What's the relationship between irreducible number and prime number and query common example
135102
How do the definitions of "irreducible" and "prime" elements differ?
78342
When is $\phi(n)$ a prime number?
105444
Possible values of prime gaps
140497
Irreducibles are prime in a UFD
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.
124037
Complex prime numbers
108265
Alternate definition of prime number
79208
Is the number $-1$ prime?
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)
65558
Irreducible in $\mathbb{Z}[\sqrt{-5}]$
6702
Intuition for the prime number theorem
148434
Ring where irreducibles are primes which is not an UFD
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
140550
Irreducible element iff prime norm in Gaussian integers?
154845
Irreducible elements in  $\mathbb{Z}[\sqrt{-2}]$ and is it a Euclidean domain?
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime