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 A183073 Prime numbers p such that each prime divisor of 2^p - 1 has the form 4j + 3. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 A120857 A233516 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

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Last modified March 18 22:11 EDT 2019. Contains 321305 sequences. (Running on oeis4.)