Irreducible and not prime
111935
Irreducible but not prime
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
151961
Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
86724
Example of a non-zero module that has no associated primes
16592
Irreducible polynomial which is reducible modulo every prime
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$
98544
Prove that in any GCD domain every irreducible element is prime
148434
Ring where irreducibles are primes which is not an UFD
155962
Are there irreducible polynomials that are partially solvable by radicals?
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
74224
On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
31215
Irreducible cyclotomic polynomial
140808
Problem on Galois theory and irreducible polynomial
10885
Existence of irreducible polynomials over finite field
24988
Prove there exists $m > 2010$ such that $f(m)$ is not prime
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.