Primeval number

In mathematics, a primeval number is a natural number n for which the number of prime numbers which can be obtained by permutating all or some of its digitss (in base 10) is larger than the number of primes obtainable in the same way for any smaller natural number. Primeval numbers were first described by Mike Keith.

The first few primeval numbers are 2, 13, 37, 107, 113, 137, 1013, 1037, 1079, 1237, 1367, ... (Sloane's A072857); the number of primes that can be obtained from the primeval numbers is 1, 3, 4, 5, 7, 11, 11, 19, 21, 26, 29, ... (Sloane's A088130). The number of primes that can be obtained from a primeval number with n digits is 1, 4, 11, 31, 106, ... (Sloane's A076730).

External links

• The Prime Glossary: Primeval number