#
# Numbers of shape: 14^(2^7) + b^(2^7) with 1 <= b < 14 and gcd(14,b) = 1
#         Filename: http://www.AlfredReich.com/GF.14.7.txt
#           Editor: Alfred Reich (zehnp@gmx.de)
#             Date: October 27, 2011
#     Contributors: Mathew and Alfred Reich
#
#           Source: http://wwwmaths.anu.edu.au/~brent/ftp/factors/factors.gz (Richard Brent): 100497382788383295179961898289105815085380571534081 (b=1)
#
#          Records: 60315681161530908483511705290036548668549286194768496386059038977 (b=3) (65 digits) (Mathew, Oct 27, 2011) (Yafu - NFS)
#
#            Notes: There are 6 numbers, each number has 147 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.
#
1 257 100497382788383295179961898289105815085380571534081 p95
3 769 38874113 60315681161530908483511705290036548668549286194768496386059038977 p72
5 311041 285467393 13070038529 46852959300097 177093812841512133994241 p86
9 257 33913454942811858811941197513239542561793 p104
11 257 2129995009 452744436331509830095361 p112
13 257 12289 261438216693153272593869725509121 p108