primeval numbers

A primeval number $n$

is a number that sets a record for the number of distinct primes that can be written using the digits of $n$

For example, 137 is a primeval number because using its digits it is possible to write 11 primes, namely, 3, 7, 11, 13, 17, 31, 37, 73, 137, 173, and 317, and it not possible to obtain 11 or more primes using the digits of any other smaller number.

The 100 primeval numbers are known. The first are 1, 2, 13, 37, 107, 113, 137, 1013, 1037, 1079, 1237, 1367, 1379, 10079, 10123, 10136, 10139, 10237, 10279, 10367, 10379, 12379 more terms

Using the digits of the 100-th primeval number (101234567789) it is possible to write 18451445 distinct primes.

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here

A graph displaying how many primeval numbers are multiples of the primes p from 2 to 71. In black the ideal line 1/p.

Useful links Mike Keith, Primeval Number
Wikipedia, Primeval number
OEIS, Sequence A072857

Primeval numbers can also be... (you may click on names or numbers and on + to get more values)

a-pointer 13 aban 13 37 107 113 137 abundant 10136 alternating 107 10123 10367 1012349 101234567 amenable 13 37 113 137 1013 1037 1237 10136 10237 + 10123469 100123457 100123469 apocalyptic 10079 10123 10136 10139 10237 10279 10367 10379 12379 13679 arithmetic 13 37 107 113 137 1013 1037 1079 1237 + 1023479 1234579 1234679 balanced p. 1367 brilliant 1037 1079 103679 10023457 c.square 13 113 1013 Chen 13 37 107 113 137 1367 10079 10139 12379 + 1012379 1023467 10034579 congruent 13 37 137 1013 1037 1079 1237 1367 1379 + 1012349 1023479 1234679 Cunningham 37 Curzon 113 1013 10012349 cyclic 13 37 107 113 137 1013 1037 1079 1237 + 1023479 1234579 1234679 de Polignac 10079 10237 10379 13679 1003679 1012379 1023479 10023479 10123579 deceptive 12345679 1123456789 deficient 13 37 107 113 137 1013 1037 1079 1237 + 1023479 1234579 1234679 dig.balanced 37 10136 10279 10379 12379 10012379 10023457 10023467 10034579 10123579 10234567 10234579 Duffinian 1037 1079 1379 10123 10237 10279 10367 10379 101237 + 1023479 1234579 1234679 economical 13 37 107 113 137 1013 1037 1079 1237 + 10234567 10234579 12345679 emirp 13 37 107 113 1237 10079 100279 100379 emirpimes 1079 1379 10123 10237 10279 10367 102347 1002379 equidigital 13 37 107 113 137 1013 1037 1079 1237 + 10234567 10234579 12345679 esthetic 10123 101234567 1012345678 10123456789 Eulerian 1013 evil 113 1013 1037 1079 1237 1379 10079 10123 10279 + 100123379 102334679 102345679 Fibonacci 13 gapful 1037 10279 100234567 1001234567 good prime 37 1367 13679 happy 13 13679 102347 103679 1002347 1003679 Harshad 10279 12345679 1012345678 hex 37 Hogben 13 Honaker 100279 iban 107 10123 102347 iccanobiF 13 idoneal 13 37 inconsummate 1037 10237 10367 10379 100379 101237 103679 interprime 10136 10123469 junction 107 113 1013 lucky 13 37 10279 12379 magic 1379 metadrome 13 37 137 1237 1367 1379 12379 13679 123479 1234579 1234679 12345679 modest 13 1037 1012345679 Moran 10279 12345679 oban 13 37 odious 13 37 107 137 1367 10136 10139 10237 10367 + 100234679 101234567 101234579 Ormiston 1012379 pancake 37 137 1379 102379 panconsummate 37 pernicious 13 37 107 137 1367 10136 10237 12379 100279 + 1012379 1023457 1234579 persistent 10123456789 Pierpont 13 37 plaindrome 13 37 113 137 1237 1367 1379 12379 13679 + 1234679 12345679 1123456789 prime 13 37 107 113 137 1013 1237 1367 10079 + 10012234679 100012345679 100123456789 Proth 13 113 pseudoperfect 10136 repunit 13 self 1379 10379 100379 1012349 1234579 10012349 10234579 100234579 semiprime 1037 1079 1379 10123 10237 10279 10367 10379 101237 + 10123469 10123679 12345679 Sophie Germain 113 1013 1003679 100234679 sphenic 1012349 1023457 1234579 10012349 10234567 10234579 star 13 37 strong prime 37 107 137 10139 13679 100379 123479 1002347 1003679 10034579 super-d 107 1012379 tribonacci 13 truncatable prime 13 37 113 137 1367 twin 13 107 137 10139 12379 13679 1002347 10034579 uban 13 37 Ulam 13 1037 1079 upside-down 37 1379 wasteful 10136 1012349 1023457 weak prime 13 113 1013 1237 10079 12379 100279 1001237 1012379 1023467 10123457 10123579 Zumkeller 10136