

A050414


Numbers n such that 2^n  3 is prime.


39



3, 4, 5, 6, 9, 10, 12, 14, 20, 22, 24, 29, 94, 116, 122, 150, 174, 213, 221, 233, 266, 336, 452, 545, 689, 694, 850, 1736, 2321, 3237, 3954, 5630, 6756, 8770, 10572, 14114, 14400, 16460, 16680, 20757, 26350, 30041, 34452, 36552, 42689, 44629, 50474, 66422, 69337, 116926, 119324, 123297, 189110, 241004, 247165, 284133, 354946, 394034, 702194, 750740, 840797, 1126380, 1215889, 1347744, 1762004, 2086750
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

With 65 known primes for n < 1762005, these primes appear to be more common than Mersenne primes. Of course at this time, the larger terms are only probable primes.  Paul Bourdelais, Feb 04 2012
The numbers 2^n3 and 2^n1 both are primes for n = 3, 5, ? The lesser number 2^p3 is prime for primes p = 3, 5, 29, 233, 42689, 69337, ...  Thomas Ordowski, Sep 18 2015


LINKS

Table of n, a(n) for n=1..66.
Keith Conrad, Square patterns and infinitude of primes, University of Connecticut, 2019.
Henri Lifchitz & Renaud Lifchitz (Editors), PRP Top Records of the form 2^n3 [From M. Frind & P. Underwood, Gary Barnes, Oct 20 2008]


MATHEMATICA

Do[ If[ PrimeQ[ 2^n 3 ], Print[n]], { n, 1, 15000 }]


PROG

(PARI) for(n=2, 10^5, if(ispseudoprime(2^n3), print1(n, ", "))) \\ Felix FrÃ¶hlich, Jun 23 2014


CROSSREFS

Cf. A045768, A050415, A057732 (numbers n such that 2^n + 3 is prime).
Sequence in context: A047250 A081944 A129948 * A342469 A266322 A136681
Adjacent sequences: A050411 A050412 A050413 * A050415 A050416 A050417


KEYWORD

nonn


AUTHOR

Jud McCranie, Dec 22 1999


EXTENSIONS

More terms from Robert G. Wilson v, Sep 15 2000
More terms from Andrey V. Kulsha, Feb 11 2001
a(40)=20757, verified with 20 iterations of MillerRabin test, from Dmitry Kamenetsky, Jul 12 2008
A new PRP term 26350 from Serge Batalov, Oct 20 2008
Corrected and extended by including two smaller (apparently known) PRP and 16 larger terms from PRP Top Records of this form, all discovered by M. Frind & P. Underwood, Gary Barnes, Oct 20 2008
a(59) and a(60) (corresponding to probable primes since they are PRP 3,5,7) discovered by Paul Bourdelais, Mar 26 2012
a(61) to a(63) correspond to probable primes discovered by Paul Bourdelais, Jun 18 2019
a(64) corresponds to a probable prime discovered by Paul Bourdelais, Jul 16 2019
a(65) corresponds to a probable prime discovered by Paul Bourdelais, Apr 20 2020
a(66) corresponds to a probable prime discovered by Paul Bourdelais, May 28 2020


STATUS

approved



