Given any finite number of non-zero prime modular residues, are there infinitely many primes that share those residues?
131241
primes congruent to 5 mod 6 and 1 mod p
82482
Proving an infinite number of primes of the form 6n+1
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
65131
Can infinitely many primes lie over a prime?
130300
Proof that every quadratic residue has two roots, modulo a prime
13901
Finitely many prime ideals lying over $\mathfrak{p}$
71788
Prove existence of multiplicative inverse modulo p when p is prime
22029
Solving modular arithmetic questions
84746
elementary proof that infinite primes quadratic residue modulo $p$
38748
There are infinitely many prime numbers $p$ for which $p + 2$ and $p + 4$ are also prime numbers
144050
Is there an infinite number of primes constructed as in Euclid's proof?
25023
How do you prove that there are infinitely many primes of the form $5 + 6n$?
44857
Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
8710
Bounds for $n$-th prime
43567
Some hints for "If a prime $p = n^2+5$, then $p\equiv 1\mod 10$ or $p\equiv 9\mod 10$"
93898
Prove that for any prime p, there is a complete set of mod p residues {q1, . . . , qp}, where each qi is prime.
103561
Residue fields of schemes of finite type (over $\mathbb{Z}$)