Check numbers for primality. Generate prime numbers or lists of prime numbers meeting certain conditions.

Determine whether a number is prime:

Specify a prime by its position in the sequence 2, 3, 5, ...:

Generate a list of primes:

Find the nearest prime to a given number:

Decompose numbers into products of primes, which are unique per the fundamental theorem of arithmetic.

Compute a prime factorization:

Work with special subsets of prime numbers. Find numbers within these sets or check for membership.

Find a twin prime pair:

Find a Mersenne prime:

Find one of the few known Fermat primes: