A188803 Primes that divide 2^(2^100) - 1 and 10^(10^100) - 1.

3, 17, 257, 641, 65537, 167772161, 2748779069441, 46179488366593, 1328165573307087716353, 188894659314785808547841

Offset: 1

Author

Arkadiusz Wesolowski, Apr 12 2011

Keywords

• fini
• full
• nonn

Comments

Probably there are no more terms. [Arkadiusz Wesolowski, Jul 12 2011]

Links

• Dario A. Alpern, Known prime factors of Googolplex - 1
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 167772161
• Eric Weisstein's World of Mathematics, Fermat Number
• Eric Weisstein's World of Mathematics, Googolplex
• Eric Weisstein's World of Mathematics, Greatest Common Divisor

Crossrefs

Cf. A023394.

Programs

Mathematica

Select[Sort[Flatten[Table[z = k*2^n + 1; If[PowerMod[2, 2^100, z] == PowerMod[10, 10^100, z] == 1, z], {k, 1, 21, 2}, {n, 75}]]], PrimeQ] (* Arkadiusz Wesolowski, Sep 08 2011 *)