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

114, 124, 388, 408, 498, 696, 738, 774, 780, 934, 978, 1104, 1156, 1176, 1216, 1278, 1368, 1480, 1578, 1680, 1698, 1710, 1740, 1794, 1806, 1864, 1950, 2188, 2268, 2320, 2334, 2476, 2608, 2646, 2784, 2808, 2950, 3216, 3274, 3288, 3388, 3484, 3768, 4020

Offset

1,1

Comments

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.

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

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..10000 [a(1013) changed to 96108 by Georg Fischer, Jan 13 2021]

C. K. Caldwell, The Largest Known Primes by Year

D. H. Lehmer, Recent Discoveries of Large Primes, Mathematics of Computation, vol. 6, No. 37 (1952), p. 61.

Mathematica

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

Crossrefs

Cf. A057441.

Sequence in context: A272303 A260213 A228961 * A113537 A352233 A127664

Adjacent sequences: A057437 A057438 A057439 * A057441 A057442 A057443

Keyword

nonn

Author

Robert G. Wilson v, Sep 08 2000

Status

approved