isPrime -- whether a integer or polynomial is prime

Synopsis

Usage:

isPrime f
Inputs:
- f, an integer, or an element in a polynomial ring
Outputs:
- a Boolean value, true if f is either a prime integer or an irreducible polynomial and false otherwise

i1 : ZZ/2[t];

i2 : isPrime(t^2+t+1)

o2 = true

i3 : isPrime(t^2+1)

o3 = false

i4 : isPrime 101

o4 = true

i5 : isPrime 158174196546819165468118574681196546811856748118567481185669501856749

o5 = true

i6 : isPrime 158174196546819165468118574681196546811856748118567481185669501856749^2

o6 = false

Since factor returns factors guaranteed only to be pseudoprimes, it may be useful to check their primality, as follows.

i7 : f = factor 28752093487520394720397634653456

      4
o7 = 2 109*1831*3014311519*2987077659845341

o7 : Expression of class Product

i8 : peek'_2 f

o8 = Product{Power{2, 4}, Power{109, 1}, Power{1831, 1}, Power{3014311519, 1}, Power{2987077659845341, 1}}

i9 : first \ toList f

o9 = {2, 109, 1831, 3014311519, 2987077659845341}

o9 : List

i10 : isPrime \ oo

o10 = {true, true, true, true, true}

o10 : List

Primality testing for integers is handled by FLINT.