A100501 Numbers n such that 3*10^n+7 is prime.

1, 2, 5, 8, 24, 29, 84, 110, 129, 176, 593, 1137, 2675, 4992, 26904, 31572, 55077, 81021, 122274

Offset

1,2

Comments

593 and 1137 both give primes. - Joao da Silva (zxawyh66(AT)yahoo.com), Sep 30 2005

a(19) > 10^5. - Robert Price, Jan 26 2015

a(20) > 2*10^5. - Robert Price, Jul 04 2015

Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

Links

Table of n, a(n) for n=1..19.

Makoto Kamada, Prime numbers of the form 300...007.

Sabin Tabirca and Kieran Reynolds, Lacunary Prime Numbers.

Formula

a(n) = A101824(n) + 1.

Example

(3*10^5)+7 = (3*100000)+7 = 300000+7 = 300007, which is prime.

Mathematica

Do[ If[ PrimeQ[ 3*10^n + 7], Print[ n ]], {n, 0, 20000}]

Prog

(PARI) is(n)=ispseudoprime(3*10^n+7) \\ Charles R Greathouse IV, May 22 2017

Crossrefs

Cf. A096774, A101824.

Sequence in context: A092097 A195295 A088144 * A291605 A142869 A086825

Adjacent sequences: A100498 A100499 A100500 * A100502 A100503 A100504

Keyword

nonn,more,hard

Author

Julien Peter Benney (jpbenney(AT)ftml.net), Nov 23 2004

Extensions

a(12) from Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 26 2004

a(13)-a(14) from Hugo Pfoertner, Nov 29 2004. The next term is > 20000.

a(15) from Kamada data by Robert Price, Dec 12 2010

a(16)-a(18) from Kamada data by Robert Price, Jan 26 2015

a(19) from Robert Price, Jul 04 2015

Status

approved