Polynomial in $\mathbb{Z}[x]$ which is irreducible but not prime.
140497
Irreducibles are prime in a UFD
70537
Irreducible polynomials have distinct roots?
57884
Number of monic irreducible polynomials of prime degree $p$ over finite fields
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
10514
Proof that no polynomial with integer coefficients can only produce primes
87101
Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
46292
Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
4105
Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
250
An irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root?
76640
Show that the polynomial $x^3-xy^2+y+1$ is irreducible in $\mathbb{Q}[x,y]$
84355
Methods to see if a polynomial is irreducible
134726
Show the polynomial is irreducible in $\textbf Z_2$
17991
Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
156940
There does not exist a polynomial $p(x)$ with integer coefficients which gives a prime number $\forall x\in \mathbb{Z}$