

A002957


Numbers k such that 2*10^k  1 is prime.
(Formerly M0680)


11



1, 2, 3, 5, 7, 26, 27, 53, 147, 236, 248, 386, 401, 546, 785, 1325, 1755, 2906, 3020, 5407, 5697, 5969, 7517, 15749, 19233, 38232, 55347, 1059002
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OFFSET

1,2


COMMENTS

Also numbers k such that 10^k + 9*R_k is prime, where R_k = 11...1 is the repunit (A002275) of length k.
Serge Batalov discovered that 1059002 belongs to this sequence but may not be the next term.  Max Alekseyev, Sep 30 2013
a(28) > 410000 (from Kamada data).  Robert Price, Oct 19 2014
Rytis Slatkevičius proved there are no undiscovered terms up to 1059002, so that term has now been added as a(28).  Jeppe Stig Nielsen, Jan 17 2023


REFERENCES

H. Riesel, "Prime numbers and computer methods for factorization," Progress in Mathematics, Vol. 57, Birkhauser, Boston, 1985, Page 162.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
C. R. Zarnke and H. C. Williams, Computer determination of some large primes, pp. 563570 in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computer Science. Vol. 2, edited R. C. Mullin et al., 1971.


LINKS



MATHEMATICA

Do[ If[ PrimeQ[ 2*10^n  1], Print[n] ], {n, 1, 15000} ]


PROG

(PARI) for(n=1, 10^5, if(ispseudoprime(2*10^n1), print1(n, ", "))) \\ Felix Fröhlich, Jun 23 2014


CROSSREFS



KEYWORD

hard,nonn,more


AUTHOR



EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008


STATUS

approved



