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# 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,(Note that we may only use as many of each digit as are present in the original number.)

139, 173, 179, 193, 197, 317, 379, 397, 719, 739, 937, 971,

1973, 3719, 3917, 7193, 9137, 9173, and 9371

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 100,000primeval integer number of

primes containedprimeval integer number of

primes contained2 1 1379 31 13 3 10079 33 37 4 10123 35 107 5 10136 41 113 7 10139 53 137 11 10237 55 1013 11 10279 60 1037 19 10367 64 1079 21 10379 89 1237 26 12379 96 1367 29 13679 106

**See Also:** DeletablePrime, PermutablePrime, LeftTruncatablePrime, MinimalPrime

Printed from the PrimePages <t5k.org> © Reginald McLean.