A056797 Numbers k such that 9*10^k+1 is prime.

3, 4, 5, 9, 22, 27, 36, 57, 62, 78, 201, 537, 696, 790, 905, 1038, 66886, 70500, 91836, 100613, 127240, 380734, 583696, 719055, 823037, 862868

Offset: 1

Author

Robert G. Wilson v, Aug 22 2005

Keywords

• more
• nonn

Comments

a(22) > 2*10^5. - Robert Price, Jan 21 2015

Examples

			For k=9 we have (9*(10^9))+1 = 9000000001, which is prime.
		

Links

• Makoto Kamada, Prime numbers of the form 900...001.
• Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.
• Index entries for primes involving repunits.

Crossrefs

Cf. A056806 (4*10^k+1 is prime), A100997.

Programs

Magma

[n: n in [0..1000] | IsPrime(9*10^n+1)]; // Vincenzo Librandi, May 25 2015

Mathematica

Do[ If[ PrimeQ[9*10^n + 1], Print[n]], {n, 0, 10000}]

PARI

is(n)=ispseudoprime(9*10^n+1) \\ Charles R Greathouse IV, Feb 17 2017

Formula

a(n) = A100997(n) + 1.

Extensions

a(18)-a(19) from Kamada data by Robert Price, Dec 14 2010

a(20) from Predrag Kurtovic, Sep 23 2013

a(21) from Robert Price, Jan 21 2015

a(22)-a(23) from Kamada data by Mohammed Yaseen, Jul 20 2021

a(24) from Predrag Kurtovic, Apr 18 2024

a(25)-a(26) from Predrag Kurtovic, Apr 22 2024