#
# Numbers of shape: 13^(2^7) + b^(2^7) with 1 <= b < 13
#         Filename: http://www.AlfredReich.com/GF.13.7.txt
#           Editor: Alfred Reich (zehnp@gmx.de)
#             Date: March 29, 2011
#
#          Records: 1381323097785502373200450121164699785950282258457881857 (b=6) (55 digits) (Reich, Mar 16, 2011) (GMP-ECM, B1=1e8, sigma=104759452)
#                   213200179638411324444595178659602342005996651727091969 (b=5) (54 digits) (Reich, Mar 29, 2011) (Msieve - QS)
#
#            Notes: There are 12 numbers, each number has 143 digits.
#                   Any number is completely factored.
#
#                   Numbers of shape a^(2^m) + b^(2^m) with 1 <= b < a and gcd(a,b) = 1 are called Generalized Fermat Numbers and denoted by GF(a,b,m),
#                   compare Hans Riesel, Prime Numbers and Computer Methods for Factorizations, 1994, 2nd ed, Birkhäuser, pp102
#                   and Wilfrid Keller, http://www.rrz.uni-hamburg.de/RRZ/W.Keller/GFNfacs.html.
#
1 2 96769 2940673 p131
2 561091485227315888036391544321 43049544463998703692282036808682641348558721537 p67
3 2 257 7164929 8704513 107365889 132234241 151334471462153121300348544293889 p78
4 769 16343645441 23239315201 126528858506497 12379465614183722551744830109441 p74
5 2 257 9473 868687570242487553 213200179638411324444595178659602342005996651727091969 p65
6 257 769 169217 10123995603511607809 1381323097785502373200450121164699785950282258457881857 p59
7 2 257 p140
8 9314208940801 1430098135583489 850631679763570668222452227745537 205918797279173565404540104946669569 p47
9 2 769 337153 1836594433 p125
10 257 36353 p136
11 2 106255361 13853564552525027018804993 354626735042729392937715284359436033 p74
12 257 337153 37912321 26351748326681417658881 470441739190811069088913138562746535665153 p63