Is there any algorithm that produces irreducible polynomials over $\mathbb{F}_2$?
35959
irreducibility of a polynomial over $\mathbb{F}_2$
97028
Find all irreducible monic polynomials in $\mathbb{Z}/(2)[x]$ with degree equal or less than 5
74777
Solvability and reducibility of a polynomial in a "chain" of finite fields
112427
Irreducibility of $p(x)=x^4-4x^2+8x+2$ over $\mathbb{Q}(\sqrt{-2})$- Dummit Foote Abstract algebra $9.4.10$
97654
Rewrite a real polynomial in real (but only linear and quadratic) factors
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$
148909
Irreducible polynomials of degree 3 and 5
77403
Finding the minimal polynomial of $\sqrt 2 + \sqrt[3] 2$ over $\mathbb Q$.
53669
Prove that the polynomial $(x-1)(x-2)\cdots(x-n) + 1$, $ n\ge1 $, $ n\ne4 $ is irreducible over $\mathbb Z$
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
120627
Reducibility of polynomials modulo p
27577
An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
102422
Irreducibly of $x^5-x-1$ over $\mathbb{F}_3$
31215
Irreducible cyclotomic polynomial
44878
Factor $x^5+x^2+1$ into irreducible polynomials in $Z[x]$
143107
Why is $X^4 + \overline{2}$ irreducible in $\mathbb{F}_{125}[X]$?