A002957 Numbers k such that 2*10^k - 1 is prime. (Formerly M0680)

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

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. 563-570 in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computer Science. Vol. 2, edited R. C. Mullin et al., 1971.

Links

Table of n, a(n) for n=1..28.

Chris K. Caldwell, Prime Pages, Search output 2*10^?-1

Makoto Kamada, Prime numbers of the form 199...99.

Index entries for primes involving repunits

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A249509 A085907 A024777 * A333955 A333960 A273726

Adjacent sequences: A002954 A002955 A002956 * A002958 A002959 A002960

Keyword

hard,nonn,more

Author

N. J. A. Sloane, Simon Plouffe

Extensions

Corrected and extended by Robert G. Wilson v, Feb 02 2001

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

a(28) from Jeppe Stig Nielsen, Jan 17 2023

Status

approved