A056805 Numbers k such that 6*10^k+1 is prime.

0, 1, 2, 8, 9, 15, 20, 26, 38, 45, 65, 112, 244, 303, 393, 560, 839, 1009, 1019, 1173, 1334, 2236, 2629, 4426, 8848, 20812, 37744, 72926, 86287, 231617, 281969, 488852, 522127, 655642, 758068, 879313, 1380098

Offset: 1

Author

Robert G. Wilson v, Aug 22 2000

Keywords

• more
• nonn

Comments

From the Kamada data, Edward Trice reports that 231617 and 522127 are in this sequence. But these may not be the next ones. There are no others less than 2*10^5, however. - Robert Price, Jul 09 2015

Examples

			For k=2 => (6*10^2+1)=601, which is prime.
		

Links

• Makoto Kamada, Prime numbers of the form 600...001.
• Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Crossrefs

Cf. A056716, A101517.

Programs

Mathematica

Do[ If[ PrimeQ[ 6*10^n + 1], Print[ n ]], {n, 0, 10000}]

PARI

is(n)=isprime(6*10^n+1) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = A101517(n-1) + 1.

Extensions

a(22)-a(25) from Hugo Pfoertner, Feb 11 2004

a(26)=20812 from Kamada link by Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 27 2007

a(27)=37744 from Jason Earls, Mar 07 2008

a(28)-a(29) from Kamada data by Robert Price, Dec 09 2010

a(30)-a(36) from Kamada data by Tyler Busby, Apr 15 2024