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A135377 Smallest n-primeval prime, i.e., minimal prime number containing all A006880(n) primes < 10^n embedded in it as permutations of some of its substrings. 1
2357, 1123465789, 10112233445566788997, 100111222333444555666777998889, 1000111222233334444555666777798889899, 100001111222233333444445555566666777778888999989 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(1) - a(4) were computed by Mike Keith in 2008 and a(4) - a(31) by Jérôme STORTI in 2002.

LINKS

Table of n, a(n) for n=1..6.

M. Keith, Integers containing many embedded primes

EXAMPLE

Mike Keith's website uses a shorthand notation for these numbers. The 4-primeval prime 100111222333444555666777998889 is written in this notation as (1) 2 3 3 3 3 3 3 3 0 998889. The (1) represents the leading 1 digit (which will always be present). The next number says how many consecutive 0's follow the leading 1 and the next says how many consecutive 1's follow that and so on up to the number of consecutive 8's. The final grouping explicitly shows how the last group of 8's and 9's are arranged.

The following are the n-primeval primes as found by Jérôme STORTI in this notation:

5 (1) 3 3 4 4 4 3 3 4 0 98889899

6 (1) 4 4 4 5 5 5 5 5 4 999989

7 (1) 5 5 5 6 5 5 5 6 3 98899999

8 (1) 5 6 7 7 6 7 7 7 6 98999999

9 (1) 7 7 8 8 8 7 8 8 6 9999989899

10 (1) 8 8 8 9 9 9 9 9 7 9999899999

11 (1) 8 9 10 10 10 9 10 10 6 9889989999999

12 (1) 10 10 10 11 11 11 10 11 9 9998999999899

13 (1) 10 11 11 12 11 12 11 12 9 99899999999899

14 (1) 11 13 13 13 12 12 12 13 11 989999989999999

15 (1) 12 13 14 14 13 14 13 14 12 9999999988999999

16 (1) 13 14 14 15 14 14 14 15 12 99999999999999889

17 (1) 14 15 15 16 15 15 15 16 14 998999999999998999

18 (1) 16 17 17 17 16 17 17 17 14 9989999999999899999

19 (1) 17 18 17 18 17 17 17 18 15 988999999899999999999

20 (1) 17 19 18 19 19 18 19 19 16 999999998999999999989

21 (1) 18 19 19 20 19 19 20 20 17 9899999999999999998999

22 (1) 18 20 20 21 20 21 21 21 18 99998999999999999998999

23 (1) 21 23 21 22 21 21 22 22 19 999999889999999999999999

24 (1) 20 22 22 23 22 22 22 23 21 999999999999999989999999

25 (1) 23 23 23 24 23 23 23 24 22 9999999999999999998999999

26 (1) 23 24 24 25 25 25 24 25 22 999999999999999999899999989

27 (1) 24 25 25 26 25 25 25 26 23 9999999998999999999999998999

28 (1) 25 26 27 27 27 26 27 27 25 9999899999999999999999999999

29 (1) 25 27 27 28 27 27 27 28 25 999999989999999999999999999989

30 (1) 26 29 28 29 29 28 28 29 27 999999999999998999999999999999

31 (1) 28 29 29 30 29 29 29 30 27 99999889999999999999999999999999

a(2) = 1123465789 because this is the smallest prime out of which each of the first 25 primes below 10^2, viz. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 can be formed using its digits.

CROSSREFS

Cf. A072857, A039993, A134649.

Sequence in context: A132904 A030473 A134649 * A081208 A250990 A269483

Adjacent sequences:  A135374 A135375 A135376 * A135378 A135379 A135380

KEYWORD

nonn,base

AUTHOR

Lekraj Beedassy, Dec 09 2007

EXTENSIONS

Link fixed by Charles R Greathouse IV, Aug 13 2009

STATUS

approved

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)