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A331038
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Residues of the Lucas-Lehmer primality test for M(127) = 2^127 - 1.
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1
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3, 7, 47, 2207, 4870847, 23725150497407, 562882766124611619513723647, 9932388036497706472820043948129789713, 102423269049837077051675109560558766898, 7949236499829405891753012242872011683, 119093374737774941856311333667076322210
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OFFSET
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0,1
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COMMENTS
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Since a(125) = 0, 2^127 - 1 = 170141183460469231731687303715884105727 is prime. This calculation was carried out by hand by Edouard Lucas. It took him 19 years from 1857 to 1876. The method works with a(0) = 3 since M(127) == 3 (mod 4). It also works with a(0) = 4 or a(0) = 10.
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LINKS
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FORMULA
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a(n) = (a(n-1)^2 - 2) mod (2^127-1) with a(0) = 3; a(125) is the final term.
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CROSSREFS
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KEYWORD
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nonn,full,fini
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AUTHOR
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STATUS
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approved
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