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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 2nd April 2018, there are 664 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.

This range was double-checked in October 2017 by a group of PrimeGrid users using Genefer.
5012802
5018538
5037620
5051980
5061272
5116810
5118642
5133416
5145708
5253350
5294072
5409612
5437480
5457588
5494054
5512242
5585864
5587332
5588988
5646646
5662786
5664466
5694560
5706362
5707854
5733504
5740330
5818018
5860384
5862222
5882504
5913256
5936508
6018420
6024496
6040266
6118926
6124548
6143024
6170158
6181528
6207124
6252182
6270938
6321252
6380566
6437832
6448000
6490214
6516776
6518712
6544904
6578642
6590956
6592626
6633742
6655204
6699248
6711782
6712142
6759968
6801524
6815084
6821194
6835794
7029212
7044108
7052518
7165762
7175768
7177422
7181918
7183816
7193788
7203700
7215092
7366508
7527834
7573160
7587476
7598670
7612140
7657876
7680434
7686398
7700456
7713306
7754156
7821562
7837542
7855062
7874486
7908474
7934108
7971374
8037322
8067766
8180000
8191880
8222130
8234718
8252062
8258976
8302898
8351796
8406936
8412998
8432714
8464330
8482336
8482818
8495166
8516196
8532690
8553266
8647632
8677024
8702362
8805088
8870460
8895114
8972980
8985626
9028376
9054322
9126878
9159942
9360278
9376236
9426358
9501006
9583124
9626624
9639128
9640680
9646160
9684172
9686330
9707146
9722910
9767830
9772136
9812998
9982240
10017674
10022676
10032178
10047800
10100690
10121408
10128796
10164732
10215866
10254352
10284560
10288816
10295214
10401038
10411702
10412132
10465678
10465966
10490566
10491434
10537880
10539300
10543468
10603074
10623814
10649436
10652130
10681498
10696884
10719632
10745506
10759560
10841090
10849902
10850806
11020996
11034772
11112156
11131260
11160336
11187894
11247554
11266222
11337522
11351644
11357364
11359480
11467406
11529556
11553690
11697918
11709684
11774432
11804804
11804938
11884060
11941374
11953994
11985004
12011214
12027734
12051150
12132858
12135834
12148764
12184782
12233168
12285410
12296406
12299722
12361240
12405334
12504068
12579034
12591000
12643862
12665258
12694874
12716802
12773270
12828512
12845442
12862498
12888802
12914942
13022684
13035634
13054588
13094538
13094572
13097084
13099420
13116886
13138408
13156484
13164802
13177970
13183222
13209070
13209896
13294670
13337012
13348856
13358374
13374684
13421806
13426254
13455068
13500958
13548786
13562664
13579158
13660772
13676330
13737558
13788506
13949744
14006982
14024816
14085400
14092966
14095194
14208490
14230992
14235464
14255028
14287380
14294522
14347574
14351060
14355628
14377432
14379996
14392794
14417012
14425726
14445604
14447842
14452510
14458050
14513400
14515830
14528130
14666250
14713096
14736952
14801350
14912648
15005166
15028970
15077062
15094704
15100368
15115340
15123696
15171364
15233822
15234416
15279168
15295836
15304234
15363334
15380758
15409030
15417834
15437100
15487618
15555526
15579846
15604756
15648418
15696070
15739474
15875452
15880294
15905576
15933010
15949986
15955570
15989544
16008362
16010114
16033610
16045976
16110950
16161620
16166254
16167746
16173238
16205172
16242912
16263162
16274988
16300238
16303970
16351502
16411270
16419904
16470520
16500500
16524044
16553974
16558026
16581268
16593478
16599282
16601894
16621638
16675424
16692064
16750376
16764084
16770522
16809048
16879406
16957834
16982636
17001238
17004268
17043484
17151464
17186384
17193840
17250748
17264738
17327326
17341194
17363872
17477494
17494730
17619756
17763378
17802368
17855030
17912430
17932518
17944744
17974986
17978644
17984190
17992028
18004560
18042600
18049276
18071884
18122558
18186552
18316354
18321602
18348636
18392552
18403884
18439064
18526430
18602992
18619714
18623924
18644982
18697234
18716644
18786210
18871234
18882962
18892498
18935098
18963210
18980844
19045088
19135874
19169530
19215302
19225662
19252200
19299050
19312058
19313378
19334646
19335794
19385814
19403060
19405124
19413006
19438048
19474654
19500344
19519998
19524276
19557126
19569236
19708070
19719202
19725410
19760838
19850162
19924162
The range b=5M to b=20M was two-pass searched between October 2017 and April 2018 by a group of PrimeGrid users using Genefer. 439 primes were found.
Between b=20M and b=30M, a two-pass search using Genefer is underway by a group of PrimeGrid users.
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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