6.5.14  Test of primality: is_prime isprime isPrime

The is_prime, isprime and isPrime commands are tests for primality.

• is_prime takes one argument:
  n, an integer.
• is_prime(n) returns 1 if n is prime and 0 if n is not prime.

isprime and isPrime are the same as is_prime, except they return true or false.

Examples.

• Input:
  is_prime(100003)
  Output:

  1

• Input:
  isprime(100003)
  Output:

  true

• Input:
  is_prime(98569898989987)
  Output:

  1

• Input:
  is_prime(14)
  Output:

  0

• Input:
  isprime(14)
  Output:

  false

You can use the command pari("isprime",n,1) (see Section 6.7.10) to get a primality certificate (see the documentation PARI/GP with the menu Help▸Manuals▸PARI-GP) and pari("isprime",n,2) to use the APRCL test.

Examples.

• Input:
  isprime(9856989898997789789)
  Output:

  true

• Input:
  pari("isprime",9856989898997789789,1)
  Output:

  ⎛ ⎜ ⎜ ⎜ ⎝        2 2 1        19 2 1        941 2 1        1873 2 1 ⎞ ⎟ ⎟ ⎟ ⎠

  which are the coefficients giving the proof of primality by the p−1 Selfridge-Pocklington-Lehmer test.