if $p$ and $q$ are successive odd primes and $p + q = 2r$ then $r$ is composite,
54359
Odd Primes Problem Proof
76644
For any odd prime $p$, a quadratic is solvable mod $p^2$ if it is solvable mod $p$, and $p$ does not divide the discriminant and leading coefficient.
135750
Prove that if a and b are integers, then there are unique integers q and r such that $a = bq + r$, $-|b|/2 < r \le |b|/2$
45454
Pairs of $(p,q)$ such that $p^2 + 1 = 2 q^2$?
3500
Compositeness of $n^4+4^n$
56229
On the difference between consecutive primes
59391
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
6119
If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$?
94209
Prove by contradiction that every integer greater than 11 is a sum of two composite numbers
86594
If $x^2 \equiv y^2 \pmod {p^r}$, where $p$ is an odd prime not dividing $x$ or $y$ then $x \equiv \pm y \pmod {p^r}$
35553
If $n$ is composite, so is $2^n-1$
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$
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 $(x+y)^p \equiv x^p+y^p \pmod{p}$
152231
Computing the product of p/(p - 2) over the odd primes
126725
If $p$ is prime and $p$ $\equiv$ $1$ (mod 4), then the congruence $x^2$ $\equiv$ $-1$ (mod $p$) has two incongruent solutions...