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A057440 Numbers n such that n*M127 + 1 is prime, where M127 = 2^127 - 1. 2

%I #35 Jan 13 2021 09:26:09

%S 114,124,388,408,498,696,738,774,780,934,978,1104,1156,1176,1216,1278,

%T 1368,1480,1578,1680,1698,1710,1740,1794,1806,1864,1950,2188,2268,

%U 2320,2334,2476,2608,2646,2784,2808,2950,3216,3274,3288,3388,3484,3768,4020

%N Numbers n such that n*M127 + 1 is prime, where M127 = 2^127 - 1.

%C In 1951 Miller and Wheeler found the primes k*M127 + 1 for k = 114, 124, 388, 408, 498, 696, 738, 744, 780, 934 and 978. These were some of the earliest primes found by electronic computers.

%C All terms so far are == {0, 4} (mod 6) == {0, 4, 6, 10, 16, 18, 24, 28} (mod 30). - _Robert G. Wilson v_, Nov 28 2020

%H Robert G. Wilson v, <a href="/A057440/b057440.txt">Table of n, a(n) for n = 1..10000</a> [a(1013) changed to 96108 by _Georg Fischer_, Jan 13 2021]

%H C. K. Caldwell, <a href="http://www.utm.edu/research/primes/notes/by_year.html">The Largest Known Primes by Year</a>

%H D. H. Lehmer, <a href="http://www.ams.org/journals/mcom/1952-06-037/S0025-5718-52-99404-0/S0025-5718-52-99404-0.pdf">Recent Discoveries of Large Primes</a>, Mathematics of Computation, vol. 6, No. 37 (1952), p. 61.

%t Select[ Range@ 10000], PrimeQ[ #(2^127 - 1) + 1] &]

%Y Cf. A057441.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Sep 08 2000

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Last modified July 9 17:23 EDT 2024. Contains 374187 sequences. (Running on oeis4.)