A183073 Prime numbers p such that each prime divisor of 2^p - 1 has the form 4j + 3.

2, 3, 5, 7, 13, 17, 19, 31, 43, 61, 79, 89, 107, 127, 193, 311, 331, 349, 389, 521, 557, 577, 607, 631, 647, 1103

Offset: 1

Author

Stuart Clary, Dec 23 2010

Keywords

• nonn
• hard
• more

Comments

The exponents of the Mersenne primes (A000043) are contained in this sequence.

Needed factorizations are in the Cunningham Project.

Also in the sequence are 1279, 2203, 2281, 2909, 3217, 4253. - Amiram Eldar, Feb 18 2019

Examples

			43 is in this sequence because 2^43 - 1 = 431 * 9719 * 2099863, and each of those primes has the form 4j + 3.
		

Links

• S. S. Wagstaff, Jr., The Cunningham Project.

Crossrefs

Cf. A000043, A136003, A183071, A183072, A183074.

Cf. A000668, A136005, A183075, A183076, A183077, A183078.

Programs

Mathematica

Select[Prime[Range[30]],And@@(IntegerQ[(#-3)/4]&/@Transpose[ FactorInteger[ 2^#-1]][[1]])&] (* Increase the value of Range to increase the number of terms generated, but processing times grow very quickly as the value increases. *)(* Harvey P. Dale, Jan 01 2013 *)

Formula

A183077(n) = 2^a(n) - 1.

Extensions

a(26) from Amiram Eldar, Feb 18 2019