Factorizations of numbers of shape 2009^32 + b^32

Release

November 21, 2009 (corrected January 18, 2010).

Contributors

Kurt Beschorner and Alfred Reich.

Notes

With (2009,b) = 1, we have 1680 so called generalized Fermat numbers, each 106 digits long.
Any number is completely factored, no composite number remains.

 2009^32+b^32    is prime for b = 521, 603, 633, 745, 897, 1059, 1087, 1091, 1119, 1157, 1181, 1209, 1501, 1649, 1783 (15 values).
(2009^32+b^32)/2 is prime for b = 178, 208, 250, 352, 358, 425, 450, 472, 486, 670, 908, 914, 960, 1140, 1244, 1278, 1334, 1370, 1420, 1538, 1550, 1552, 1660, 1670, 1704, 1718, 1990, 2006 (28 values).

Using Kamada notation, we have "nice splits" for b = 134, 475, 509, 612, 748 (largest, 52 digits, found by Kurt Beschorner), 957, 1201, 1202, 1755, 1836 (10 values).

The largest prime factor is 8013902297155662554722163936523164833742105487714497 (52 digits) for b = 1318, found by Kurt Beschorner.

Factorizations