Infinitely many primes not congruent to 1 mod n
107381
Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$
22023
Infinitely number of primes in the form $4n+1$ proof
75528
$x^2-x+1$ has a root $\!\bmod p\,$ for infinitely many primes $p$
45461
Is there a prime which is the form of $10^n + 1$ except $2, 11, 101$?
52530
There exists a prime congruent to $m$ mod $p$
107990
Does there exist an integer $x$ satisfying the following congruences?
53469
C(0, 1) has infinitely many prime ideals not of the form Mp
75581
Is the sum of the first $n$ primes a prime infinitely many times?
144050
Is there an infinite number of primes constructed as in Euclid's proof?
19761
Show for prime numbers of the form $p=4n+1$,  $x=(2n)!$ solves the congruence $x^2\equiv-1 \pmod p$. $p$ is therefore not a gaussian prime.
68688
n-th prime number is less than $4^n$
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.
46803
Proof that there are infinitely many primes congruent to 3 modulo 4
136279
Infinitely many primes $\equiv 3 \mod 4$
5142
Infinitely many primes of the form $pn+1$
109490
Modular arithmetic problem (mod $13$)
132132
Are there infinitely many primes of the form $6^{2n}+1$ or only finitely many?