Let $n$ be a number such that $n>3$ and $n$ and $n+2$ are prime numbers. Show that $m=n+1$ is divisible by $6$.
70308
Prove that if $p$ and $p+2$ are both prime integers greater than $3$, then $6$ is a factor of $p+1$.
44857
Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
26503
Suppose that $p$ ≥ $q$ ≥ $5$ are both prime numbers. Prove that 24 divides ($p^2 − q^2$)
45793
How do you prove a number is prime?
74512
How to show $n(n+1)(2n+1) \equiv 0 \pmod 6$?
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
130842
Prime factors + number of Divisors
131488
Show that $p^3+4$ is prime
102064
Prime number between $n$ and $n!+1$
9302
Questions about Divisibility of $2^n$ by $3$
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
124816
Using the fact that $n^3 + 5n$ is divisible by $6$, infer that $n^4 - 2n^3 + 11n^2 + 14n$ is always divisible by $24$
59036
If $a^{n}-1$ is prime then $a=2$ and $n$ is prime?
65430
Using the Well Ordering Principle to Show that n^3 - n is divisible by 6.
97805
$n+1$ is a divisor of $\binom{2n} {n}$
1702
Proving that there are infinitely many primes with remainder of 2 when divided by 3