A056806 Numbers n such that 4*10^n + 1 is prime.

0, 1, 2, 3, 13, 229, 242, 309, 957, 1473, 1494, 3182, 3727, 4177, 23210, 25719, 32835, 36990, 103958, 789955, 1038890

Offset: 1

Author

Robert G. Wilson v, Aug 22 2000

Keywords

• more
• nonn

Comments

Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

Links

• Makoto Kamada, Prime numbers of the form 400...001.
• Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Crossrefs

Cf. A056797 (9*10^n+1 is prime), A101712.

Programs

Mathematica

Do[ If[ PrimeQ[ 4*10^n + 1], Print[ n ]], {n, 0, 30000}]

PARI

is(n)=isprime(4*10^n+1) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = A101712(n-1) + 1.

Extensions

a(12)-a(16) using PrimeForm from Hugo Pfoertner, Jul 08 2004

32835 from Ray Chandler, Aug 30 2010

36990 from Peter Benson, Aug 23 2003 confirmed as next term by Ray Chandler, Sep 07 2010

103958 from Peter Benson, Dec 31 2004 confirmed as next term by Ray Chandler, Feb 18 2012

a(20)-a(21) from Kamada data by Tyler Busby, May 03 2024