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
Examples
8 is a term since 10^8 + 7 = 100000007 is a prime.
Links
- 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.
Programs
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Mathematica
Do[ If[ PrimeQ[ 10^n + 7], Print[n]], {n, 0, 10000}] (* Robert G. Wilson v, Dec 16 2004 *) -
PARI
is(n)=isprime(10^n + 7) \\ Charles R Greathouse IV, Apr 29 2015
Formula
a(n) = A102007(n) + 1.
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
Comments