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A182300
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Gaussian-Mersenne primes: primes of the form ((1+i)^p - 1)((1-i)^p - 1).
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3
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5, 13, 41, 113, 2113, 525313, 536903681, 140737471578113, 9444732965601851473921, 604462909806215075725313, 10384593717069655112945804582584321, 2854495385411919762116496381035264358442074113
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OFFSET
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1,1
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COMMENTS
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Primes of the form q = 2^p +- 2^((p+1)/2) + 1. Note that q == 1 (mod p). - Thomas Ordowski, Apr 18 2019
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REFERENCES
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John Brillhart et al., Factorizations of b^n +/- 1, b=2,3,5,6,7,10,12 up to high powers, Amer. Math. Soc., Providence RI, 1988, pp. xcvi+236.
R. K. Guy, Unsolved Problems in Number Theory, New York: Springer-Verlag, 1994, pp. 33-36.
Miriam Hausmann and Harold N. Shapiro, Perfect Ideals over the Gaussian Integers, Comm. Pure Appl. Math. 29 (1976), pp. 323-341.
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LINKS
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MATHEMATICA
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lst = {}; Do[a = (1 + I)^n - 1; b = a*Conjugate[a]; If[PrimeQ[b], AppendTo[lst, b]], {n, 151}]; lst
gmp[n_]:=Module[{x=(1+I)^n-1}, x*Conjugate[x]]; Select[Table[gmp[n], {n, 200}], PrimeQ] (* Harvey P. Dale, Apr 27 2016 *)
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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STATUS
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approved
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