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

Offset

1,2

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

Links

Table of n, a(n) for n=1..22.

Makoto Kamada, Prime numbers of the form 100...009.

Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A049054, A088274, A102008.

Sequence in context: A346777 A338585 A145027 * A274836 A322783 A014281

Adjacent sequences: A088272 A088273 A088274 * A088276 A088277 A088278

Keyword

nonn,hard,more

Author

Amarnath Murthy, Sep 28 2003

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

Status

approved