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A072857 Primeval numbers: numbers that set a record for the number of distinct primes that can be obtained by permuting some subset of their digits. 12
1, 2, 13, 37, 107, 113, 137, 1013, 1037, 1079, 1237, 1367, 1379, 10079, 10123, 10136, 10139, 10237, 10279, 10367, 10379, 12379, 13679, 100279, 100379, 101237, 102347, 102379, 103679, 123479, 1001237, 1002347, 1002379, 1003679, 1012349, 1012379 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

RECORDS transform of A039993. - N. J. A. Sloane, Jan 25 2008. See A239196 and A239197 for the RECORDS trasform of the closely related sequence A075053. - M. F. Hasler, Mar 12 2014

"73 is the largest integer with the property that all permutations of all of its substrings are primes." M. Keith.

Smallest monotonic increasing subsequence of A076449. - Lekraj Beedassy, Sep 23 2006

REFERENCES

J.-P. Delahaye, Merveilleux nombres premiers ("Amazing primes"), "1379's quite primeval, is it not?", pp. 318-321, Pour la Science, Paris 2000.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..100

C. K. Caldwell, The Prime Glossary, primeval number

J. P. Delahaye, Primes Hunters, 1379 is very primeval (in French)

M. Keith, Integers containing many embedded primes

W. Schneider, Primeval Numbers

N. J. A. Sloane, Transforms

G. Villemin's Almanach of Numbers, Nombre Primeval de Mike Keith

Wikipedia, Primeval number

EXAMPLE

1379 is in the sequence because it is the smallest number whose digital permutations form a total of 31 primes, viz. 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, 9371.

MATHEMATICA

(*first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Length[ Select[ FromDigits /@ Flatten[ Permutations /@ Subsets[ IntegerDigits[ n]], 1], PrimeQ[ # ] &]]; d = -1; Do[ b = f[n]; If[b > d, Print[n]; d = b], {n, 2^20}] (from Robert G. Wilson v Feb 12 2005)

CROSSREFS

Cf. A039993, A075053, A076497, A239196, A239197.

A076449 gives a similar sequence.

Cf. A119535 (prime subsequence).

Sequence in context: A085497 A005113 A239196 * A119535 A210849 A216155

Adjacent sequences:  A072854 A072855 A072856 * A072858 A072859 A072860

KEYWORD

base,nonn

AUTHOR

Lekraj Beedassy, Jul 26 2002

EXTENSIONS

Edited, corrected and extended by Robert G. Wilson v, Nov 12 2002

Comment corrected by N. J. A. Sloane, Jan 25 2008

STATUS

approved

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Last modified September 30 19:57 EDT 2014. Contains 247475 sequences.