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GFN Prime Search Status and History

This page summarises the search history for Generalised Fermat Primes b^2^n+1, for all n >= 13 which have been searched. We record all the known primes for each n, along with notes on when each range was searched and by whom. The data has been compiled by Iain Bethune from a range of sources, including the the Top 5000 database, Yves Gallot's GFN Prime Search and PrimeGrid's own records.

It will be periodically updated, especially when new primes are found.

Note: 16 February 2021, 7 typos were corrected in GFN-15 b-values. These entries are marked with "!"

Note: 03 December 2021, 1 typo was corrected in GFN-17 b-values. This entry is marked with "!". Added old GFN-17 prime with b=47179704 which was missing from the table.

Quick links: n=13, n=14, n=15, n=16, n=17, n=18, n=19, n=20, n=21, n=22

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=15

As of 2nd August 2024, there are 4348 known primes of the form b^2^15+1 = b^32768+1.

The following values of b give primes:

b	Range status
70906 167176 204462 249830 321164 330716 332554 429370 499310 524552 553602 743788 825324 831648 855124 999236 1041870 1074542 1096382 1113768 1161054 1167528 1169486 1171824 1210354 1217284 1277444 1519380 1755378 1909372 1922592 1986700 2034902 2147196 2167350	Up to b=2.2M was first searched by Yves Gallot's GFN Search. A single-pass check was made using Proth.exe, completed on 21st February 2002. 35 primes were found. A full double-check has been carried out on BOINC by PrimeGrid using Genefer in October 2015.
2279250 2282862 2329148 2351172 2354572 2354618 2435410 2510928 2538626 2585646 2619572 2679502 2696506	The range between b=2.2M and 2.8M was searched by Heuer and Sun (and others?) using Proth.exe between August 2003 and December 2004. 13 primes were found. A full double-check has been carried out on BOINC by PrimeGrid using Genefer in October 2015.
2973894 3000336 3042376 *	The ranges b=2.8M-3M and b=3M-3.1M were reserved by Heuer and Sun respectively, and were are least partly searched using Proth.exe. 2 primes were found. A full double-check on BOINC by PrimeGrid using Genefer found 1 previously undiscovered prime (*) on 23rd October 2015.
3109540 3134838 3149688	3 Primes in this range were found by Ayeni using Proth.exe between April 2004 and April 2005. A full double-check has been carried out on BOINC by PrimeGrid using Genefer in October 2015.
3391432 3394960 3417444 3467622 3472100 3532700 3642296 3664554 3756658 3769892 4004620 4042212 4053566 4108672 4184696 4197530 4323648 4396444 4403010 4465132 4487952 4578290 4698564 * 4826770 4971052 5014954 5042524 5079358 5144952 5177652 5446484 5667050 5761466 6041274 * 6068406 * 6199694 * 6275442 * 6318186 * 6412528 * 6607866 6656034 6700428 6731948 6960350 7039132 7284770 7285278 7510824 7528624 7663846 7680822 7736350 7869772 8010848 8100176 8102494 8106614 8123056 8125520 8157528 8191116 8244666 8273506 8285500 8307368 8345790 8380046 8442162 8461246 8464936 8483782 8635576 8712924 8796286 8883278 9011408 9148556 9214318 9302934 9342420 9458852 9543806 9622594 9693048 9744750 9850652 9863800 9926910 9973932 10021136 10120074 10403098	This range was first tested on PRPNet by PrimeGrid using Genefer, LLR and PFGW from January 2011 finishing at b=10428486 on 18th October 2015 , finding 85 primes. A full double-check has been carried out on BOINC by PrimeGrid using Genefer in October and November 2015. 7 previously undiscovered primes (*) were found during this check.
10448246 10689024 10742748 10758842 10877222 11428394 11600204 11623354 11688764 11741086 11756060 11967372 12007538 12013942 12177788 12500316 12525142 12563092 12825258 12952476 13004344 13062632 13236710 13268134 13421628 13516486 13522632 13526546 13535820 13553636 13649540 13685572 13782404 13984036 14023640 14090140 14212786 14466952 14662858 14805912 14933582 14953270 14996602	Starting in November 2015, PrimeGrid ran a two-pass search on BOINC using Genefer, finding 43 primes.
15079730 15297664 * 15547296	This range was at least partly searched by Siegert using PFGW in 2011, yielding 2 primes. The range was double-checked by PrimeGrid on BOINC using Genefer in December 2015 and found 1 additional prime (*). All b up to 16253972 have been checked as of 23rd December 2015.
15674780 15731584 15800610 15804124 15859134 16217720 16307584 16341644 16391094 16676202 16710646 16715766 16933402 16990688 17132938 17166276 17213996 17255882 17498720 17503170 17630048 17746956 ! 17821922 ! 17914162 17957740 17978924 18027484 18162892 18318176 18376198 18860674 18900442 18930698 18959384 19011418 19045454 19159066 19297056 19353558 19444332 19454016 19510862 19523144 19567100 19587542 19661856 19814292 19864152 19884080 19998404 20009904 20033660 20037206 20190116 20228770 20294998 20507016 20583814 20586806 20607250 20738336 20805908 21080328 21232188 21300678 21411466 21444466 21479990 21510206 21661504 21702126 21950862 22040372 22102946 22155010 22217326 22459694 22574138 22631632 22783708 22799674 22844832 22875794 22996256 23054064 23142958 23171048 23343918 23447300 23544450 23566592 23625178 23717922 23842202 23962732 24057570 24154818 24261684 24264168 24354070 24452630 24607410 24641706 24698156 24710848 24745350 24802522 24811616 24953074 24994852 25013972 25213932 25319642 25339900 25361258 25404726 25521108 25580284 25676304 25676940 25853424 25942142 25980454 26055736 26088376 26195856 26346504 26467316 26621776 26752326 26775424 27021706 27047488 27271312 27285676 27390636 27505842 27525168 27543360 27550814 27843292 27893132 27939240 27958104 28049668 28268460 28301302 28557808 28571334 28586446 28650834 28673162 28755186 28869440 28891074 28892870 28993696 29173516 29242790 29252466 29420948 29615708 29652588 29667260 29712396 29721802 29785538 29815500 29921086 30010294 30021856 30207658 30239030 30404404 30434172 30802884 30974216 30986868 31036206 31239744 31445750 31447144 31511860 31697302 31798656 31935886 32358434 32396118 32405610 32422084 32463028 32891372 32910540 32915544 33034040 33112556 33381416 33424304 33430490 33573070 33573138 33644288 33966024 34410222 34468032 34554354 34639564 34674870 34822194 34875654 34890750 34934836 35033874 35242026 35252438 35417398 35429674 35499568 35538016 35550710 35593678 35694480 35701238 35791356 35967498 36170182 36188718 36258288 36367446 36429026 36465632 36554880 36591234 36619214 36955096 37012138 37014478 37069104 37080844 37222692 37289184 37477478 37525066 37539082 37731398 37732960 ! 37919898 37955742 38166398 ! 38204376 38296030 38398404 38437674 38532442 38572858 38672504 38732164 38794556 38796892 38808992 38876358 38884144 38914702 39109462 39142864 39163776 39280014 39507650 39563960 39615996 39646302 39647020 39772158 39801432 39884560 40134364 40197348 40232118 40257652 40313088 40381188 40604624 40624084 40655430 40697230 40894766 40899438 40951164 40958948 41015312 41022582 41097904 41373534 41376648 41545108 41577848 41585720 41770314 41980792 42026370 42155204 42159980 42204108 42214528 42379292 42463906 42581378 42584798 42648386 42724662 42777640 43083602 43127998 43406228 43613034 43617780 43796074 43845888 43953704 44001880 44220114 44224774 44262564 44273124 44353554 44358274 44371796 44435560 44477904 44543696 44605320 ! 44613578 44755938 44818970 44935222 45030014 45063980 45090978 45119780 45143836 45376298 45629164 45637798 45659574 45698978 45839458 45863930 46022608 46056952 46170810 46582454 46698964 46960218 46983936 47378690 47472846 47569014 47595950 47651824 47946238 47984028 48062530 48066320 48096646 48135770 48149268 48157002 48239150 48331236 48603326 48677646 48769710 48845872 49159028 49298736 49303742 49496924 49523650 49527560 49564282 49578898 49651148 49652988 49655768 49704390 49922164 50123936 50221936 50587866 51031756 51198384 51410204 51492082 51501460 51616728 51728384 51906054 51910848 52075406 52224456 52256606 52294700 52331768 52545018 52773748 52874414 52927856 53007214 53022198 53250488 53513474 53523364 53579878 53738372 53819034 53841266 54032224 54044372 54049292 54070422 54232280 54269880 54609780 54859632 55144710 55175134 55433918 55491168 55742096 55879658 55904786 56226958 56247626 56568622 56738172 56838966 56841438 56991358 57203908 57317368 ! 57361710 57390028 57565718 57591252 57743714 57759468 57833524 57837322 57978144 58228590 58306260 58430022 58446698 58641604 58796050 58836382 58896930 59213912 59241586 59473128 59581078 59587840 59850740 59858148 59909644 60143970 60155332 60197028 60327268 60395700 60672378 60693544 60693660 60737802 60781272 60838920 60852976 61123304 61250164 61281396 61374756 61377584 61388912 61445596 61586622 61605660 61608268 61696642 61715470 61722492 61777432 61862814 61961696 61975666 61978760 62032036 62094976 62105082 62137258 62318154 62327894 62422592 62537488 62647522 62751960 63044270 63345338 63777050 63806314 63810168 63832458 63874536 63930486 63972944 64162084 64353012 64365734 64713412 64714688 64741068 64760412 64804044 64855922 64867956 64898128 64985968 65054868 65068286 65089562 65093132 65266240 65320658 65344212 65387276 65514106 65520628 65529328 65772334 65783514 66178446 66193158 66353184 66489992 66581228 66619406 66702198 66732020 66794266 66797836 66880828 66994438 67131166 67543536 67647742 67799868 67804828 67840636 67889194 68002908 68207494 68274864 68436968 68962894 69043610 69187606 69190662 69204292 69500606 69541996 69753964 69756930 69789832 69858944 69945900 70048258 70122604 70246422 70272906 70440684 70464022 70495740 70501724 70526044 70604480 70730318 71049528 71072080 71266866 71270310 71317522 71396914 71402554 71424294 71566294 71717128 71846790 71924716 71990306 72018316 72039366 72078378 72220632 72507322 72517714 72557802 72871570 73258252 73344746 73490616 73568254 73605148 73633862 73702246 73849266 73908134 74175006 74177258 74184902 74395440 74423074 74462706 74761736 75110388 75121068 75144604 75170884 75572312 75813694 75830238 75874810 75909350 75943868 75998140 75998954 76021108 76163854 76256192 76292748 76303116 76621244 76765734 76830754 76839878 77030532 77151556 77251600 77336548 77456816 77653214 77732740 77799572 77854474 78005582 78056554 78088106 78170154 78204572 78346746 78513342 78592730 78854230 78888570 78908368 78927912 78979192 78995780 79313098 79741450 79997300 80009158 80190300 80454716 80502418 80612174 80627682 80654880 80721324 80885288 80949468 81092448 81204086 81248152 81370822 81419654 81464226 81479200 81510990 81524524 81542662 81643512 81917748 81963086 82021296 82216948 82419040 82456836 82510414 82721056 82797180 83436332 83532916 83551588 83955848 84034616 84100142 84238684 84607726 84657054 84779654 84828582 85231318 85326618 85426480 85509180 85538174 85724774 85810740 85904522 ! 85962194 86085882 86197780 86266356 86316726 86357100 86390618 86416078 86559824 86560194 86786930 86852980 86906874 86907000 87404222 87538694 87586782 87602080 87822288 87888966 87888968 88040256 88139808 88169528 88188718 88375556 88457536 88499486 88593558 88705770 88711024 88875842 88907932 88913808 88950444 88973858 89057846 89191710 89534186 90036322 90044424 90098824 90158524 90191700 90216162 90493102 90500380 90537066 90558822 90681404 90853870 90897136 90918816 91042040 91053092 91159406 91325814 91442036 91542430 91657968 91670880 91688986 91729308 91960990 91992926 92248286 92332160 92788434 93026652 93029694 93167764 93195672 93218150 93335534 93343682 93449606 93472028 93495032 93544108 93577266 93583888 93768930 93822920 93970766 94191588 94526242 94533120 94561956 94569926 94719100 94821812 94907042 95031798 95156930 95204390 95318702 95444178 95528838 95714646 95750230 95796272 95948598 95980204 96116880 96395974 96621912 96656682 96736254 96778520 96959666 96991342 97020428 97080698 97249732 97399786 97595800 97658504 97736584 97750172 97834996 97956048 98028126 98031034 98036302 98042092 98042196 98139802 98144326 98238170 98286810 98373986 98656258 98680448 98757266 98831066 98880316 98929908 98934138 99004668 99040102 99077450 99247622 99282174 99330552 99504624 99716006 99779472 99908610 100079598 100080540 100137488 100173532 100208254 100250876 100418806 100490012 100776958 100778678 100977640 101158366 101240250 101393334 101434660 101489504 101512992 101526052 101689974 101949048 101988578 101998994 102033070 102056320 102094462 102299438 102464942 102484816 102759712 102847564 102975702 103116568 103455878 103459020 103480164 103495684 104057368 104285146 104390902 104426750 104523164 104576908 104603164 105007526 105041474 105053266 105435112 105640168 105708518 105767496 105788430 105790416 106026636 106133142 106135980 106212248 106340468 106424198 106431156 106474810 106500736 106542368 106742024 106752044 106854672 106985040 106995882 107116548 107220838 107350192 107357408 107365100 107464120 107707870 107780864 108050104 108136908 108149056 108197446 108223996 108303180 108307338 108386190 108404954 108560618 108703324 108703714 108712428 108727736 108735762 108789048 108806416 108822924 108869288 108929594 109019970 109062296 109088076 109276020 109299102 109517072 109525774 109874214 109898424 109928134 110023796 110094890 110184446 110306176 110355826 110529774 110626990 110708294 110801370 110848790 111154606 111157632 111157738 111228130 111455630 111460014 111522566 111581946 111757816 111955452 111957916 112041878 112189290 112205972 112239238 112448974 112475504 112478472 112492494 112681410 112858572 112862222 112939304 113012558 113038368 113133656 113152938 113286988 113343692 113408570 113421678 113724088 113737400 113860144 113895548 113943848 114064376 114215062 114264510 114305010 114334744 114629320 114728542 114875196 114948618 114953634 115084128 115209218 115240536 115281896 115311892 115393790 115436946 115500540 115544042 115561678 115671650 115676240 115706334 115753524 115908692 116237186 116322280 116464482 116466252 116833532 117063974 117267320 117598176 117831370 117877884 118053990 118107128 118127042 118181854 118320340 118348118 118447928 118449282 118619024 118766366 118799578 118915778 119167392 119222366 119292856 119407944 119482198 119831538 119891980 119940200 119945902 120012294 120135074 120210350 120253740 120425712 120588714 120613100 120617390 120624124 120668518 121347184 121394090 121395346 121404522 121605858 121629290 121730360 121912350 122173916 122301614 122389380 122579374 122792010 123039032 123039444 123050852 123123492 123129916 123223850 123439084 123547534 123648418 123651180 123687502 123744998 123793436 123821232 123860002 123871566 124031102 124036464 124046522 124382792 124458880 124506354 124632414 124753256 125178918 125441338 125481170 125548464 125712016 125721964 125847628 125904228 126055746 126081182 126113708 126243998 126286018 126369034 126386534 126496204 126525240 126680064 126741312 126759080 126770508 127004592 127176348 127302742 127481584 127609948 127647656 127756224 128032060 128222368 128347158 128386010 128449944 128558152 129078590 129260770 129336252 129361846 129386350 129435824 129494874 129601344 129665114 129791962 129946346 130030996 130068716 130240748 130297916 130344692 130398368 130634016 130890164 131107928 131174206 131260652 131343746 131530228 131667228 131754280 131970806 132030834 132163528 132235966 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142078578 142099916 142311656 142321292 142577126 142638850 142641980 142707876 142767314 142877214 142966126 143093566 143130154 143134352 143198438 143263372 143605556 143722214 143760606 143776348 143834570 144281882 144337430 144396234 144449976 144492642 144529334 144545644 144898672 144899186 145192138 145215608 145555560 145662094 146181796 146202432 146226064 146475964 146525644 146572182 146685258 146690944 146719304 146815534 146827058 146952102 147090352 147157046 147157962 147275742 147373906 147385214 147425438 147527780 147583850 147726244 147762136 147786300 147833820 147858404 147910114 147966452 147994098 147997924 148058530 148224464 148234094 148341772 148481900 148617680 148623552 148633688 148797008 148876904 148955204 149056352 149088542 149171862 149286476 149328506 149401482 149414248 149422114 149532408 149585794 149729238 149734692 149796934 149895900 150013360 150301366 150436806 150626076 150634468 150692600 150753680 150922832 151017738 151057074 151059988 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405970094 406061100 406210240 406348254 406357510 406436906 406568730 406798836 406901570 407134340 407499698 407679416 407780186 407791918 407798706 407805252 407835850 407947914 407987870 408129528 408159634 408240948 408286444 408319832 408332896 408425708 408573022 408624032 408716764 408756310 408855392 408931670 409202256 409344882 409408836 409541192 409940484 409998108 410003748 410439278 410446620 410542748 410586342 410686916 410719906 410970240 411012068 411150372 411209860 411237180 411283384 411363548 411647478 411653016 411764794 412059388 412141026 412221816 412618932 412652794 412766826 412903886 412922034 413016520 413079640 413323730 413575942 413711256 413721872 413808250 413905758 414138434 414311634 414641692 414649456 414668454 414669390 414869946 415055672 415082562 415258556 415387230 415546286 415783624 415908032 416013740 416173884 416448744 416653354 416765182 416767938 416873244 417080240 417198304 417200984 417273794 417559202 417662162 417787266 417789568 417823972 417863140 418034210 418067380 418076120 418081236 418207236 418226392 418332626 418453942 418543322 418579252 418584220 418723048 418750816 418788920 419233326 419466822 419806366 419824036 419838546 420133124 420133588 420330520 420383540 420470672 420471940 420534264 420715612 420761160 420762692 421234656 421316808 421354512 421817794 422027884 422062834 422185712 422200704 422229358 422283026 422534256 422739076 422766498 422818500 423268768 423312762 423433850 423482128 423724732 423762104 423894840 424025188 424080138 424122192 424196024 424275762 424296018 424314468 424626020 424768904 424808370 424875558 425001734 425048636 425249782 425361440 425368296 425383064 425937016 425983380 425995820 426349770 426510402 426849462 427395054 427676306 428094608 428184108 428196718 428240308 428256622 428296886 428527950 428528716 428903218 429243066 429360566 429416076 429604720 429644458 429754208 429866256 429952790 430056426 430077954 430430142 430469122 430613184 430620834 430664506 430718512 430744758 430787518 431018024 431092028 431095678 431130300 431175874 431186570 431377566 431390586 431507704 431797230 431872648 431896632 431934778 431976602 432027540 432112392 432141218 432273878 432405204 432443764 432563308 432613490 432632590 432719418 433230688 433301068 433393634 433487186 433620120 433830146 433957100 433987734 433993952 434018292 434202040 434401898 434478386 434520342 434629374 434766516 434812168 435182504 435213712 435216404 435459730 435626940 435653342 435663838 435741818 435878178 436307990 436452196 436499940 436676362 436725822 436736698 436787220 437273076 437318672 437401328 437513864 437686432 437702692 437714766 437810402 437893240 437970392 438112604 438206462 438543924 438739540 438808998 438904760 439135754 439301520 439449700 439498912 439637362 439833410 439850962 440020638 440195764 440648198 440726984 440742552 440828134 441063014 441075534 441077534 441138598 441221476 441227446 441293526 441446330 441527970 441764550 441774962 442106488 442147288 442199188 442358818 442466420 442475382 442893770 443019382 443498974 443526086 443607414 443673470 443945294 443972960 444152646 444303884 444594848 444675156 444901848 444946316 445097004 445274266 445308208 445479838 445688442 445776434 446081982 446216958 446256862 446321420 446504802 446543428 446601880 446675954 446762806 446834064 447050820 447123888 447249876 447392940 447859110 447966152 448001972 448012722 448212942 448482262 448531384 448582508 448808334 448818232 448842602 448895772 448951770 449050870 449240066 449337988 449345788 449743162 449775170 449888914 450133880 450258330 450349208 450583940 450628404 450663700 450799640 450921372 451014734 451501710 451545946 451581210 451590920 451643974 451644258 451676456 451854286 451907282 451912036 451961564 452110946 452146742 452273906 452427974 452473754 452587180 452659766 452721812 452898432 452926892 452936900 452982466 453185964 453266220 453268636 453315174 453491614 453499848 453542380 453579908 453585836 453655270 453681596 453788432 454271590 454369102 454467750 454572644 454647530 454840644 454971412 455145946 455146978 455235326 455251916 455283534 455409230 455567822 455613786 456056350 456250992 456255322 456269894 456393006 456398666 456470580 456695104 456703954 456710738 456711032 456731554 457075746 457093080 457267920 457561754 457661836 457757024 457759994 457902500 457917230 458083152 458092946 458097942 458161598 458257392 458323710 458344136 458418448 458523608 458631590 458644414 458668202 458760640 458784972 458849926 458864482 458998904 459027408 459138276 459304796 459315614 459512158 459524992 459532960 459594144 459744356 459896482 459986590	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer, finding 4153 primes as of 2nd August 2024.
	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer. As of 2nd August 2024, the trailing edge is b=0 and leading edge is b=459986590.
3292665455999520712131951625894 * 3292665455999520712131951642528 *	Between June 2020 and December 2020, a two-pass search for GFN-15 MEGA prime was performed by a group of PrimeGrid users, using LLR2. The search was performed from minimal b value required to produce GFN-15 MEGA prime (1000000 digits): b_mega = 3292665455999520712131951278260 up to b_mega + 1000000. Two GFN-15 MEGA primes were found.
3292665455999520712131952624640 *	1 GFN-15 MEGA prime was reported by independent seachers.

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GFN Prime Search Status: n=16

As of 2nd August 2024, there are 3781 known primes of the form b^2^16+1 = b^65536+1.

The following values of b give primes:

b	Range status
48594 108368 141146 189590 255694 291726 292550 357868 440846 544118 549868 671600 843832 857678 1024390 1057476 1087540 * 1266062 1361846 1374038 1478036 1483076 1540550	Searched up to b=1.86M by Yves Gallot's GFN Search, using Proth.exe. According to this page, all of the range was reserved but it is unclear if all the reserved tests were completed. 22 primes were reported up to May 2003 PrimeGrid restarted the search in Dec 2011 using PRPNet and Genefer, LLR and PFGW. This effort found 1 previously undiscovered prime (*). A full double-check was carried out on BOINC by PrimeGrid using Genefer in October 2015.
1828502 1874512 1927034 *	2 primes were reported in this range in March 2005 and June 2008, found using Proth.exe. The range has been covered by the PrimeGrid PRPNet search, and has been fully double-checked on BOINC using Genefer, finding 1 previously undiscovered prime (*).
1966374 * 2019300 * 2041898 * 2056292 * 2162068 2177038 2187182	3 primes were reported in this range by Ayeni between July 2008 and April 2009, using Proth.exe. A double-check on BOINC by PrimeGrid using Genefer in November 2015 found 4 previously undiscovered primes (*).
2251082 2313394 2336976 2483590 2484264 2679102 * 2689202 * 2738848 2744940 2779470 2829122 2909834 * 3095674 3422670 3446048 3461954 3462728 3503138 3553248 3785880 3803826 3872228 3877352 3912496 3939670 3966304	This range was checked by PrimeGrid's PRPNet search using Genefer, LLR and PFGW, yielding 23 primes. A single-pass up to b=4205312 was completed on 13 October 2015. A double-check on BOINC by PrimeGrid using Genefer was completed in December 2015. 3 previously undiscovered primes (*) were found.
4280722 4470420 4603702 4615890 4855782 4891596 5143624 5176028 5200658 5222640 5263190 5350408 5416598 5645768 5879074 5905206 5911446 6031270 6068296 6104728 6379668 6490328 6526168 6553414 6628260 6837196 6885798 6902598 6918698 6919394 7107770 7188654 7307674 7373894 7427232 7439308 7464550 7622010 7634800 7832756 7954812 8036146 8099100 8146592 8188038 8326702 8412634 8525558 8596942 8718098 8749120 8844704 9074206 9132408 9214424 9223072 9373148 9392774 9444368 9518248 9584088 9624110 9628238 9841672 9920216 10090890 10221008 10464954 10663638 10755500 10771330 10808098 10957508 11033686 11110588 11168512 11215796 11224312 11292580 11611202 11793760 11804536 11844886 11948010 12084448 12102810 12376146 12508790 12510100 12620940 12660574 12764608 12914686 12941970 13029860 13332130 13398688 13466298 13657452 13830802 13944760 13968798 14050484 14059910 14518950 14705866 14750712 14778298 14807318 14832074 14832496 14914230 14914430 14947856 15005274 15069494 15454262 15471020 15499198 15603948 15800506 15893070 15948188 16034826 16120142 16326986 16787702 16858742 17157558 17265602 17328156 17493552 17594396 17629398 * 17655444 * 17684828 * 17716338 17757426 17770454 17931126 18255116 18364744 18387422 18612352 18682542 18788582 19149988 19165998 19194688 19415886 19432158 19451454 19502212 * 19514276 19810832 19916902 20109598 20317650 20338564 20338906 20368808 20416586 20417546 20495674 20670628 20673706 20794390 20958760 21003082 21123886 21207594 21298612 21352892 21438976 21632926 21697066 21844548 21928344 21946386 21990626 22082900 22191882 22230230 22402670 22602162 22672358 22677562 22684548 22696662 22738600 22740816 22858812 22872882 22877386 23077164 23080390 23138154 23582210 23864352 23947122 24163706 24220066 24293444 24510980 24528070 24722142 24730888 24813140 24859030 25069382 25226438 25281714 25355170 25369696 25815054 25893048 25894728 25939926 25981818 25987186 26477248 26484668 26578974 26886748 26916240 26987486 27243670 27264470 27326204 27372028 27441534 27548300 27625562 27639120 27678634 27738902 27768276 28027008 28099080 28413758 28487278 28580718 28768058 29048042 29097708 29202654 29247740 29340732 29350290 29500622 29501096 29509260 29585874 29723118 29863462 30046920 30101988 30216696 30250088 30328508 30376064 30799220 30813412 30877996 30946880 31125356 31154730 31342854 31380744 31448254 31492936 31515202 31613530 31647504 31689074 31812740 31887064 31988978 32056116 32161210 32235030 32370056 32517922 32574488 32675102 32697566 32778852 32987968 33058194 33075870 33112172 33160366 33255290 33388034 33406946 33417368 33468724 33531480 33790428 33910364 33963124 34197950 34327650 34397974 34503816 34575414 34640098 34904540 35255372 35419084 35458620 35534500 35599734 35648406 35753376 36037446 36127768 36187924 36251736 36279762 36362214 36427586 36614838 36633974 36968128 37219594 37284376 37463776 37592308 37732056 37878964 37887878 38040628 38199804 38385824 38472570 38481086 38485606 38542914 38659632 38670832 38770952 38849156 38881766 38951594 39089796 39108392 39162320 39418466 39542162 39641162 39641632 39672694 39809082 39822410 39822830 40348160 40374324 40522376 40547834 40726656 40782880 40858208 40934648 40951894 41023954 41378136 41661376 41785194 41956924 41960754 41982488 42045360 42177946 42439456 42620908 42743760 42757860 43084562 43173706 43176248 43216120 43242432 43439336 43581628 43662354 43712198 43746498 43748016 43857722 43867006 44282836 44285794 44401238 44408348 44427620 44533068 44690560 44799596 44836986 45070994 45126534 45251962 45254752 45288396 45327802 45340828 45394036 45536968 45642558 45660678 45727976 45837186 46131706 46145120 46475746 46539762 46587924 47083532 47124682 47368516 47831888 47854178 47911922 48036128 48078610 48169782 48202934 48210372 48424300 48637118 48683018 48693126 48843798 48967836 49008360 49353010 49433304 49473608 49975182 50124978 50140536 50164202 50546746 50781728 50907674 50969866 51337006 51443210 51455452 51506978 51686702 51708088 51888044 51927094 51944436 52054552 52067302 52186612 52250632 52301890 52333192 52462148 52531754 52558020 52690172 52871154 52963984 53146516 53258832 53475642 53507594 53510900 53566068 53607314 53660144 53704982 53797422 53847196 53869266 53874510 53942572 54234920 54377542 54387024 54435560 54587920 54739648 54889620 54937732 54949840 55072040 55110930 55292592 55317972 55396316 55740434 55836122 55837944 56170642 56318206 56339292 56586100 56731448 56749480 56795992 56857098 57117422 57413758 57652882 57666292 57955358 57984540 58065838 58077056 58226162 58384684 58528880 58644648 58665154 58838172 58897838 59015944 59071146 59136274 59214242 59282734 59841338 59911840 59923820 59973204 60056188 60084272 60568416 60620338 60740702 60791522 60801962 60892852 60912388 61135724 61193080 61216832 61298290 61395720 61425072 61754924 62038276 62064626 62064808 62142718 62151540 62199942 62286896 62322622 62336612 62384838 62384964 62464130 62479964 62554864 62555084 62702572 62840404 62841156 62876900 62951326 63096178 63132142 63190552 63240724 63246814 63322122 63367880 63434268 63722348 63783272 63786378 63827844 63850468 63853188 64008220 64029766 64093074 64172582 64297742 64510644 64758794 64908524 64962674 65159860 65188204 65217852 65357568 65432626 65444914 66537066 66656676 66657214 66659348 66968818 67074678 67095494 67115446 67128624 67135830 67174482 67182906 67217514 67226590 67254608 67291176 67437280 67607058 67641884 67659536 67797528 67886910 67946296 67988572 68022564 68332062 68353724 68417666 68519002 68535830 68634098 68699002 68787794 68819462 68825266 68876616 68887742 68923948 69145164 69177340 69255526 69385726 69415014 69504360 69649212 69691840 69718316 69921942 69967876 70278190 70313466 70431290 70492424 70527284 70569854 70788928 70800832 71042934 71083738 71256288 71411244 71419208 71422068 71453170 71533230 71729282 71830642 72189436 72477906 72489324 72583992 72589302 72656320 72708334 72734952 72832432 72835678 72905222 72986366 72987012 73175654 73314542 73458528 73527600 73579576 73611228 73735306 73770820 73861084 73910008 73948090 74019600 74036056 74111056 74316862 74561982 74581688 74851056 74897306 75029382 75151890 75333588 75605586 75707404 75802920 75869946 76057320 76067780 76382388 76387412 76467064 76580342 76596200 76766300 76780072 76785568 76937478 77169226 77177176 77264234 77306490 77355598 77372478 77507298 77704986 77744918 77781726 77796830 78034592 78294900 78450806 78504140 78562090 78567948 78622096 78635388 78726134 78794796 78884478 79056616 79172346 79183586 79225864 79265412 79321064 79343116 79461958 79483110 79633084 79697298 79871216 80008854 80243510 80243888 80304896 80317468 80350524 80573056 80658514 80795988 80954588 80961052 80976720 81033034 81065064 81126070 81254306 81301530 81312044 81379624 81495116 81712996 81760016 81791240 81868890 81976552 81992548 82055998 82102578 82328650 82409922 82476416 82481836 82516824 82585780 82608282 82615290 82664200 82727298 82853956 82883694 83007704 83728230 83811756 83816404 84020394 84063046 84088876 84178554 84182766 84216216 84221130 84332576 84490864 84580630 84720600 84860922 84876466 84881776 84930776 85003716 85143326 85209154 85316028 85516188 85598554 85636536 85770052 85908438 86037836 86160832 86254706 86431122 86470130 86553044 86736718 86779344 86796322 86814912 86892902 86909560 86990562 86998958 87033652 87036596 87131084 87216048 87409818 87419762 87514470 87557214 87758254 87955518 88121890 88167594 88271606 88320078 88583112 88596754 88732114 88753612 88837150 88875524 89024442 89136336 89420980 89443326 89510134 89539970 89571726 89657350 89783122 89923590 89929872 89973416 90013258 90014942 90033898 90240344 90277882 90330702 90486274 90692090 90705094 90825194 90825332 90888234 90961322 91048790 91087586 91217580 91744150 91771676 91842670 91903298 91987174 92048794 92081038 92102646 92548750 92674306 92690940 92766842 92914140 92914244 92966428 93043462 93063952 93098062 93125776 93218152 93229866 93294956 93680368 93780678 93786286 93815892 93838842 93899840 94127096 94134450 94148218 94238958 94371750 94395438 94560386 94683814 95020906 95031090 95060694 95306976 95330936 95476682 95485038 95658826 95668512 95740866 96048808 96228408 96255150 96338398 96534690 96670202 96763400 97104830 97496720 97610728 97646596 97647644 97689780 97784106 97789752 97796840 97876302 98014656 98046450 98087154 98160134 98165150 98174624 98638136 98679336 98752904 99086572 99184362 99316110 99416780 99443134 99458608 99543174 99605678 99605982 99717520 99811816 99812398 99873084 99938996 99949404 99985498 100033834 100061390 100278340 100292652 100366730 100394394 100445354 100480774 100492452 100541736 100547206 100635028 100809238 101053038 101328148 101330432 101373072 101542004 101588976 101833680 101940908 102001552 102077788 102152180 102179404 102240736 102290630 102413650 102770410 102815216 102820362 102871184 102905922 102927846 102936406 103014016 103232286 103244358 103410380 103607034 103793686 103917130 103917532 103965794 103980898 104153644 104397268 104719178 104985656 105109090 105121886 105201924 105253618 105317236 105352114 105542202 105579852 105629226 105814272 105825012 105830180 105831918 105956334 106125374 106206510 106297214 106449610 106579844 106599192 106616682 106665218 106679112 106795692 106830890 106913102 106967132 106997372 107058940 107137714 107167054 107658460 107747194 107894268 107970076 108153408 108244272 108306062 108551550 108618244 109000284 109031182 109034994 109144682 109287254 109323574 109464346 109564026 109649344 109655942 109986750 110077040 110139930 110280272 110395028 110431446 110835044 110980170 111001326 111075226 111149164 111391036 111402066 111749388 111841318 111979738 112138030 112155968 112707138 112822300 112832188 112897156 112904842 113006358 113106664 113148382 113219876 113290542 113296320 113385930 113399408 113430012 113441586 113499172 113547832 113583948 113630364 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344229910 344602792 344756250 344843244 344962980 345245366 345269996 345388764 345423080 345459718 345611912 345741216 345770530 345858072 346160142 346173012 346184660 346907922 347177644 347355134 347356484 347392540 347628648 347672996 347695312 347779780 347951086 347965452 348100466 348324292 348544134 348715208 348781748 348850644 348997566 349004920 349018972 349137690 349168250 349363454 349378864 349442048 349489508 349631338 349690966 350006744 350006744 * 350063050 350225686 350533712 350562736 350597340 350740636 350781920 350862890 350960468 351076040 351093510 351108142 351352954 351708236 351711414 351836030 351981866 352046126 352161454 352376368 352503390 352679404 353182526 353290002 353418730 353637844 353660712 353974846 354092874 354653350 354771458 354809712 354875478 354881646 354894892 355170870 355170950 355195970 355298880 355355928 355527042 355730036 355756468 355978068 356304902 356374022 356633956 356756294 356914730 357002874 357083314 357147010 357255082 357274576 357285868 357419934 357425936 357470200 357500320 357507960 357544402 357607972 357665204 358900982 359103418 359128672 359283274 359317644 359329758 359340994 359401116 359596244 359635634 359960324 360101346 360217860 360311032 360320800 360334378 360439464 360471286 360546710 361170170 361480404 361549912 361939980 362063340 362073816 362088290 362091594 362219658 362268428 362513158 362649036 362789154 362825894 362933480 362955892 363168068 363483670 363513574 363805226 363851882 363868682 363872636 363910224 363920134 364090394 364182932 364347774 364656502 364803888 364861092 364885900 364895936 364991432 364993792 365052638 365199322 365207168 365215706 365262244 365457014 365505668 365559080 365697132 365745842 365772958 365784042 365953364 365985352 366022980 366089294 366115838 366216162 366224790 366241970 366275912 366607990 366699834 366704014 366833600 366891470 366913000 367194644 367312472 367318386 367335960 367404392 367501288 367592108 367911510 367947714 368074798 368276164 368296724 368331472 368381098 369094978 369147924 369269766 369343272 369413428 369591406 369658262 369982446 370049982 370060054 370102662 370125692 370457470 370523524 370526720 370631060 370645494 370682770 370688938 371224188 371298826 371301256 371360212 371439644 371456960 371665334 372195162 372389476 372445672 372572460 372705274 372811454 372815228 372824658 372959772 372964108 373280594 373289162 373449408 373644824 373674782 373807422 373993468 374093462 374238784 374315392 374883654 374933940 375055550 375107660 375163438 375560950 375755340 375785674 375978028 376193262 376195030 376205042 376275968 376677380 376878748 376910242 376943564 376979094 377138598 377357490 377460800 377468342 377501042 377501088 377578078 377962212 378011588 378041402 378082812 378233426 378358400 378381756 378638186 378801206 378899878 379023288 379165090 379229500 379295494 379383748 379513186 379599994 379611188 379662332 379708246 379731210 379862498 379883928 379964958 380148760 380162310 380459312 380502860 380506088 380554066 380554836 380949250 380956058 381008994 381025666 381356210 381677316 381698220 381744932 381786730 381901696 382230886 382240580 382281972 382288562 382413624 382493604 382703902 382762246 382773950 382876668 382987492 383188974 383733442 383826194 383862962 384070366 384201230 384751372 384867232 384989902 385305212 385414398 385471428 385548832 385566144 385586214 385592558 385640662 385686144 385873214 385979228 386135148 386326952 386458368 386497826 386631754 386989390 386997048 386997250 387186988 387286112 387402046 387532670 387542040 387576420 387583592 387667882 387901724 388160790 388246276 388303692 388505314 388612498 388685434 388763268 388766522 389171208 389307718 389313258 389597730 389631360 389713964 389788754 389813580 389865064 389953050 389955702 390220718 390249862 390302998 390342716 390354004 390385264 390427710 390536346 390694914 390760818 390785048 390797312 390882410 390892426 391002762 391328794 391431698 391487858 391600686 391604856 391653864 391730320 391734926 391744752 391811120 391826686 391990722 392067676 392279296 392515696 392620562 392703112 392821362 393111626 393154782 393169410 393307498 393790196 393850390 393861430 393906278 393918174 394042416 394082216 394114102 394322240 394661454 394667206 394678386 394814756 395005156 395635020 395771950 395917710 395981110 396019860 396326740 396461150 396713956 396733568 396735532 396888530 396902696 396906862 396992338 397025306 397252180 397300232 397548270 397550068 397633594 397812148 397896594 398045298 398098966 398154992 398269814 398549190 398601174 398692630 398776380 398909066 398945252 398953896 399250776 399407888 399573960 399623296 399802788 399834306 399878576 * 400041174 400076442 400147432 400222732 400341182 400369026 400588198 400612742 400635432 400819094 400838802 400904484 400949372 400976842 401170746 401477610 401540454 401591220 401719930 401747416 401768016 401936228 402146322 402151594 402151846 402222084 402406064 402484836 402768306 402912790 403072918 403201706 403294836 403315928 403412214 403609814 403868406 404064366 404138444 404405632 404613798 404646268 405044660 1010036096 * 12192710656 * 1814570322977518 * 1814570322984178 *	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer, finding 3711 primes. 11 primes (*) were reported by independent searchers. (2nd August 2024)
	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer. As of 2nd August 2024, the trailing edge is b=402822506 and leading edge is b=405164300.

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GFN Prime Search Status: n=17

As of 2nd August 2024, there are 1139 known primes of the form b^2^17+1 = b^131072+1.

The following values of b give primes:

b	Range status
62722 130816 228188 386892 572186 689186 909548 * 1063730 1176694 1361244 1372930	Between 2002 and July 2004, Yves Gallot's GFN Prime Search tested ranges up to b=1.4M using Proth.exe, but left several gaps. As a result, only 6 primes were found in this initial search. Several independent searchers, including David Underbakke continued working in the gaps, and another 4 primes were reported between 2009 and 2013. Between June and October 2015, PrimeGrid completed a full re-check of this range on BOINC using Genefer, finding 1 previous undiscovered prime (*)
1560730 1660830 1717162 1722230 1766192 1955556 2194180 2280466 2639850 3450080 3615210 3814944 4085818 4329134 4893072 4974408 5326454 5400728 5471814 5586416 5734100 5877582 6391936 6403134 6705932 7379442 7832704 7858180 7926326 8150484 8704114 8770526 9240606 9419976 9785844 9907326 10037266 10368632 10453790 10765720 10921162 10962066 10994460 11036888 11195602 11267296 11292782 11778792 11876066 12343130 12357518 12512992 12661786 12687374 12851074 12961862 12978952 13083418 13433028 13613070 13800346 14020004 14217182 14613898 14790404 15091270 15147290 15237960 15342502 15567144 15667716 15731520 16329572 16741226 16985784 17025822 17052490 17119936 17138628 17141888 17643330 17814792 17958952 18298534 18309468 18501600 18509226 18608780 18813106 18968126 19216648 19464034 20185276 20227142 20234282 20674450 20968936 21517658 21582550 21757066 21869554 21917442 22007146 22705306 22718284 22808110 22901508 22980158 23011666 23045178 23363426 24297936 24486806 24522386 24641166 24642712 24644826 24734116 25124378 25128150 26172278 26500832 26599558 26757382 26896670 27022768 27408050 27544748 27557876 27758510 27822108 28175634 28294666 28398204 28497098 29169314 29505368 29607314 29959190 30022816 30059800 30225714 30300414 30315072 30318724 30819256 30844300 31044982 31145080 31469984 31768014 31821360 32055422 32096608 32137342 32200644 32286660 32348894 32417420 32430486 32608738 32704348 32792696 32869172 33191418 33395198 33474284 33732746 34087952 34530386 34585314 34763644 34871942 34957136 35047222 35139782 35141602 35282096 35327718 35372304 35391288 35957420 35997532 36038176 36416848 36422846 36531196 37909914 38152876 38196496 38310998 38734748 38824296 39100746 39324372 39502358 39597790 39746366 40151896 40463598 40550398 41001148 41007562 41102236 41237116 41364744 41688706 42168978 42230406 42243204 42254832 42414020 42550702	PrimeGrid run two-pass search of this range (b < 42658774) on BOINC using Genefer from October 2015 to February 2022, finding 213 primes.
42654182 43163894 43165206 44049878 44085096 44330870 44438760 44919410 45315256 45570624 46077492 46371508 46385310 46413358 46730280 46736070 46776558 47090246 47179704 48273828 48370248 48643706 49038514 49090656 ! 49225986 49243622 49331672 49397682 49530004 49817700 50055102 50110436 50217306 50495632 50844724 50963598 51269192 51567684 51570250 51580416 51872628 51954384 52043532 52412612 52712138 53078434 53161266 53659976 54032538 54161106 54206254 54212352 54334044 54361742 54548788 55015050 55184170 55268442 55579418 55645700 56307420 56383242 56459558 56584816 56735576 56917336 57438404 57594734 57694224 57704312 58247118 58447642 58447816 58523466 58589880 59161754 59210784 59305348 59362002 59405420 59515830 59692546 59720358 60133106 60455792 60540024 60642326 61030988 61267078 61837354 62146946 62276102 63112418 63165756 63168480 63823568 64024604 64476916 64506894 64568930 64791668 64911056 65200798 65305572 65569854 65791182 66131722 66272848 66901180 66982940 67371416 67725850 67894288 68275006 68372810 68536972 68811158 68918852 68924112 68999820 69534788 69565722 69622572 69689592 69742382 69915032 70022042 70050828 70421038 70658696 70893680 70934282 70948704 70960658 71450224 71679108 71732900 72070092 72602370 73099962 73132228 73160610 73404316 73690464 73839292 74325990 74363146 74381296 74396818 74817490 74833516 75521414 75647276 75861530 76018874 76026988 76416048 77281404 77469882 77918854 77924964 78089172 78240016 78439440 78714954 78851276 78880690 78910032 79201682 79383608 79428414 79485098 79789806 79801426 79912550 80146408 80284312 81096098 81444036 81477176 81976506 82003030 82008736 83003850 83328182 83364886 84149050 84384358 84445014 84679936 84715930 84723284 84757790 84765338 84817722 84924212 85115888 86060696 86295564 86347638 86413544 86829162 87039658 87116452 87192538 87268788 87352356 87370574 87454694 87547832 87920992 88068088 88166868 88243020 88760062 89113896 89285798 89790434 89977312 90006846 90382348 90857490 90938686 90942952 91033554 91049202 91069366 91655310 91685784 91689894 91707732 91767880 92198216 92460588 93035888 93514592 93773904 93886318 93950924 94978760 95308284 95596816 95635202 95940796 96111850 96475576 96734274 96821302 97046574 97512766 98137862 98200338 98240694 98518362 98557818 98652282 98922946 98978354 99189780 99351950 99557826 99650934 99665972 100010426 100324226 100369508 100382228 100441116 100520930 100534258 100719472 100865034 101270816 101328382 101607438 101856256 101915106 102021074 102050324 102257714 102397132 102469684 102507732 103013294 103094212 103209792 103280694 103289324 103605376 103828182 104641854 104808996 104907548 105058710 105534478 105850338 105861526 105937832 106019242 106440698 106508704 106901434 107126228 107222132 107404768 107420312 107492880 107627678 107732730 107922308 107979316 108080390 108161744 108195632 108581414 108584736 109082020 109142690 109654098 109678642 110406480 110428380 110824714 110866802 111181588 111673524 112023072 112053266 112248096 112580428 112719374 112852910 112958834 112996304 113170004 113191714 113313172 113325850 113327472 113328940 113431922 113521888 113550956 113807058 113904214 114009952 114055498 114159720 114340846 114643510 114687250 115256562 115409608 115479166 115704568 115873312 115992582 116017862 116036228 116402336 116936156 117088740 117153716 117196584 117345018 117375862 117687318 117906758 118109876 118583824 118888350 119137704 119246256 119510296 119541900 119604848 119744014 120106930 121158848 121462664 121854624 122372192 122414564 122481106 122869094 122941512 123195196 123306230 123338660 123856592 123910270 124080788 124133348 124219534 124393514 124543852 124582356 124586054 124749274 124875502 124877454 125006494 125141096 125714084 125966884 126189358 126199098 126334514 126423276 126611934 127093036 127720948 128520182 128558886 129159632 129292212 130048816 130051980 130128232 130148002 130198372 130518578 130593462 130907540 131112524 131309874 131370186 131412078 131820886 133096042 133180238 133345154 133569020 133676500 133954018 134176868 134206304 134322272 134447516 134459616 134706086 135135930 135332960 135458028 135497678 135513092 135623220 135695350 135744154 136122686 136124076 136192168 136227118 137486564 137521726 137878102 137900696 138000006 138527284 138626864 138830036 138894074 138896860 139352402 139941370 140237690 140473436 140649396 140824516 140859866 140928044 141554190 141636602 142195844 142207386 142527792 142589776 143126384 143416574 143421820 143844356 144602744 144810806 144926960 145132288 145137270 145245346 145728478 145949782 146031082 146465338 146520528 146994540 147265916 147310498 147433824 147539992 147816036 147988292 148070542 148093952 148154288 148425726 148592576 148598024 149057554 149142686 149665588 149972788 150014492 150863054 150908454 151030068 151044622 151108236 151218242 151609814 151999396 152542626 152966530 153413432 153432848 153485148 153966766 154368914 154478286 154492166 154553092 155006218 155305266 155339878 155536474 155650426 155778562 156171526 156203340 156468140 156519708 156625064 156756400 156789840 156978838 157374268 157541220 157923226 158472238 158696888 158831096 159214418 159509138 159784822 159784836 159794566 159800918 160146172 160228242 160325616 160607310 160998114 161569668 161571504 161588716 161619620 161706626 162817576 162850104 162874590 162950466 163044252 163152818 163193584 163214942 163359994 163585288 163666380 163820256 163821336 163838506 163871194 164440734 164660428 164800594 164922680 165036358 165258594 165361824 165427494 165430644 166052226 166277052 166288612 166393356 166397330 166609122 166964502 167206862 167604930 167845698 168576546 168602250 168885632 169059224 169299904 169369502 169929578 170626040 170982934 171128300 171518672 171610156 171677924 172004036 172026454 173343810 173561300 173717408 173962482 174103532 174142738 174534362 174697724 174728608 175200596 175271418 175482140 176085282 176207346 176799404 177129922 177296064 177319028 177398652 177648552 177775606 177796222 178045832 178086108 178311240 178435022 178437884 178743858 179913814 180002474 180045220 180084608 180111908 180455838 180680920 181302244 181913260 181969816 182166824 182252536 183157240 183383118 183392536 183591732 183839694 184119204 184310672 184317182 184523024 184653266 184814078 184835362 184855564 185015722 185110536 185248324 185411044 187007398 187184006 187231212 187330820 187584550 187643362 187731580 187961358 188646712 188655374 188766416 189240324 189411830 190144032 190187176 190309640 190810274 191194450 191567332 191678526 192606308 192651588 192866222 193247784 193935716 194159546 194202254 194263106 194584114 194644872 194730404 194819864 194911702 195048992 195834796 195950620 196687752 196703802 196722548 197018872 197197506 197212998 197230100 197352408 197607368 197752702 198319118 198320982 198402358 199502780 199971120 200053318 200280100 200433382 200459670 200519642 201239624 201249512 201389466 201536524 201593074 202045732 202114688 202251688 202391964 202515696 203238918 203250558 203275588 204016062 204079052 204382086 204695540 205010004 205150506 205160722 205339678 205963322 205990406 206021166 206230080 206473754 206585726 206594738 206640054 206709064 207213640 207264358 207296788 207445740 207514736 207753480 207985150 208003690 208236434 208352366 208374066 208392300 208497360 208565926 209101202 209108558 209385420 209494470 209637998 209839940 209917216 210088618 210160342 210397166 210434680 210564358 210908700 211326826 211407740 211448294 211719438 212121206 212497738 212838152 212862096 212865234 212894100 212912634 213151104 213162592 213425082 213580840 213656000 213736552 213879170 214059556 214134178 214321816 214403112 214814516 214992758 215004526 215237318 215462154 215717854 215783788 215945398 215949788 216018002 216027436 216039994 216084296 216307766 217170570 217176690 217423702 217458668 217559364 217820568 218012734 219331584 219430370 219447698 219525472 219556482 219984494 220288248 220317996 220325976 220838206 220956326 221008432 221174400 221325712 221330854 221528336 221636362 222486400 222593516 222888506 222996490 223010262 223074802 223490796 224072278 224249932 224330804 224347630 224635814 225124888 225580118 226100602 226249042 226341130 226453444 226639300 226710488 226782570 226881840 227009830 227135580 227239620 227406222 227669832 230267830 230275166 230396424 230655072 230663736 231295516 231583998 232050760 232485778 232796676 233034976 233349574 233447012 233559012 233903532 233937376 234291722 234307964 234385314 234523400 234566344 234661134 234806100 234962380 235108160 235566676 235577802 235947986 236240868 236417078 236500052 236602468 236924362 237108488 237185928 237260908 237601644 238109742 238168282 271643232 * 314187728 * 399866798 * 1000032472 * 1777034894 * 2022202116 *	PrimeGrid is also running a two-pass search on BOINC using Genefer starting from b=42597774 (which would give a million digit prime). As of 2nd August 2024, 909 primes have been found. 6 primes (*) were reported by independent searchers
	As of 2nd August 2024, the leading edge of this search is 238361874.

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GFN Prime Search Status: n=18

As of 2nd August 2024, there are 121 known primes of the form b^2^18+1 = b^262144+1.

The following values of b give primes:

b	Range status
24518 40734 145310 361658	Yves Gallot's GFN Prime Search tested several ranges up to b=589708 using Proth.exe but did not find any primes. In 2008, Stephen Scott reported 1 prime: 24518^262144+1, found using Proth.exe. Starting in 2011, PrimeGrid ran a single-pass search on PRPNet, using Genefer, LLR and PFGW, and found the other 3 primes. A full double-check of this range by PrimeGrid using Genefer on BOINC was completed in August 2015.
525094 676754 773620	This range has been searched by PrimeGrid partly on PRPNet using Genefer, LLR and PFGW and partly on BOINC using Genefer. A total of 3 primes were found A full double-check of this range by PrimeGrid using Genefer on BOINC was completed in August 2015.
1415198 1488256 1615588 1828858 2042774 2514168 2611294 2676404 3060772 3547726 3596074 3673932 3853792 3933508 4246258 4489246 5152128 5205422 5828034 6287774 6291332 8521794 8883864 9125820 9450844 9750938 9812766 10578478 10627360 10793312 10829576 10979776 11081688 12189878 12304152 12529818 12582496 12959788 13039868 13553882 13640376 13911580 14103144 14399216 14741470 15417192 15859176 15913772 16048460 16769618 17191822 * 18395930 * 19322744 19527922 19859450 20105956 20543682 20710506 20866766 22470828 22479752 22480000 22790808 22984886 23479122 23591460 24429706 24678636 25333402 25461468 25635940 25690360 25875054 26128000 26640150 27615064 27789002 28004468 28259150 28342134 29097000 29333122 29353924 29445800 29614286 29645358 30941436 31371484 32067848 32171198 32497152 33061466 33491530 33798406 34443124 35196086 36210400 36717890 36748386 36778106 37047448 37349040 37689944 37700936 37787006 37986650 38108804 38214850 38738332 38786700 38786786 39164812 39896728 40460760	PrimeGrid ran a two-pass search of this range on BOINC using Genefer starting in November 2015, finding 112 primes. 2 primes (*) were reported by independent searchers
	PrimeGrid is currently running a two-pass search on BOINC using Genefer. As of 2nd August 2024, the trailing edge is b=40294414 and the leading edge is b=40514928.

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GFN Prime Search Status: n=19

As of 2nd August 2024, there are 19 known primes of the form b^2^19+1 = b^524288+1.

The following values of b give primes:

b	Range status
75898 341112 356926 475856 1880370 2061748 2312092 2733014 2788032 2877652 2985036 3214654 3638450 4896418 5897794 * 6339004 8630170 9332124 10913140	Starting in 2011, PrimeGrid ran a single-pass search on PRPNet, using Genefer, LLR and PFGW, and found 1 prime. A full double-check of this range was then carried out by PrimeGrid using Genefer on BOINC. The range was extended with a two-pass search on BOINC using Genefer, finding 17 primes. 1 prime (*) was reported by independent searchers
	A two-pass search on BOINC using Genefer is currently running. As of 2nd August 2024, the trailing edge is b=10849174 and the leading edge is b=11435570.

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GFN Prime Search Status: n=20

As of 2nd August 2024, there are 4 known primes of the form b^2^20+1 = b^1048576+1.

The following values of b give primes:

b	Range status
	Between November 2012 and June 2015, PrimeGrid ran a two-pass search on BOINC using Genefer, finding no primes up to b=720000.
919444 1059094 1951734 1963736	Starting in November 2015, PrimeGrid ran a two-pass search on BOINC using Genefer. As of 2nd August 2024, 4 primes have been found.
	A two-pass search on BOINC using Genefer is currently running. As of 2nd August 2024, the trailing edge is b=3447308 and the leading edge is b=3562874.

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GFN Prime Search Status: n=21

As of 2nd August 2024, there are 0 known primes of the form b^2^21+1 = b^2097152+1.

b	Range status
	Between September and November 2015, PrimeGrid ran a two-pass search on BOINC using Genefer, finding no primes up to b=1350.
	A two-pass search on BOINC using Genefer is currently running. As of 2nd August 2024, the trailing edge is b=1479664 and leading edge is b=1540046.

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GFN Prime Search Status: n=22

As of 2nd August 2024, there are 0 known primes of the form b^2^22+1 = b^4194304+1.

b	Range status
	Between February 2012 and November 2015, PrimeGrid ran a two-pass search on BOINC using Genefer, finding no primes up to b=54650.
	A two-pass search on BOINC using Genefer is currently running. As of 2nd August 2024, the trailing edge is b=357186 and the leading edge is b=377222.
	Between the leading edge of the previous range and b=846402, no primes are known.
	PrimeGrid is also running a two-pass search on BOINC using Genefer starting from b=846404 (which would give a world-record prime). As of 2nd August 2024, no primes have been found.
	As of 2nd August 2024, the trailing edge is b=1173844 and the leading edge of this search is 1200840.

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