$n$ is a prime number $\iff $ $\frac{Tn(x)}{x}$ is irreducible on $Q[x]$
101454
Chebyshev Polynomials and Primality Testing
6700
An Olympiad problem in prime numbers :can we proof that "n" is prime in this case "
76813
The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
147777
If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
111037
Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime.
98544
Prove that in any GCD domain every irreducible element is prime
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
46292
Find all primes $p>2$ for which $x^2+x+1$ is irreducible in $\mathbb{F}_p[x]$
65511
Proving the following false: $f(x)=2x+1$ produces a prime number if and only if x is prime
17670
If $p\in R[X_1,\dots,X_n]$ is irreducible, is it still irreducible in $R[X_1,\dots,X_n,\dots,X_N]$?
108767
Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition
154360
Show $f$ can't be irreducible over a finite field if $f^\prime$ is the zero polynomial.
127830
proof that $\sqrt(2)$ is irrational / why is the fraction irreducible
135152
Non-UFD integral domain such that prime is equivalent to irreducible?
113763
Let $p$,$\ q$ be prime numbers and $n\in \mathbb{N}$ such that $p \nmid n-1$. If $p \mid n^q-1$, then $q \mid p-1$.