#
# Numbers of shape: 18^(2^7) + b^(2^7) with 1 <= b < 18 and gcd(18,b) = 1
#         Filename: http://www.AlfredReich.com/GF.18.7.txt
#           Editor: Alfred Reich (zehnp@gmx.de)
#             Date: Jul 27, 2011
#     Contributors: Mathew and Alfred Reich
#
#           Source: http://wwwmaths.anu.edu.au/~brent/ftp/factors/factors.gz (Richard Brent): 13183521051511297 and 4944182613719870977 (b=1)
#
#            Notes: There are 6 numbers, each number has 161 digits.
#                   Any number is competely 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.
#
#    Contributions: b=5: 15148995144049669736823101074010963319553 (Mathew, Jul 27, 2011 (Yafu - NFS))
#
1 13183521051511297 4944182613719870977 p126
5 257 126220178986620673 597486995352376186994689 15148995144049669736823101074010963319553 p78
7 257 769 3975036625276314500776646401 p128
11 40193 49536769 1409066277150009857 32216922901085123329 2070025943687558148442605537057067559306857547009 p63
13 110606593 14521781870370884962049 35370089146957778343856897 93755000476168980803378479743696462552546896129 p58
17 317380082689 879805431469429249 p132