A088274 Numbers k such that 10^k + 7 is prime.

1, 2, 4, 8, 9, 24, 60, 110, 134, 222, 412, 700, 999, 1383, 5076, 5543, 6344, 14600, 15093, 21717, 23636, 30221, 50711, 221628, 350071, 371696, 487291, 995256, 1043372

Offset

1,2

Comments

No other terms less than 59500.

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

a(28) > 500000. - Alfred Reich, Jun 10 2021

a(29) > 1000000. - Alfred Reich, Nov 20 2021

a(30) > 1075000. - Alfred Reich, Jan 10 2022

Links

Table of n, a(n) for n=1..29.

G. L. Honaker, Jr. and Chris Caldwell, eds., Prime Curios!

Makoto Kamada, Prime numbers of the form 100...007.

Alfred Reich, ProofFile.

Alfred Reich, ProofFile2.

Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Formula

a(n) = A102007(n) + 1.

Example

8 is a term since 10^8 + 7 = 100000007 is a prime.

Mathematica

Do[ If[ PrimeQ[ 10^n + 7], Print[n]], {n, 0, 10000}] (* Robert G. Wilson v, Dec 16 2004 *)

Prog

(PARI) is(n)=isprime(10^n + 7) \\ Charles R Greathouse IV, Apr 29 2015

Crossrefs

Cf. A088275, A049054, A102007, A159031.

Sequence in context: A046685 A248741 A140141 * A118418 A074810 A028984

Adjacent sequences: A088271 A088272 A088273 * A088275 A088276 A088277

Keyword

nonn,more

Author

Amarnath Murthy, Sep 28 2003

Extensions

a(7)-a(14) from Ray Chandler, Oct 09 2003

a(15)-a(19) from Robert G. Wilson v, Jan 18 2005

Corrected and extended by Jason Earls, Nov 27 2007 and Dec 07 2007. (14600 was missing and 23636 and 50711 are new. These are presently only probable primes, found with WinPFGW.)

Missing term 30221 added by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(24)-a(27) from Alfred Reich, Jun 10 2021

a(28) from Alfred Reich, Nov 20 2021

a(29) from Alfred Reich, Jan 10 2022

Status

approved