prime number a prime number or prime integer often simply called a prime for short is a positive integer that has no positive integer divisors other than 1 and itselfmore concisely a prime number is a positive integer having exactly one positive divisor other than 1 meaning it is a number that cannot be factoredarge primes caldwell include the large mersenne primes ferrier s prime and the digit counterexample showing that 5359 is not a sierpiÅski number of the second kind helm and norris the largest known prime as of january 2013 is the mersenne prime which has a whopping decimal digits