A088275 Numbers k such that 10^k + 9 is prime.

1, 2, 3, 4, 9, 18, 22, 45, 49, 56, 69, 146, 202, 272, 2730, 2841, 4562, 31810, 43186, 48109, 92691, 237670, 400310, 482706

Offset: 1

Author

Amarnath Murthy, Sep 28 2003

Keywords

• nonn
• hard
• more

Comments

No others less than 9000. - Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

No others less than 39254. - Dirk Augustin, Oct 24 2006

2730, 2841 and 4562 all give primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Sep 30 2005

Verified existing terms. No other terms less than 40001. - Robert Price, Aug 14 2010

No other terms <= 100000. - Robert Price, Mar 03 2011

a(23) > 3*10^5. - Robert Price, Oct 26 2023

Examples

			4 is a member since 10^4 + 9 = 10009 is a prime.
		

Links

• Henri Lifchitz and Renaud Lifchitz (Editors), Search for 10^k+9, PRP Top Records.
• Makoto Kamada, Prime numbers of the form 100...009.
• Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers, Smarandache Notions Journal, 2003.

Crossrefs

Cf. A049054, A088274, A102008.

Programs

Mathematica

Do[ If[ PrimeQ[ 10^n + 9], Print[n]], {n, 0, 10000}] (* Robert G. Wilson v, Dec 16 2004 *)

PARI

is(n)=isprime(10^n + 9) \\ Charles R Greathouse IV, Apr 29 2015

Formula

a(n) = A102008(n) + 1.

Extensions

a(8)-a(16) from Ray Chandler, Oct 10 2003

a(17) from Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

a(18) (a PRP) found by Dirk Augustin, Oct 16 2006

a(19)-a(20) (probable primes), found with WinPFGW. No others less than 60400. - Jason Earls, Dec 22 2007

a(21) from Robert Price, Mar 03 2011

a(22) from Robert Price, Oct 26 2023

a(23) from Boyan Hu, Jun 15 2025

a(24) from Boyan Hu, Jun 24 2025