

A100501


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


3



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



