^2+2p+1$ is prime number
131488
Show that $p^3+4$ is prime
47162
Proving there are infinitely many primes of the form $a2^k+1.$
148713
If $p\geq 5$ is a prime number, show that $p^2+2$ is composite.
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
70308
Prove that if $p$ and $p+2$ are both prime integers greater than $3$, then $6$ is a factor of $p+1$.
37093
If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
15348
prime divisor of $3n+2$ proof
58114
For which primes p is $p^2 + 2$ also prime?
65511
Proving the following false: $f(x)=2x+1$ produces a prime number if and only if x is prime
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
142584
Confusion in proof that primes $p = 4k + 1$ are uniquely the sums of two squares
22023
Infinitely number of primes in the form $4n+1$ proof
75733
Divisibility of prime numbers
144851
For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
45700
How can I know if $2^{2^{2^{2^{2}}}}+1=?$ is prime?