A108344 Least positive k such that k * Z^n + 1 is prime, where Z = 10^100+267, the first prime greater than a googol.

114, 1368, 1152, 232, 3336, 1872, 1206, 228, 1780, 1318, 700, 1038, 3534, 6652, 192, 1948, 9624, 850, 1980, 5022, 4218, 5658, 3556, 3936, 7936, 240, 660, 11838, 14136, 438, 3934, 1228, 18160, 2178, 762, 6048, 10060, 7438, 13062, 13306, 2154, 3454, 10950, 6808, 354

Offset

1,1

Comments

Other terms are a(30)=438 and a(45)=354. All values have been proved prime. Primality proof for a(45): PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing 354*(10^100+267)^45+1 [N-1, Brillhart-Lehmer-Selfridge] Reading factors from helper file help.txt Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 99.94% 354*(10^100+267)^45+1 is prime! (2.5654s+0.0037s) - N. J. A. Sloane, Jul 19 2005

In the b-file, all terms up to index 100 have been verified with the n-1 test. - Lucas A. Brown, Jun 02 2023

Links

Lucas A. Brown, Table of n, a(n) for n = 1..100

Lucas A. Brown, Python program.

Crossrefs

Sequence in context: A002952 A296403 A262416 * A200551 A230464 A200891

Adjacent sequences: A108341 A108342 A108343 * A108345 A108346 A108347

Keyword

nonn

Author

Jason Earls, Jul 01 2005

Extensions

a(17)-a(100) from Lucas A. Brown, Jun 02 2023

Status

approved