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GFN Prime Search Status and History

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Range status key:

Range has been double-checked Range is currently being searched Range has been single-checked Primes have been reported in this range but the complete search history is unknown

GFN Prime Search Status: n=14

As of 14th March 2016, there are 225 known primes of the form b^2^14+1 = b^16384+1.

The following values of b give primes:

b Range status
67234
101830
114024
133858
162192
165306
210714
216968
229310
232798
422666
426690
449732
462470
468144
498904
506664
509622
528614
572934
581424
638980
641762
656210
698480
704930
730352
795810
840796
908086
975248
976914
990908
1007874
1037748
1039970
1067896
1082054
1097352
1102754
1132526
1162996
1171010
1177808
1181388
1202504
1202960
1238044
1247000
1287484
1453920
1481240
1485968
1514888
1619726
1651902
1793176
1796476
1815844
1833448
1867514
1882122
1894202
1902110
1915122
1930294
1943532
1991098
2007168
2018670
2050734
2054122
2150540
2153890
2158304
2178220
2182804
2322552
2339134
2402244
2524150
2545880
2596382
2608724
2612362
2638788
2643978
2661788
2663862
Up to b=2.7M was first searched by Yves Gallot's GFN Search. A single-pass check was made using Proth.exe, completed on 13th April 2002. 89 primes were found.

A full double-check has been carried out by Steven Wong using Genefer in December 2015. No additional primes were found.
2754180
2800354
2813914
2814924
2845242
2861500
2869920 *
2907874
2935148
2946916 *
3008012
3111582
3120840
3143872
3162748
3170760
3242824
3297072
3316198
3348390
3385868
3405588
3485838
3500456
3520320
3620610
3627188
3634206
3645132
3678824
3744512
3803326
3818714
3833822
3901926
3908840
3923868
3987582
4004684 *
4007186 *
4032994
4033958
4052976 *
4104210
4127396
4154024
4205332
4247456 *
4278866 *
4286504 *
4286546
4293066 *
4342802
4360316
4385460 *
4424120 *
4435184
4459794
4460954 *
4507390 *
4552274 *
4559602
Up to b=4.56M was searched by various people including Michael Angel, Raffi Chaglassian, Yary Hluchan and David Underbakke. A single-pass check is believed to have been made using Proth.exe between September 2002 and March 2005. 48 primes were found.

This range was double-checked by Iain Bethune and Steven Wong between January and March 2016 using Genefer. 14 previously missed primes (*) were found!
4648872
4687884
4705116
4790694
4805090
4809186
4838758
4922426
4936584
4960620
Between b=4.56M and b=5M was searched by Steven Wong between January and March 2016 using Genefer, finding 10 primes.
Between b=5M and b=30M, no organised testing has been carried out and no primes are known.
30007074
30009126
30059146
30099102
4 primes were reported by David Underbakke around b=30M between December 2002 and December 2004, found using Proth.exe.
Between b=30M and b=54M, no organised testing has been carried out and no primes are known.
54004880
54023654
54042710
54051066
54052762
54199574
55026030
55118968
55136716
55147892
55175806
55215776
55283082
55299412
55370912
55405392
55425678
55432900
55479860
55500860
55526886
55913248
55928654
55958846
56045006
56079028
26 primes in the range b=54M to b=56.1M were reported by David Underbakke and Bo Xiao between December 2002 and September 2004, found using Proth.exe.
Between b=56.1M and b=60M, no organised testing has been carried out and no primes are known.
60007514
60061724
60210198
60328602
4 primes were reported by David Underbakke around b=60M in July and August 2004, found using Proth.exe.
Between b=60M and b=98M, no organised testing has been carried out and no primes are known.
98022150
98025372
98248330
98301094
98321104
98363472
98473506
98475208
98503336
98504246
98806376
98921468
98954424
98983770
99003480
99033888
99333406
99426472
99468970
99567100
99597976
99685758
99712832
99712838
99735606
99787180
99838222
99841934
99852128
99941872
30 primes between b=98M and b=100M were reported by Shoichiro Yamada, Senji Yamashita, Satoshi Noda, and Rolf Nilsson during December 2004 to May 2009, found using Proth.exe.

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