References External links The primality of certain integers of the form 2Arn − 1 Some prime numbers of the forms 2·3n + 1 and 2·3n − 1 Chris Caldwell, The Largest Known Primes Database at The Prime Pages A Williams prime of the first kind base 2: (2−1)·274207281 − 1 A Williams prime of the first kind base 3: (3−1)·31360104 − 1 A Williams prime of the second kind base 3: (3−1)·31175232 + 1 A Williams prime of the first kind base 10: (10−1)·10383643 − 1 A Williams prime of the first kind base 113: (113−1)·113286643 − 1 Williams prime at PrimeWiki List of Williams primes Classes of prime numbers Mersenne primes