#
#       Numbers: 17^(2^7) + b^(2^7) with 1 <= b < 17
#          File: http://www.AlfredReich.com/GF.17.7.txt
#        Editor: Alfred Reich (zehnp@gmx.de)
#          Date: January 2, 2012
#  Contributors: Mathew and Alfred Reich
#
#         Notes: There are 16 numbers, each number has 158 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, Birkhäuser.
#
#                If you are interested in GF(a,b,m) with a <= 12 please look at
#                http://www.rrz.uni-hamburg.de/RRZ/W.Keller/GFNfacs.html (Wilfrid Keller).
#
#       Records: 43097786681340378587576359055866185053868532383524233846273 (b=16) (59 digits) (Mathew, Nov 23, 2011) (Yafu - NFS)
#                3239886666749136384355156349468133900676439199268559873 (b=5) (55 digits) (Reich, Dec 27, 2011) (snfs)
#                412173747168531433270119131647482006765971708569292033 (b=9) (54 digits) (Reich, Jan 2, 2012) (snfs)
#
# Contributions: 68261303418635950219024028115546881 (b=6) (Mathew, Nov 14, 2011) (Yafu - ECM (B1=1e7, sigma=3591844135))
#                131186594611052601522559697893874722561 (b=10) (Mathew, Nov 14, 2011) (Yafu - ECM (B1=1e7, sigma=556694663))
#                43097786681340378587576359055866185053868532383524233846273 (b=16) (Mathew, Nov 23, 2011) (Yafu - NFS)
#
1 2 3329 544513 p148
2 5180889286913 9698733341542564609 1076690337169862606831168513 43178218120003287308047157014035457 p65
3 2 257 9473 151303681 19163853741940957425874369529358955189249 p103
4 20316644609 p148
5 2 257 336452353 73442133698866433 3239886666749136384355156349468133900676439199268559873 p75
6 257 367173377 65894426399044609 5165935004412598529 68261303418635950219024028115546881 p77
7 2 257 769 193169298951365214635713793 11724248231341955513402575157922049 p92
8 11777 191984786689 119449151682359876609 351044639600079828809451775408052540417 p84
9 2 755516616474332556370752921089 412173747168531433270119131647482006765971708569292033 p74
10 257 228097 982273 854208769 1260595054483867929089 131186594611052601522559697893874722561 p76
11 2 64513 253552241219551017402513366105817880554575990017 p105
12 257 576769 18715675889153 42337973048489473 11756160450995607809 8120874077206315568104929281 p73
13 2 388576960320423937 p140
14 257 257 p153
15 2 3859201 1492639065037017268358714113 169147412688028972915852974337 p95
16 10753 14593 95233 5051393 41413121 43097786681340378587576359055866185053868532383524233846273 p72