# primeval number

Have you every played the game where you take a word like "prime" and see how many other words you can find in it? For example, you might find: `prime, prim, ripe, imp, pie, rip,`... Why not play the same game with integers and look for primes? For example, in 1379 we find the following thirty-one primes:
3, 7, 13, 17, 19, 31, 37, 71, 73, 79, 97, 137,
139, 173, 179, 193, 197, 317, 379, 397, 719, 739, 937, 971,
1973, 3719, 3917, 7193, 9137, 9173, and 9371
(Note that we may only use as many of each digit as are present in the original number.)

Mike Keith defined a primeval number to be a positive integer which contains more primes (in the way discussed above) than any smaller positive integer. Below are all of the primeval numbers less than 100,000 (from Keith's web page).

All primeval numbers less than 100,000
primeval integer number of
primes contained
primeval integer number of
primes contained
21 137931
133 1007933
374 1012335
1075 1013641
1137 1013953
13711 1023755
101311 1027960
103719 1036764
107921 1037989
123726 1237996
136729 13679106

See Also: DeletablePrime, PermutablePrime, LeftTruncatablePrime, MinimalPrime