The factorization of generalized Fermat numbers (k+1)^2^n + k^2^n < 10^60

2^2^1 + 1^2^1		= 5
2^2^2 + 1^2^2		= 17
2^2^3 + 1^2^3		= 257
2^2^4 + 1^2^4		= 65537
2^2^5 + 1^2^5		= 641 * 6700417
2^2^6 + 1^2^6		= 274177 * 67280421310721
2^2^7 + 1^2^7		= 59649589127497217 * 5704689200685129054721

3^2^1 + 2^2^1		= 13
3^2^2 + 2^2^2		= 97
3^2^3 + 2^2^3		= 17 * 401
3^2^4 + 2^2^4		= 3041 * 14177
3^2^5 + 2^2^5		= 1153 * 1607133116929
3^2^6 + 2^2^6		= 769 * 121899667073 * 36629538145348481

4^2^1 + 3^2^1		= 5 * 5
4^2^2 + 3^2^2		= 337
4^2^3 + 3^2^3		= 17 * 4241
4^2^4 + 3^2^4		= 4338014017
4^2^5 + 3^2^5		= 11969 * 1541364950613953
4^2^6 + 3^2^6		= 337153 * 1009281751473729386230842057136129

5^2^1 + 4^2^1		= 41
5^2^2 + 4^2^2		= 881
5^2^3 + 4^2^3		= 17 * 26833
5^2^4 + 4^2^4		= 4801 * 32677121
5^2^5 + 4^2^5		= 641 * 5953 * 59925889 * 101900353
5^2^6 + 4^2^6		= 1699132282369 * 319046040234900998188151306914049

6^2^1 + 5^2^1		= 61
6^2^2 + 5^2^2		= 17 * 113
6^2^3 + 5^2^3		= 2070241
6^2^4 + 5^2^4		= 2973697798081
6^2^5 + 5^2^5		= 193 * 577 * 645313 * 9104321 * 12199937
6^2^6 + 5^2^6		= 257 * 1189782673537 * 207149065298675818568214979118531969

7^2^1 + 6^2^1		= 5 * 17
7^2^2 + 6^2^2		= 3697
7^2^3 + 6^2^3		= 353 * 21089
7^2^4 + 6^2^4		= 36054040477057
7^2^5 + 6^2^5		= 257 * 4328351499431389288675841
7^2^6 + 6^2^6		= 1441838081 * 45814876214017 * 18466054092468533735568034082561

8^2^1 + 7^2^1		= 113
8^2^2 + 7^2^2		= 73 * 89
8^2^3 + 7^2^3		= 17 * 1326001
8^2^4 + 7^2^4		= 314707907280257
8^2^5 + 7^2^5		= 33857 * 1347511751681 * 1760802861761
8^2^6 + 7^2^6		= 1153 * 257921 * 865537 * 186270593 * 130947618578460692408608101578574209

9^2^1 + 8^2^1		= 5 * 29
9^2^2 + 8^2^2		= 10657
9^2^3 + 8^2^3		= 577 * 103681
9^2^4 + 8^2^4		= 193 * 1217 * 16001 * 567937
9^2^5 + 8^2^5		= 3512911982806776822251393039617

10^2^1 + 9^2^1		= 181
10^2^2 + 9^2^2		= 16561
10^2^3 + 9^2^3		= 17 * 1249 * 6737
10^2^4 + 9^2^4		= 97 * 2689 * 45442946977
10^2^5 + 9^2^5		= 9601 * 55861633561729 * 192855438828289

11^2^1 + 10^2^1		= 13 * 17
11^2^2 + 10^2^2		= 41 * 601
11^2^3 + 10^2^3		= 113 * 2781937
11^2^4 + 10^2^4		= 97 * 3617 * 159469543489
11^2^5 + 10^2^5		= 2211377674535255285545615254209921

12^2^1 + 11^2^1		= 5 * 53
12^2^2 + 11^2^2		= 17 * 2081
12^2^3 + 11^2^3		= 113 * 5702129
12^2^4 + 11^2^4		= 929 * 2689 * 262369 * 352193
12^2^5 + 11^2^5		= 449 * 80831997464815383957493223207873

13^2^1 + 12^2^1		= 313
13^2^2 + 12^2^2		= 49297
13^2^3 + 12^2^3		= 17 * 73277201
13^2^4 + 12^2^4		= 120833 * 780193 * 9019553
13^2^5 + 12^2^5		= 476961452964007550415682034114910337

14^2^1 + 13^2^1		= 5 * 73
14^2^2 + 13^2^2		= 66977
14^2^3 + 13^2^3		= 17 * 134795281
14^2^4 + 13^2^4		= 203617 * 13964305274081
14^2^5 + 13^2^5		= 193 * 25537 * 10705153 * 58700051713 * 1674540815873

15^2^1 + 14^2^1		= 421
15^2^2 + 14^2^2		= 89041
15^2^3 + 14^2^3		= 17 * 97 * 2449169
15^2^4 + 14^2^4		= 8746361693522261761
15^2^5 + 14^2^5		= 11329 * 14657 * 60353 * 3439297 * 111662081 * 12442594817

16^2^1 + 15^2^1		= 13 * 37
16^2^2 + 15^2^2		= 17 * 6833
16^2^3 + 15^2^3		= 19009 * 360769
16^2^4 + 15^2^4		= 257 * 51447329 * 1891939297
16^2^5 + 15^2^5		= 193 * 577 * 3443093679549729105914863949003521

17^2^1 + 16^2^1		= 5 * 109
17^2^2 + 16^2^2		= 149057
17^2^3 + 16^2^3		= 1009 * 11170193
17^2^4 + 16^2^4		= 257 * 577 * 5281 * 16993 * 5042881
17^2^5 + 16^2^5		= 193 * 10433 * 1344972018183337998006266934360193

18^2^1 + 17^2^1		= 613
18^2^2 + 17^2^2		= 233 * 809
18^2^3 + 17^2^3		= 17995718017
18^2^4 + 17^2^4		= 577 * 769 * 7047457 * 54396577
18^2^5 + 17^2^5		= 193 * 449 * 4131025280257 * 47810948556918361424513

19^2^1 + 18^2^1		= 5 * 137
19^2^2 + 18^2^2		= 17 * 13841
19^2^3 + 18^2^3		= 1361 * 1553 * 13249
19^2^4 + 18^2^4		= 97 * 1529249 * 2763171170369
19^2^5 + 18^2^5		= 193 * 507492273439627745630601554889674601409

20^2^1 + 19^2^1		= 761
20^2^2 + 19^2^2		= 41 * 73 * 97
20^2^3 + 19^2^3		= 17 * 17 * 147347969
20^2^4 + 19^2^4		= 86209 * 10947829270350209
20^2^5 + 19^2^5		= 449 * 1141860086104426442386255983308556612289

21^2^1 + 20^2^1		= 29 * 29
21^2^2 + 20^2^2		= 113 * 3137
21^2^3 + 20^2^3		= 17 * 3730756433
21^2^4 + 20^2^4		= 129793 * 16071195597928897
21^2^5 + 20^2^5		= 52753460092876993 * 46935755545539904474067137

22^2^1 + 21^2^1		= 5 * 5 * 37
22^2^2 + 21^2^2		= 41 * 10457
22^2^3 + 21^2^3		= 17 * 113 * 48255457
22^2^4 + 21^2^4		= 4441930186581050471617
22^2^5 + 21^2^5		= 37889 * 347329 * 512236801 * 1648836744864293624130497

23^2^1 + 22^2^1		= 1013
23^2^2 + 22^2^2		= 17 * 30241
23^2^3 + 22^2^3		= 308017 * 432401
23^2^4 + 22^2^4		= 257 * 673 * 3041 * 328481 * 52924897
23^2^5 + 22^2^5		= 46677208572152524490331633250547044320123137

24^2^1 + 23^2^1		= 5 * 13 * 17
24^2^2 + 23^2^2		= 193 * 3169
24^2^3 + 23^2^3		= 188386299457
24^2^4 + 23^2^4		= 203873 * 280001 * 319686415969
24^2^5 + 23^2^5		= 2482987185473 * 74273558983331655960352420017089

25^2^1 + 24^2^1		= 1201
25^2^2 + 24^2^2		= 137 * 5273
25^2^3 + 24^2^3		= 17 * 15450776753
25^2^4 + 24^2^4		= 16284449 * 2173830944868449
25^2^5 + 24^2^5		= 3200994501889 * 4886618497153 * 44042370272332781953

26^2^1 + 25^2^1		= 1301
26^2^2 + 25^2^2		= 847601
26^2^3 + 25^2^3		= 106321 * 3399281
26^2^4 + 25^2^4		= 97 * 258815489 * 2664470596897
26^2^5 + 25^2^5		= 257 * 18433 * 151553 * 3403895042406826213217398689465857

27^2^1 + 26^2^1		= 5 * 281
27^2^2 + 26^2^2		= 988417
27^2^3 + 26^2^3		= 17 * 2129 * 13573249
27^2^4 + 26^2^4		= 5857 * 21064569912293219041
27^2^5 + 26^2^5		= 38586205045121 * 425210323827137 * 503704552377552961

28^2^1 + 27^2^1		= 17 * 89
28^2^2 + 27^2^2		= 1146097
28^2^3 + 27^2^3		= 241 * 2739549937
28^2^4 + 27^2^4		= 97 * 265249 * 15493601 * 558153569
28^2^5 + 27^2^5		= 682531009 * 2730227777 * 45837612929 * 313003792384869121

29^2^1 + 28^2^1		= 5 * 5 * 5 * 13
29^2^2 + 28^2^2		= 17 * 77761
29^2^3 + 28^2^3		= 60161 * 14594977
29^2^4 + 28^2^4		= 19937 * 19711131244772147041
29^2^5 + 28^2^5		= 1430645947637953 * 58013229884849302058399963013569

30^2^1 + 29^2^1		= 1741
30^2^2 + 29^2^2		= 977 * 1553
30^2^3 + 29^2^3		= 17 * 113 * 601950241
30^2^4 + 29^2^4		= 4673 * 289889 * 502501038597793
30^2^5 + 29^2^5		= 51137 * 84673 * 57258594428966842629416980351905034241

31^2^1 + 30^2^1		= 1861
31^2^2 + 30^2^2		= 41 * 42281
31^2^3 + 30^2^3		= 17 * 127649 * 695377
31^2^4 + 30^2^4		= 290113 * 11191937 * 356611201601
31^2^5 + 30^2^5		= 13123009 * 54442271352370817905933763658993052388929

32^2^1 + 31^2^1		= 5 * 397
32^2^2 + 31^2^2		= 1972097
32^2^3 + 31^2^3		= 17 * 23473 * 4892737
32^2^4 + 31^2^4		= 1936348941361814438534657
32^2^5 + 31^2^5		= 769 * 3137 * 825188533926553548722187327732351681985729

33^2^1 + 32^2^1		= 2113
33^2^2 + 32^2^2		= 17 * 131441
33^2^3 + 32^2^3		= 2505920246017
33^2^4 + 32^2^4		= 353 * 1621729 * 5566945246068161
33^2^5 + 32^2^5		= 2983873 * 2699484696449 * 667160869177034668544161881281

34^2^1 + 33^2^1		= 5 * 449
34^2^2 + 33^2^2		= 2522257
34^2^3 + 33^2^3		= 3192202523137
34^2^4 + 33^2^4		= 97 * 101704961 * 523755236475041
34^2^5 + 33^2^5		= 138885889 * 101396393959938517627828587538992791914753

35^2^1 + 34^2^1		= 2381
35^2^2 + 34^2^2		= 2836961
35^2^3 + 34^2^3		= 63793 * 63293297
35^2^4 + 34^2^4		= 8260002645666200230661441
35^2^5 + 34^2^5		= 257 * 766721 * 182111422140701790077181229202218527225473

36^2^1 + 35^2^1		= 2521
36^2^2 + 35^2^2		= 17 * 187073
36^2^3 + 35^2^3		= 5072985298081
36^2^4 + 35^2^4		= 1017889 * 1067489 * 11991330783041
36^2^5 + 35^2^5		= 1601 * 25601 * 2172745274538485986133882161870613603987521

37^2^1 + 36^2^1		= 5 * 13 * 41
37^2^2 + 36^2^2		= 3553777
37^2^3 + 36^2^3		= 17 * 372564080081
37^2^4 + 36^2^4		= 97 * 2689 * 77812903367915743969
37^2^5 + 36^2^5		= 193 * 246596929 * 4529101927325059936608676611108659015041

38^2^1 + 37^2^1		= 29 * 97
38^2^2 + 37^2^2		= 3959297
38^2^3 + 37^2^3		= 17 * 2017 * 3169 * 72337
38^2^4 + 37^2^4		= 193 * 14401 * 64513 * 174230854190273
38^2^5 + 37^2^5		= 85882052629656956129921 * 5933123422482402978732708097

39^2^1 + 38^2^1		= 5 * 593
39^2^2 + 38^2^2		= 4398577
39^2^3 + 38^2^3		= 17 * 570576552881
39^2^4 + 38^2^4		= 77287393 * 160734913 * 3827427553
39^2^5 + 38^2^5		= 449 * 7489 * 13697 * 25572954892612276774237676295966776791681

40^2^1 + 39^2^1		= 3121
40^2^2 + 39^2^2		= 17 * 286673
40^2^3 + 39^2^3		= 11905609260481
40^2^4 + 39^2^4		= 449 * 2207969 * 72216319340102881
40^2^5 + 39^2^5		= 257 * 9473 * 33857 * 59906162177 * 539736223956774484874617683649

41^2^1 + 40^2^1		= 17 * 193
41^2^2 + 40^2^2		= 5385761
41^2^3 + 40^2^3		= 97 * 433 * 449 * 770929
41^2^4 + 40^2^4		= 3617 * 29501991671178616075873
41^2^5 + 40^2^5		= 257 * 155137 * 909889 * 1701121 * 9373692353 * 10216366246455531079937

42^2^1 + 41^2^1		= 5 * 13 * 53
42^2^2 + 41^2^2		= 89 * 66713
42^2^3 + 41^2^3		= 17 * 1039269248561
42^2^4 + 41^2^4		= 157512780598351804823277697
42^2^5 + 41^2^5		= 581502209 * 22106501753511528715457335286036459409267713

43^2^1 + 42^2^1		= 3613
43^2^2 + 42^2^2		= 2393 * 2729
43^2^3 + 42^2^3		= 21370852274017
43^2^4 + 42^2^4		= 193 * 764470887841 * 1561361505889
43^2^5 + 42^2^5		= 2113 * 341569 * 436088122241 * 3497012121052993 * 24942671238193217

44^2^1 + 43^2^1		= 5 * 757
44^2^2 + 43^2^2		= 7166897
44^2^3 + 43^2^3		= 17 * 97 * 4481 * 3482993
44^2^4 + 43^2^4		= 108769 * 3070420917296187945953
44^2^5 + 43^2^5		= 449 * 128310547062505615989210631900978873491478539698113

45^2^1 + 44^2^1		= 17 * 233
45^2^2 + 44^2^2		= 1289 * 6089
45^2^3 + 44^2^3		= 9521 * 3241607921
45^2^4 + 44^2^4		= 353 * 1360059572029797541271777
45^2^5 + 44^2^5		= 2654593 * 576603357377 * 28734547696559489 * 2703230691730339009

46^2^1 + 45^2^1		= 41 * 101
46^2^2 + 45^2^2		= 17 * 504593
46^2^3 + 45^2^3		= 97 * 241 * 241 * 6543073
46^2^4 + 45^2^4		= 684655198104511486296198721
46^2^5 + 45^2^5		= 193 * 1601 * 390721 * 1085922049 * 1841871921771737150551330913522753

47^2^1 + 46^2^1		= 5 * 5 * 173
47^2^2 + 46^2^2		= 2713 * 3449
47^2^3 + 46^2^3		= 17 * 657473 * 3924017
47^2^4 + 46^2^4		= 97 * 4348577 * 2296957412061076993
47^2^5 + 46^2^5		= 6529 * 19457 * 3802049204558207269288925860193818994829706369

48^2^1 + 47^2^1		= 4513
48^2^2 + 47^2^2		= 89 * 114473
48^2^3 + 47^2^3		= 17 * 3058268652401
48^2^4 + 47^2^4		= 12770386817 * 106578542803112321
48^2^5 + 47^2^5		= 257 * 921428835119159382593 * 4020204596868823291588949190337

49^2^1 + 48^2^1		= 5 * 941
49^2^2 + 48^2^2		= 11073217
49^2^3 + 48^2^3		= 17 * 193 * 593 * 31564129
49^2^4 + 48^2^4		= 5153 * 573073889 * 642894526152961
49^2^5 + 48^2^5		= 24730753 * 14343330604887617 * 5216236626222564388830006565697

50^2^1 + 49^2^1		= 13 * 13 * 29
50^2^2 + 49^2^2		= 17 * 706753
50^2^3 + 49^2^3		= 330689 * 218620609
50^2^4 + 49^2^4		= 12042113 * 218425668360189000577
50^2^5 + 49^2^5		= 257 * 10280321 * 62127485625857 * 21615646359005877837007648272769

51^2^1 + 50^2^1		= 5101
51^2^2 + 50^2^2		= 1609 * 8089
51^2^3 + 50^2^3		= 593 * 143053026257
51^2^4 + 50^2^4		= 97 * 449 * 3169 * 26232414872124140993
51^2^5 + 50^2^5		= 769 * 1496414281729 * 5836313462548938889559129912622145392001