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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 12th August 2022, there are 2948 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 132307068 132362052 132438554 132779816 133172694 133173648 133254120 133260836 133456286 133463856 133520240 133737568 133746878 133772004 133777458 133982700 134002050 134094794 134137784 134158218 134188934 134338750 134433148 134525750 134661120 134763136 134774502 134816082 134836274 134879398 134892668 134958534 134984916 135038646 135138484 135487184 135545788 135651244 135830526 135902608 135904858 135908104 136031644 136289322 136435090 136567848 136637624 136660406 136682352 136691734 136699650 136886522 136888478 136951538 136972034 137006170 137018148 137081180 137081730 137119120 137148446 137211778 137257978 137366688 137507442 137557074 137802120 137928332 137984918 138043852 138045532 138295938 138328250 138392358 138510438 138537172 138783258 138915246 139266342 139271916 139291268 139438732 139610150 139797606 139819134 140044508 140427660 140803850 141073806 141196216 141209178 141290360 141480056 141586052 141593740 141607284 141793204 141796680 141833750 142063164 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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182488560 182648138 183012534 183107954 183278330 183349152 183552858 183597648 183712260 183745392 184215238 184322386 184478710 184483248 184489872 184632832 184634868 184797304 185163598 185348142 185365392 185367024 185754914 185844690 186197914 186448488 186507466 186653202 186866120 186904122 187332718 187464822 187539432 187905136 187922612 187993282 188074644 188292328 188374856 188428752 188602178 188607700 188625786 188833028 188938256 188955634 189048614 189374278 189378650 189482602 189713064 189853818 189977566 190124156 190158960 190197854 190509212 190559618 190632480 190683246 190702572 190846458 191197636 191230070 191345318 191381564 191385768 191392506 191533888 191787568 192000288 192049398 192326456 192530436 192543010 192577062 193093670 193136666 193181478 193190512 193206632 193268336 193395216 193526634 193744168 193839444 193997396 194094796 194216696 194252346 194560988 194616190 194657308 194665256 194686730 194780408 195087050 195272764 195502106 195666888 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208477400 208501088 208546076 208703786 208884052 208885376 208953082 209094146 209166084 209198278 209260936 209309582 209313716 209338926 209630160 209920228 210070830 210099528 210149204 210223772 210442788 210486162 210654818 210659826 210788216 210897744 211118074 211178232 211233906 211282028 211563648 211732394 211837760 211944672 212064220 212097504 212100174 212310336 212382112 212396008 212404708 212474288 212523646 212789174 212804004 212812996 213029456 213079334 213187078 213250422 213286988 213338064 213509494 213543842 213766854 213790952 214274376 214501300 214573408 214657906 214663462 214690332 214758270 215003158 215050414 215185374 215309560 215462330 215535566 215548116 215680230 215916618 216198648 216241002 216370532 216466896 216517688 216593238 216672502 216703772 216717058 216734036 216823876 216830350 216860406 216927954 217022334 217085704 217265374 217267202 217490378 217565494 217604272 217892334 218167110 218216494 218225720 218290986 218598416 218660446 218768580 218771342 218860348 218921786 219004754 219170566 219452656 219496332 219622554 219651082 219697914 219847352 219977370 220129842 220149758 220245994 220333296 220518602 220594290 220631558 220718390 221090078 221587458 221635608 221660204 221777274 221787544 221991480 222529118 222532538 222578416 222584940 222698520 222953458 223016058 223289408 223301844 223503450 223574982 223694950 223736638 223899674 224029504 224057990 224272408 224320596 224504288 224663232 224725958 224776764 224806594 224811074 225007830 225136452 225263296 225387670 225490318 225592076 225736494 225820842 225840874 226078578 226129622 226296276 226435802 226543946 226552028 226646446 226657530 226854526 226919270 227063058 227107086 227421290 227457738 227604258 227609038 227720294 227779032 227811550 227865286 227900868 227930452 228005810 228098820 228168224 228548010 229016658 229045558 229368972 229590362 229617404 229645356 229722076 229727024 229760790 229935068 229953116 229958594 230172640 230369438 230615486 230653476 230713684 230744914 230884512 230967216 231115208 231154952 231222458 231253278 231264858 231303824 231395100 231444056 231547564 231685456 232098556 232122766 232259190 232282242 232527752 232585596 232610952 232660898 232713018 233145930 233263836 233333904 233350762 233366882 233375986 233546122 233552566 233581664 233663292 233824414 234040180 234161378 234213128 234223214 234240904 234302940 234490470 234611560 234853646 234994942 235001488 235060768 235150362 235156266 235287036 235323694 235529406 235624402 235968826 236132480 236135864 236310548 236450160 236827398 236951610 237051576 237107788 237167624 237175250 237225978 237322768 237384588 237420230 237539320 237574496 237594028 237763668 238080608 238106290 238109586 238155374 238193572 238484250 238836752 238852626 239048280 239102680 239292320 239949308 240160650 240188952 240190178 240353452 240502190 240525112 240564014 240614486 240714606 240714818 240756234 240813434 240822826 240826688 240927422 241061980 241064094 241072738 241079646 241211930 241295284 241457652 241878910 241961030 242172774 242229390 242405716 242437172 242515392 242550728 242746416 242984374 243272648 243528972 243655668 243698606 244102348 244204546 244211190 244380920 244404740 244535780 244645072 244658148 245046456 245079900 245174194 245314246 245328822 245349630 245380466 245385716 245393402 245425782 245658390 245786122 246156648 246299134 246356166 246357212 246558848 246611682 246721586 246843238 247119758 247127946 247511394 247712590 247801900 247842490 247867992 248275544 248465796 248547612 248555198 248602304 248684094 248743358 248766960 248773840 248985844 249001646 249056144 249125314 249231320 249334972 249421388 249538476 249564970 249628014 249636690 249681470 249705802 250058960 250930556 251057858 251073354 251178778 251200880 251240492 251329456 251407822 251425374 251431112 251544940 251622608 251719770 251760532 251871510 251910124 252067256 252216696 252250752 252265332 252319300 252442514 252506814 252569408 252614186 253177522 253265370 253323226 253381550 253402568 253415582 253516618 253828896 254020742 254271954 254300704 254422742 254442764 254584894 254604078 254606478 254880462 254997860 255045642 255114314 255274268 255526464 255620682 255722498 255733628 255751016 255851318 256089574 256206346 256350432 256364514 256420306 256425164 256443034 256465680 256640678 256839836 256855018 256884712 257005584 257107876 257274500 257373982 257444282 257548682 257662730 257834464 257885412 258120168 258478076 258588900 258776494 258919498 259153304 259173320 259205252 259286492 259679138 259684786 259920270 259979028 260068502 260147596 260185302 260268082 260320210 260333950 260373024 260593290 260889136 260912348 261181216 261244198 261304964 261345854 261648762 261767108 261781254 261798928 261913936 261930050 262016900 262100274 262162868 262385560 262388562 262477620 262620186 262671890 262679860 262694980 262780274 263043742 263093320 263118604 263301742 263411066 263473708 263556556 263665534 263754200 263802504 263974952 264122040 264247440 264331596 264355954 264368940 264389870 264445000 264448630 264538170 264656424 264810906 264923010 265023736 265037926 265070702 265120080 265135798 265168258 265168598 265235994 265365342 265384474 265517360 265545690 265574418 265992090 266180168 266457540 266457994 266468178 266673712 266827540 266940358 267148782 267197554 267584208 267597384 267744778 267762716 267829318 268020412 268029242 268029884 268133460 268177982 268413884 268552944 268936368 268948166 268985518 269031364 269130488 269140524 269186036 269518886 269709704 269785708 269865678 269939812 270922466 270972794 271064250 271186836 271296730 271385070 271628694 271781518 271847618 271938714 272251554 272503150 272831282 272917308 272937064 273013854 273209120 273399460 273607832 273762968 273849438 273855058 273968062 273979930 274056740 274132842 274142334 274183224 274254774 274288030 274320524 274491350 274537092 274555586 274699240 274732154 274822182 274902670 275108530 275214226 275540100 275577620 275625098 275828152 275888454 276281962 276363386 276611824 276615146 276633270 276986388 277152022 277217298 277275528 277443336 277504324 277530244 277530502 277677776 277688900 277843510 278096348 278139660 278208682 278240018 278661876 278706676 279380076 279801330 280001182 280006444 280030734 280197588 280319590 280357338 280443092 280586924 280617166 280656148 280658558 280773688 280876358 280889278 281096276 281309406 281426676 281532198 281648028 281785520 281824506 281848936 281997084 282292922 282319302 282386444 282544090 282719760 282773218 282848114 283149488 283220858 283384738 283410550 283428652 283526874 283954848 284326270 284387770 284467186 284516826 284554288 284767128 284795448 284865358 284936430 284966162 285085186 285158974 285236858 285421590 285517470 285700106 285917576 286167538 286311248 286350482 286353028 286382040 286795074 286889356 287268292 287302818 287330552 287338068 287458406 287743776 287812110 288026332 288064026 288097924 288243980 288248600 288600704 288644458 288662052 288871522 288878514 288916364 289038018 289123210 289219998 289417960 289442738 289496742 289692440 289696696 289751986 289991418 290098592 290156988 290324168 290407304 290428298 290588844 290592776 290829792 290851938 290999946 291259852 291391568 291533760 291631910 291639080 291651362 291699252 291770824 291773156 291832736 291895680 291986522 292102322 292434276 292465534 292566864 292582908 292717474 292778316 292804476 292840336 292923852 293082250 293198854 293247386 293280298 293389346 293481824 293489364 293509712 293609176 293647592 293688192 293982820 294066014 294105688 294138698 294199618 294250564 294383550 294547276 294580106 294617150 294842800 294876126 294876774 294907304 294917010 295293408 295458374 295537188 295800100 296078296 296141434 296186402 296234474 296327922 296355114 296550900 296581420 296641862 296682420 296776988 296938198 297061142 297122526 297299626 297328752 297356214 297711508 297997870 298172292 298174918 298178294 298212978 298285478 298343492 298453520 298471778 298565518 298612804 298800414 298935764 298985058 299073068 299088226 299122306 299171028 299423892 299463050 299631692 299718048 299785110 299847246 300136794 300253742 300576300 300633308 300719114 300832774 300850936 300880548 300912112 300989820 301126654 301143572 301174018 301180130 301469626 301552148 301554368 301659252 301801802 301886502 301976758 302034816 302086442 302122386 302257864 302287562 302304722 302494082 302566990 302647602 302685136 302732898 302759376 302876234 302894486 303030240 303095570 303105196 303234800 303378872 303382614	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer, finding 2754 primes. All b up to 302533820 have been checked as of 12th August 2022.
	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer. As of 12th August 2022, the leading edge is b=303522764.
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.

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GFN Prime Search Status: n=16

As of 12th August 2022, there are 1690 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 113743008 113743984 113766500 113821900 113856050 113899746 113912436 113930586 113950766 114065784 114119336 114250806 114277670 114302338 114387906 114630516 114681358 114698234 114722794 115157240 115220208 115268620 115294854 115347856 115354566 115357190 115408880 115457324 115707022 115709936 115797490 116249158 116462144 116501302 116572908 116701162 116720780 116911588 116954070 117048732 117457872 117686134 117701722 117805866 117874676 118050932 118147416 118192550 118264992 118270626 118589830 118641422 118708030 119032648 119063128 119199112 119298770 119418048 119452152 119491626 119624454 119690728 119717536 119738978 120186908 120681448 120749884 121000342 121075332 121086190 121140458 121237796 121238358 121281656 121372932 121568608 121857822 121974060 122011650 122264264 122354882 122691846 122700492 122745454 122809274 122873426 122938900 123104850 123133394 123364798 123388310 123440486 123507760 123590068 123999938 124389098 124490560 124575028 124583790 124698848 124703608 124801100 125045320 125238224 125418570 125469830 125472480 125489168 125515108 125540838 125564488 125772166 125961714 125988718 125998694 126041092 126171566 126416802 126474178 126681288 126713710 126749898 126861078 126867872 126973536 127023728 127034204 127201666 127252554 127405738 127951638 127973506 128132420 128144964 128210296 128212560 128375820 128445376 128565012 128663166 128866024 128965452 128990040 129047526 129053932 129232776 129254948 129320968 129358462 129420854 129448306 129574744 129630358 129640544 129697198 129750926 129790924 129811608 129834872 129984458 130060566 130181574 130271172 130408582 130452302 130585094 130612142 130660644 130897212 131105428 131123850 131130622 131255146 131419368 131450430 131691588 131714718 131728816 131775982 131796386 131814642 132003152 132120644 132186042 132266908 132285402 132358424 132372878 132385596 132429416 132488280 132970814 132987318 133048112 133065238 133140712 133215546 133271846 133334188 133350482 133400670 133433854 133476288 133555442 133593704 133629454 133718586 133853526 133931782 133971864 134014306 134117398 134343600 134346884 134584144 134624202 134695448 134719104 134819600 135052616 135237122 135367280 135579990 135731100 135805928 135811052 135915704 136030188 136268486 136292214 136342206 136440590 136632020 136637696 136787614 136884136 136992032 137017216 137160034 137162364 137461508 137591622 137657614 137781496 137817880 137877692 137907846 137963452 138484612 138554746 138628730 138688732 138710732 138793926 138973204 139061582 139065554 139082038 139138610 139145838 139168954 139241582 139275160 139295348 139462208 139530936 139878242 139948998 139976206 140069668 140173342 140182506 140278338 140561102 140563252 140596486 140825230 141127960 141159612 141176792 141368280 141477572 141821432 141868280 142015204 142036092 142293110 142306284 142505312 142563056 142701560 142840816 142911028 143155562 143228594 143258560 143476918 143620534 143676278 143735714 143862854 143877852 143963966 143986848 144084846 144086288 144128416 144248374 144386092 144470894 144485588 144568054 144585734 144675274 144684440 144716102 144756106 144882226 144973524 144973634 145016656 145066756 145072510 145585776 145932888 146425914 146504914 146653986 146680212 146780644 146826798 146924772 146925950 146933674 147170456 147202056 147208122 147382164 147512094 147570204 147761138 147796196 147834014 148221832 148275334 148302820 148366966 148402470 148806450 148896558 149265044 149465356 149491768 149495200 149578510 149579792 149621682 149814764 149957710 149996492 150034754 150061008 150078542 150098876 150132248 150142948 150482286 150591018 150644616 150722260 150809098 150994194 151009320 151336498 151514532 151556938 151648712 151770050 152024526 152143536 152246980 152257544 152329200 152482638 152702128 152866426 152899418 152967836 153012732 153431116 153583464 153760922 154011386 154210752 154546726 155253336 155257984 155750578 155788986 155883376 155990522 156384608 156400210 156413292 156414678 156491914 156566756 156606194 156614630 156828668 156830996 156882252 157080152 157254464 157372184 157479388 157568692 157582320 157640030 157696604 157778292 157792502 157878038 158097404 158184126 158345700 158375834 158534146 158595406 159424086 159548422 159660244 159679014 159680478 160144132 160186476 160278312 160280252 160300770 160459326 160477270 160652984 160896206 161019960 161040604 161155178 161284686 161336170 161336572 161373520 161390048 161533952 161552358 161652768 161729494 161812882 161892534 161961620 162244902 162341418 162423200 162494828 162512058 162521980 162722282 162841028 162936076 162990842 163096432 163148472 163241232 163335900 163384952 163415294 163667476 163714676 163837248 163984990 164331980 164410268 164541530 164585942 164607472 164634446 164664420 164688674 164947166 164961074 164975524 165006098 165035994 165042714 165071282 165107060 165119758 165182046 165300848 165693636 165758598 166133392 166199362 166245178 166444082 166579910 166695390 166707658 166787224 166987494 167061856 167217958 167333098 167367704 167392398 167552298 167555208 167692050 167786168 167811262 167952588 168070968 168158620 168272988 168392570 168441316 271018852 * 350006744 * 399878576 * 12192710656 * 1814570322977518 * 1814570322984178 *	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer, finding 1621 primes. 10 primes (*) were reported by independent searchers. As of 12th August 2022, all b up to 168008818 have been checked.
	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer. As of 12th August 2022, the leading edge is b=168568074.

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GFN Prime Search Status: n=17

As of 12th August 2022, there are 571 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 271643232 * 314187728 * 399866798 *	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 12th August 2022, all b up to 113619146 have been checked and 344 primes have been found. 3 primes (*) were reported by independent searchers
	As of 12th August 2022, the leading edge of this search is 113887924.

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GFN Prime Search Status: n=18

As of 12th August 2022, there are 54 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	PrimeGrid ran a two-pass search of this range on BOINC using Genefer starting in November 2015, finding 47 primes.
	PrimeGrid is currently running a two-pass search on BOINC using Genefer. As of 12th August 2022, the trailing edge is b=15876918 and the leading edge is b=15911538.

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GFN Prime Search Status: n=19

As of 12th August 2022, there are 14 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	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 13 primes. As of 12th August 2022, all candidates up to b=5397196 have been double-checked.
	A two-pass search on BOINC using Genefer is currently running. As of 12th August 2022, the trailing edge is b=5397212 and the leading edge is b=5410906.

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GFN Prime Search Status: n=20

As of 12th August 2022, there are 2 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	Starting in November 2015, PrimeGrid ran a two-pass search on BOINC using Genefer. As of 12th August 2022, all b up to 1941168 have been checked and 2 primes have been found.
	A two-pass search on BOINC using Genefer is currently running. As of 7th July 2018, the leading edge is b=1129578. No primes have been found.

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GFN Prime Search Status: n=21

As of 12th August 2022, 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 12th August 2022, the leading edge is b=818824.

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GFN Prime Search Status: n=22

As of 12th August 2022, 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 12th August 2022, the trailing edge is b=226278 and the leading edge is b=233620.
	Between the leading edge of the previous range and b=846402, no organised testing has been carried out, and 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 12th August 2022, all b up to 969366 have been checked and no primes have been found.
	As of 12th August 2022, the leading edge of this search is 975754.

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