A230537 Numbers n such that 3^7*2^n - 1 is prime.

1, 2, 6, 13, 22, 29, 30, 33, 36, 50, 61, 118, 180, 226, 405, 433, 522, 789, 929, 960, 1026, 1030, 1118, 1266, 1521, 1718, 2536, 3029, 3366, 4253, 9157, 10165, 23641, 29877, 30648, 47265, 56097, 90501, 101981, 103021, 108370, 117909, 157237, 169156, 174168

Offset: 1

Author

Lei Zhou, Oct 22 2013

Keywords

• nonn
• hard

Comments

Riesel Primes with k = 3^7 = 2187.

Checked up to n = 1000000.

Examples

			2187*2^1-1=4373 is a prime number.
		

Links

• Lei Zhou, Table of n, a(n) for n = 1..52
• K. Bonath, Riesel Prime Database
• C. K. Caldwell, a(51) = 2187*2^449776-1
• C. K. Caldwell, a(52) = 2187*2^916686-1
• C. K. Caldwell, a(53) = 2187*2^992632-1

Crossrefs

Cf. A002235, A002236, A050539, A050566, A050880, A230527.

Programs

Mathematica

b=3^7;i=0; Table[While[i++; cp=b*2^i-1; !PrimeQ[cp]]; i, {j, 1, 30}]

PARI

is(n)=ispseudoprime(3^7*2^n-1) \\ Charles R Greathouse IV, May 22 2017

Extensions

Lei Zhou, Nov 08 2013, added a Mathematica program for small elements.