#
# Numbers of shape: 49^(2^6) + b^(2^6) with 1 <= b < 49 and gcd(49,b) = 1 and b not a perfect square
#         Filename: http://www.AlfredReich.com/GF.49.6.txt
#           Editor: Alfred Reich (zehnp@gmx.de)
#             Date: February 7, 2011
#
#            Notes: There are 36 numbers, each number has 109 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.
#
2 257 4021340611349702108929 p85
3 2 18433 39041 112129 247626881 2503022386817 573275734006995319450538668346098049 p38
5 2 69210881 90504833 p93
6 p109
8 257 19457 46812420097 42015101488109840081153 7233054937016228419141782017 p41
10 19073 206081 p99
11 2 257 25601 54540060871947817582352511503424160147298561 p58
12 769 37485051521 p95
13 2 6367873 113685889 p94
15 2 257 1409 13313 527275649 p90
17 2 257 641 21370836780855041 p87
18 67073 1015461243361855660453467787796919041 p68
19 2 7681 86017 34008001088648924082049 p77
20 1153 293125121 p97
22 257 13209857 2630524611457 3190311532153637249 p68
23 2 257 96769 20572033 3098428156370292718366117100033 p63
24 447617 5825804417 p93
26 76483355393 21494653994445541466881 520211871706736230076929 p52
27 2 641 769 13760889820106369 181707098217031360621263744242689 p54
29 2 1409 571103932590164737 21687704699266252479331480520696721618868097 p44
30 257 1153 56242457473 56477293721093902338433 p70
31 2 10369 482711681 8308012417 184422868728074369 79263344392265405954293735076353 p37
32 257 212347393 1034897153 38761250542337 46492243759361 p62
33 2 16848641 810254363425685376641 p80
34 257 641 4993 185324929 1486103041 1122653938656769 p67
37 2 2440961 30252574145992128600569825796313601 p68
38 1409 2015612347305353259649 p84
39 2 641 593984194529786147713 1577493590180960543508599571208321 p52
40 769 7134593 p99
41 2 11777 1283969 96262273 2179273459201 54635435392473857 p61
43 2 769 1409 176641 755329 378984449 p83
44 257 16169473 248302902536321 p85
45 2 1153 3457 19460952679212890497 242624187808779429459600829703481089 p47
46 257 27141504741889 267887092852727345550382233473 p63
47 2 18059903368006587328216193 p83
48 1108993 1869764892253275649 p84