Prove or disprove: There exists a prime p > 3 such that p + 2 and p + 4 are also prime
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
135586
Prove that the preimage of a prime ideal is also prime.
68221
Question regardles primes and the fundamental theorem of arithmetic
95162
For a odd prime $p, \exists a,b$ such that $a^2 + ab + b^2 \equiv 0 \pmod{p} \iff \exists x,y $ such taht $x^2 + xy + y^2 = p$?
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
106111
Understanding that there are infinitely many primes of form $4n+3$
83721
If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]
148713
If $p\geq 5$ is a prime number, show that $p^2+2$ is composite.
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
111037
Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime.
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
23830
Proof that if $p\equiv3\,\left(\mbox{mod 4}\right)$ then $p$ can't be written as a sum of two squares
15348
prime divisor of $3n+2$ proof
88036
Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$