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

1,1

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

Links

Table of n, a(n) for n=1..26.

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

Formula

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

Example

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

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 *)

Crossrefs

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

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

Sequence in context: A136003 A215799 A237057 * A123856 A336721 A120857

Adjacent sequences: A183070 A183071 A183072 * A183074 A183075 A183076

Keyword

nonn,hard,more

Author

Stuart Clary, Dec 23 2010

Extensions

a(26) from Amiram Eldar, Feb 18 2019

Status

approved