How to continue: Show that there are infinite prime numbers $1 + 2mp$, $p >2$ prime and $m > 0$ integer.
5142
Infinitely many primes of the form $pn+1$
79389
Is there an intuitionist (i.e., constructive) proof of the infinitude of primes?
75206
If $a$, $a+2$ and $a+4$ are prime numbers then, how can one prove that there is only one solution for $a$?
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
78044
Sieve of eratosthenes infinite primes
60706
Proof that there are infinitely many prime numbers starting with a given digit string
152591
For which prime numbers $p$ does the congruence $x^2 + x + 1 \equiv 0 \pmod{p}$ have solutions?
106111
Understanding that there are infinitely many primes of form $4n+3$
119051
Show that only finitely many positive integers $n$ have the property that for all $m$ for which $1<m<n$ and $\text{gcd}(m,n) = 1$, $m$ is prime.
136856
Diophantine equation with a prime number
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
140949
Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
144050
Is there an infinite number of primes constructed as in Euclid's proof?
107381
Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.