Prove: Any prime of the form $3n+1$ is also in the form $6m+1$
34692
Prove if $ p$ is a prime of the form $3n+1$, then $p$ is also of the form $6m+1$
73515
Primes Number Theory
54286
Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
106847
Proof that $n^3+2n$ is divisible by $3$
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
62169
Product of all prime numbers on the interval [m+1, 2m] is $\le \left(\begin{matrix} 2m \\m\end{matrix}\right)$
76282
Prime number expressible as $2^2+3^3+5^5+7^7+11^{11}+\cdots$
12862
Prove that two distinct numbers of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $\gcd=2$ if $a$ is odd
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
44063
Suppose k is an integer such that $6k + 1$, $12k + 1$, $18k + 1$ are primes. Show that $n = (6k + 1)(12k + 1)(18k + 1)$ is a Carmichael number.
21612
How to prove this form of $n$?
116361
Relationship between prime factorizations of $n$ and $n+1$?
6700
An Olympiad problem in prime numbers :can we proof that "n" is prime in this case "
15348
prime divisor of $3n+2$ proof
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
82482
Proving an infinite number of primes of the form 6n+1