A056804 Numbers k such that 7*10^k + 1 is prime.

1, 2, 3, 4, 5, 8, 9, 45, 136, 142, 158, 243, 923, 1235, 2196, 4650, 6119, 7324, 9543, 13494, 20310, 20360, 232920, 830865, 902708, 1454508

Offset: 1

Author

Robert G. Wilson v, Aug 22 2000

Keywords

• more
• nonn

Comments

7*10^902708+1 was the 84th-largest known prime in the world as of Jun 28 2013. Also largest known "base-10" form for a prime number. There are no other values of k in this sequence between 232920 and 902708 that yield a prime. - Edward A. Trice, Jul 03 2013

Apparently Edward A. Trice found another term in the gap mentioned above in May 2014. - Ray Chandler, Apr 29 2015

Links

• Makoto Kamada, Prime numbers of the form 700...001.
• René-Louis Clerc, Nombres S+P, maxSP, minSP et |P-S|, hal-04507547 [math.nt], 2024. (In French)
• Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.
• Index entries for primes involving repunits.

Crossrefs

Cf. A101128.

Programs

Mathematica

Do[ If[ PrimeQ[ 7*10^n + 1], Print[ n ]], {n, 0, 10000}]

PARI

is(n)=ispseudoprime(7*10^n+1) \\ Charles R Greathouse IV, Feb 20 2017

Formula

a(n) = A101128(n) + 1.

Extensions

a(15)-a(20) from Robert G. Wilson v, Jan 19 2005

a(21)-a(22) from Kamada data by Robert Price, Dec 14 2010

a(23) from Edward A. Trice, Jan 11 2013

a(25) (thought to be a(24) at the time) from Edward A. Trice, Jun 28 2013

a(24) from Edward A. Trice, inserted by Robert G. Wilson v, May 15 2014

a(26) from Edward A. Trice, Mar 13 2024