#
# Numbers: 20^(2^7) + b^(2^7) with 1 <= b < 20 and gcd(20,b) = 1
#    File: http://www.AlfredReich.com/GF.20.7.txt
#  Editor: Alfred Reich (zehnp@gmx.de)
#    Date: January 27, 2012
#
#  Source: http://wwwmaths.anu.edu.au/~brent/ftp/factors/factors.gz (Richard Brent) for b=1 and 12818782843691777 and 1824448644331953437805185594358681323803649
#
#   Notes: There are 8 numbers, each number has 167 digits.
#
#          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: 23790292197771536467654796895801186402060557477377 (b=17) (50 digits) (Reich, Jan 27, 2012)
#
1 257 36097 12818782843691777 1824448644331953437805185594358681323803649 p102
3 14081 41729 32518695770689026049 17347949205656717243904159440302081 p105
7 30977 232961 20890369 18000444673 11924463452550352790823352150273 524203098319364069380497222017909235360990209 p64
9 257 680870401 98334364035002369 1373533295965928583390209 412253165915112858535285146188142376429824508673 p67
11 257 769 25177879646261219618866927873 p133
13 257 769 84737 23314030409107952641 13674165481788790122727743311015681 5394145520236072235422487949610296885960193 p61
17 257 122084708609 1040310817187918849 23790292197771536467654796895801186402060557477377 p86
19 36097 19906781011215041409281 5202019691304333927548860958977 p109