A002957 Numbers k such that 2*10^k - 1 is prime.

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

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• hard
• nonn
• more

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

• 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

Programs

Mathematica

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

PARI

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

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