#
#        Numbers: 41^(2^7) + b^(2^7) with 1 <= b < 41
#           File: http://www.AlfredReich.com/GF.41.7.txt
#         Editor: Alfred Reich (zehnp@gmx.de)
#           Date: February 6, 2012
#   Contributors: Kurt Beschorner and Alfred Reich
#         Status: 14 composites
#
#         Source: http://wwwmaths.anu.edu.au/~brent/ftp/factors/factors.gz (Richard Brent): 12686178270308353 (b=1).
#
#          Notes: 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 (ecm): 669390245189179761075536185390908705377293599579649 (b=8) (51 digits) (Beschorner, May 19, 2011) (GMP-ECM, B1=48e6, sigma=1799161392)
#                 11236771528803948975846710133135459092361036208897 (b=13) (50 digits) (Beschorner, Apr 14, 2011) (GMP-ECM, B1=43e6, sigma=1983897402)
#
# Records (snfs): b=6: c207 = p66.p67.p74
#                       p66 = 814554648666414975248663225606036961623298580352499035339733929729
#                       p67 = 5982506453657238715905749897263607992021605120161250203243245476097
#                       p74 = 56044146261093907419662513476200228952804445236761583166959045093982952449
#
#                 b=16: c205 = p60.p66.p79
#                        p60 = 223403702453339689372929571262154160123706486841015119860993
#                        p66 = 607038946911632042765906619595513661179039228479741491349273218561
#                        p79 = 7835985336508904880565734014084030139438607999668762249646669213746928905527297
#
# Records (gnfs): b=33: c134 = p64.p71
#                        p64 = 3293093027149879388836980341949059183918261698737046532416824577
#                        p71 = 13676322543265153430628440426670572459899906695039674656540158430589441
#
#  Contributions: b= 8: 669390245189179761075536185390908705377293599579649 (Beschorner, May 19, 2011 (GMP-ECM, B1=48e6, sigma=1799161392))
#                 b= 9: 46227641869864801516109832287018397257387521 (Beschorner, May 16, 2011 (GMP-ECM, B1=48e6, sigma=3015448168))
#                 b=13: 11236771528803948975846710133135459092361036208897 (Beschorner, Apr 14, 2011 (GMP-ECM, B1=43e6, sigma=1983897402))
#                 b=25: 3749197605288305343473653783104430849 (Beschorner, Feb 11, 2011)
#                 b=26: 37930698759911546490143527168742217217 (Beschorner, Feb 10, 2011)
#                 b=29: 2146853938592394027420679514902836737 (Beschorner, Feb 2, 2011)
#                 b=35: 3463876283419460584072116670203934433422337 (Beschorner, Jan 19, 2011)
#                 b=40: 14415041380564586302619439644134010790913 (Beschorner, Jan 11, 2011 (GMP-ECM, B1=11e6, sigma=4055434517))
#         
1 2 257 838913 12686178270308353 p182
2 257 79873 15372289 41554433 194705921 2908615681 27424016129 17794098329666350849 c137
3 2 9473 23203073 c195
4 257 14188600226444285206574372353 c176
5 2 233952236033 54942327679947428095165697 p170
6 814554648666414975248663225606036961623298580352499035339733929729 5982506453657238715905749897263607992021605120161250203243245476097 p74
7 2 2292737 2507777 6646945537 345265233440818087325953 p161
8 257 8601423862529 3990970746822401 669390245189179761075536185390908705377293599579649 p125
9 2 257 566994476338423445228801 46227641869864801516109832287018397257387521 p137
10 183041 14944001 18406998017 24048225281 17207181953537 c161
11 2 257 769 11804496710401 3795495887693571036062977 p164
12 384257 c201
13 2 257 769 32121223672164097 413129748449258012929 422154958405740193457921 11236771528803948975846710133135459092361036208897 p92
14 43436784479489 816690883785473 c178
15 2 257 3329 118529 1384961 14195201 517323731428230913 19720182573423060637867991041 3899944823243263488037411185322547713 p100
16 257 223403702453339689372929571262154160123706486841015119860993 607038946911632042765906619595513661179039228479741491349273218561 p79
17 2 257 26881 143617 c195
18 257 1158821649647215078913 446426131275124055548139982337 p154
19 2 189837313 76453103235134061285096193 p172
20 8457217 1437795329 156827466057998295809 p171
21 2 257 3329 26881 51713 24993793793 c181
22 257 101377 357377 484751338241 25266238140273326081 p163
23 2 257 11777 68592349073104029664206760096843299132929 p159
24 260609 c202
25 2 257 59289371917997057 475185961688225612801 877480831478441938177 2272407031531475325525974017 3749197605288305343473653783104430849 p82
26 257 168193 35097089 933609217 37930698759911546490143527168742217217 p145
27 2 113921 c202
28 769 702599339136615169 10809567913075947440129994838529 13238815912818566860085560118273 3545747184090378905846636288426497 27073070472390377053039953138432257 p56
29 2 257 2146853938592394027420679514902836737 c168
30 257 12817921 554670688001 428071464281089 p171
31 2 257 76801 p199
32 257 647249153 c196
33 2 18433 1349552641 3325365653249 12667040886466243073 2893542721135631724098414593 3293093027149879388836980341949059183918261698737046532416824577 p71
34 257 61652657363201 p191
35 2 257 218311937 2014679081998030337 3463876283419460584072116670203934433422337 p135
36 257 p205
37 2 769 231169 33402530597377 2565952431437766006005158824449 38419448764456554743548707973889 p123
38 13313 116993 79507201 4120680837121 80489264735489 561358648074282497 c146
39 2 7681 158209 7333633 8268701012426713601 c172
40 168449 79566337 113272547021462011649 2718032478023739578369 142284684270246304076611781377 14415041380564586302619439644134010790913 p83