If a prime $p$ is divided by 30, remainder is either prime or 1
110809
What can primes, except 2, 3, and 5, be congruent to $\pmod {30}$?
52530
There exists a prime congruent to $m$ mod $p$
147101
Show that if $p>5$ is prime, then $240 \mid (p^4-1)$
75528
$x^2-x+1$ has a root $\!\bmod p\,$ for infinitely many primes $p$
85042
Write $1/1 + 1/2 + ...1/ (p-1)=a/b$ with $(a,b)=1$. Show that $p^2 \mid a$ if $p\geq 5$ is prime [Wolstenholme's theorem]
146066
Fastest way to find if a given number is prime
111967
Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.
65826
Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.
158106
Prove that 1 less than the number of equivalence classes divides $p-1$ where $p$ is prime
113763
Let $p$,$\ q$ be prime numbers and $n\in \mathbb{N}$ such that $p \nmid n-1$. If $p \mid n^q-1$, then $q \mid p-1$.
80502
$p(x)$ divided by $x-c$ has remainder $p(c)$? [Polynomial Remainder Theorem]
102046
If all primes greater than some fixed value are congruent one modulo an integer, then said integer is equal two.
157766
Are primes (ignoring $2$) equally likely to be $1~\text{or}~3\pmod 4$?
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
84733
Why $a\equiv b\pmod n$ implies $a$ and $b$ have equal remainder when divided by $n$?
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
144622
Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime