A058958 Numbers k such that 3^k + 4 is prime.

0, 1, 2, 3, 6, 9, 10, 22, 30, 42, 57, 87, 174, 195, 198, 562, 994, 2421, 2487, 4629, 5838, 13698, 14730, 16966, 25851, 98634, 117222, 192819, 226038, 296115, 318465, 355902

Offset: 1

Author

Robert G. Wilson v, Jan 13 2001

Keywords

• nonn
• hard
• more

Comments

Next term > 15000. The primes corresponding to 4629, ..., 14730 pass PARI's ispseudoprime() and the Rabin-Miller test for the first 100 prime bases. - Joerg Arndt, Jul 19 2012

Used PFGW (Fermat and Lucas, BLS) to determine (probable) primality of a(24)-a(26). - Robert Price, Jun 30 2013

a(27) > 10^5. - Robert Price, Jun 30 2013

a(29) > 2*10^5. - Robert Price, Dec 10 2013

a(31) > 3*10^5. - Tyler NeSmith, Dec 10 2020

Crossrefs

Cf. A102903 (corresponding primes).

Programs

Magma

[n: n in [0..700] | IsPrime(3^n+4)]; // Vincenzo Librandi, Aug 25 2015

Mathematica

Do[ If[ PrimeQ[3^n + 4], Print[n] ], {n, 0, 3000} ]
Select[Range[0,3000],PrimeQ[3^#+4]&] (* Harvey P. Dale, Sep 07 2022 *)

PARI

for(n=0,10^5,if(ispseudoprime(3^n+4),print1(n,", "))); /* Joerg Arndt, Jul 19 2012 */

Extensions

Terms 4629 ... 14730 from Joerg Arndt, Jul 19 2012

0 added by Bruno Berselli, Oct 04 2012

a(24)-a(26) from Robert Price, Jun 30 2013

a(27)-a(28) from Robert Price, Dec 10 2013

a(29)-a(30) from Tyler NeSmith, Dec 10 2020

a(31)-a(32) from Aurelien Gibier, Oct 02 2024