A156166 Numbers k > 0 such that (10^(k+2) + 666)*10^k + 1 is prime.

1, 14, 43, 507, 609, 2473, 2624, 28292, 181299

Offset: 1

Author

M. F. Hasler, Feb 10 2009

Keywords

• more
• nonn
• base

Comments

Or, indices of primes in the sequence 16661, 1066601, 100666001, 10006660001,... Ondrejka calls these "beastly palindromic primes".

In popular culture: the number generated by a(2), 1000000000000066600000000000001, also known as Belphegor's Prime, was used as a plot device in Episode "Just a Regular Irregular" of the "Elementary" TV series (first aired Nov/13/2014). - Serge Batalov, Nov 15 2014

Links

• C. Caldwell, H. Dubner (Eds): The top ten prime numbers: from the unpublished collections of R. Ondrejka (May 2001), p. 32
• Internet Movie Database, Elementary: Season 3, Episode 3: Just a Regular Irregular
• Clifford A. Pickover, Belphegor's Prime: 1000000000000066600000000000001
• Eric Weisstein's World of Mathematics, Belphegor Prime
• Eric Weisstein's World of Mathematics, Integer Sequence Primes
• Wikipedia, Belphegor's prime

Crossrefs

Cf. A082700 and search results for 16661.

Cf. A232448 (a(n) - 1).

Programs

Magma

[n: n in [1..500] | IsPrime((10^(n+2)+666)*10^n+1)]; // Vincenzo Librandi, Nov 15 2014

Maple

A156166:=n->`if`(isprime((10^(n+2)+666)*10^n+1), n, NULL): seq(A156166(n), n=1..10^3); # Wesley Ivan Hurt, Nov 16 2014

Mathematica

Select[Range[10^3], PrimeQ[(10^(# + 2) + 666)*10^# + 1] &] (* Arkadiusz Wesolowski, Sep 08 2011 *)

PARI

for( n=1,9999, ispseudoprime((10^(n+2)+666)*10^n+1) & print1(n","))

Formula

a(n) = A232448(n) + 1.

Extensions

a(8) = 28292 (discovered on Jan 05 2004, by Daniel Heuer), Arkadiusz Wesolowski, Mar 16 2011

a(9) = 181299 from Serge Batalov, Nov 15 2014