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A129226
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Residues of the Lucas - Lehmer primality test for M(31) = 2147483647.
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8
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4, 14, 194, 37634, 1416317954, 669670838, 1937259419, 425413602, 842014276, 12692426, 2044502122, 1119438707, 1190075270, 1450757861, 877666528, 630853853, 940321271, 512995887, 692931217, 1883625615, 1992425718
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OFFSET
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0,1
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COMMENTS
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Since a(29) = 0, M(31) = 2147483647 is prime. Mersenne numbers are only prime if a(p-2) = 0.
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LINKS
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FORMULA
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a(0) = 4, a(n) = a(n-1)^2 mod 2^p-1. Last term: a(p-2).
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EXAMPLE
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a(29) = 65536^2 - 2 mod 2147483647 = 0.
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PROG
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(Python)
p = 31; Mp = 2**p - 1
from itertools import accumulate
def f(anm1, _): return (anm1**2 - 2) % Mp
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CROSSREFS
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KEYWORD
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fini,nonn
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AUTHOR
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STATUS
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approved
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