A257864 Numbers n such that n!! - 2^7 is prime.

11, 13, 21, 47, 59, 77, 109, 129, 155, 163, 245, 337, 511, 1417, 3013, 3757, 4989, 8977, 12479, 12869

Offset: 1

Author

Robert Price, May 11 2015

Keywords

• nonn
• hard
• more

Comments

a(21) > 50000. - Robert Price, May 11 2015

a(n) is odd. - Chai Wah Wu, May 12 2015

Links

• C. K. Caldwell, The Prime Glossary, multifactorial prime
• Joe McLean, Interesting Sources of Probable Primes

Crossrefs

Cf. A007749, A094144, A123910 (other forms of n!!-2^k)

Cf. A080778, A076185, A076186, A076188, A076189, A076190, A076193, A076194, A076195, A076196, A076197 (other forms of n!!+2^k)

Programs

Mathematica

Select[Range[0, 50000], #!! - 128 > 0 && PrimeQ[#!! - 128] &]

PARI

is(n)=ispseudoprime(prod(i=0,(n-1)\2, n-2*i)-128) \\ Charles R Greathouse IV, May 11 2015

Perl

use ntheory ":all"; use Math::GMPz;
sub mf2 { my($n,$P)=(shift,Math::GMPz->new(1)); $P *= $n-($_<<1) for 0..($n-1)>>1; $P; }
for (1..100000) { say if is_prob_prime(mf2($)-128) } # _Dana Jacobsen, May 13 2015

Python

from gmpy2 import is_prime, mpz
A257864_list, g, h = [], mpz(105), mpz(128)
for i in range(9,10**5,2):
    g *= i
    if is_prime(g-h):
        A257864_list.append(i) # Chai Wah Wu, May 12 2015