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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.

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 18th January 2021, there are 2160 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 17746856 17821911 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 37723960 37919898 37955742 38166298 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 41022582 41015312 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 44605360 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 47595950 47569014 47651824 47946238 47984028 48066320 48096646 48135770 48149268 48157002 48062530 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 57317268 57361710 57390028 57565718 57591252 57743714 57759468 57837322 57833524 57978144 58228590 58306260 58430022 58446698 58641604 58796050 58836382 58896930 59213912 59241586 59473128 59581078 59587840 59850740 59858148 59909644 60143970 60155332 60197028 60327268 60395700 60672378 60693660 60693544 60737802 60781272 60838920 60852976 61123304 61250164 61281396 61374756 61377584 61388912 61445596 61586622 61608268 61605660 61696642 61715470 61722492 61777432 61862814 61961696 61975666 61978760 62032036 62094976 62105082 62137258 62318154 62327894 62422592 62537488 62647522 62751960 63044270 63345338 63777050 63810168 63806314 63832458 63874536 63930486 63972944 64162084 64353012 64365734 64714688 64741068 64713412 64760412 64804044 64855922 64867956 64898128 64985968 65054868 65068286 65089562 65093132 64714688 65266240 65320658 65344212 65387276 64714688 65514106 65520628 65529328 65772334 65783514 66178446 66193158 66353184 66489992 66581228 66619406 66702198 66732020 66794266 66797836 66880828 66994438 67131166 67543536 67647742 67804828 67799868 67840636 67889194 68002908 68207494 68274864 68436968 69190662 69204292 69187606 69500606 69541996 69789832 69858944 69945900 69043610 70122604 68962894 69756930 70246422 70272906 69753964 70440684 70464022 70495740 70048258 70526044 70730318 70604480 70501724 71049528 71072080 71266866 71270310 71317522 71396914 71424294 71402554 71717128 71924716 71990306 72039366 72078378 72220632 72018316 72507322 72517714 71846790 72557802 72871570 71566294 73258252 73344746 73490616 73568254 73633862 73605148 73702246 73908134 73849266 74177258 74184902 74175006 74395440 74423074 74462706 74761736 75110388 75144604 75170884 75121068 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 80654880 80627682 80721324 80885288 80949468 81092448 81248152 81204086 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 85962194 86085882 86197780 86266356 86316726 86357100 86390618 86416078 86560194 86559824 86786930 86852980 86907000 86906874 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 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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 151083578 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171681228 171692768 171811808 171826892 171965040 172107186 172318768 172601918 172641742 172696852 172769604 172847008 173248698 173267706 173368080 173640596 173685354 173718608 173853348 174061342 174118440 174245308 174252102 174275122 174371730 174380082 174582874 174604448 174669366 174681314 174762710 174890458 174951626 175042602 175155192 175196794 175248222 175491890 175651330 175694662 175723762 175942068 176103256 176148024 176358228 176454914 176511484 176681750 176729830 176745036 176796218 177006900 177014132 177096534 177289456 177305380 177528738 177554196 177611308 177710394 178077154 178125558 178194054 178223696 178656772 178914064 179020582 179055642 179170416 179192400 179277868 179354082 179457246 179496234 179623214 179693644 179809354 179952868 180056322 180234942 180375872 180407980 180794420 180939248 181097570 181139822 181370268 181398836 181469422 181516468 181666260 181735254 181966256 182101004 182152210 182163938 182197872 182297502 182470778 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 195806294 195888104 195894632 195937772 196035674 196061666 196074590 196170604 196189694 196231736 196272640 196299442 196354878 196409928 196461026 197173584 197357162 197411010 197424572 197605592 197656450 197851350 198373324 198498956 198511622 198596176 198766506 198811474 198898472 198925434 199079870 199096326 199208578 199320290 199467184 199740412 199989932 200295018 200309478 200440162 200516136 200845256 201345470 201530518 201592624 201685334 201740626 201818678 201919632 202482090 202550546 202658588 202786452 202898294 203417192 203694172 204196470 204411662 204437438 204615740 204745774 204841922 204889424 205116804 205136186 205467922 205499098 205591626 205692642 205823688 206118026 206325772 206346962 206355000 206482186 206519972 206706230 206879364 206897602 206987022 207006166 207063722 207233034 207362990 207368822 207472422 207652136 207747014 207783296 207915546 208013448 208025122 208121164 208123846 208178000 208245116 208256586 208412214 208431222 208437040 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 216734036 3292665455999520712131951625894 * 3292665455999520712131951642528 *	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer, finding 1966 primes. All b up to 212863570 have been checked as of 18th January 2021.
	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer. As of 18th January 2021, the leading edge is b=216777840.

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GFN Prime Search Status: n=16

As of 18th January 2021, there are 1055 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 5645768 5350408 5416598 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 17716338 17757426 17629398 * 17655444 * 17684828 * 17770454 17931126 18255116 18364744 18387422 18612352 18682542 18788582 19149988 19165998 19194688 19415886 19432158 19451454 19502212 * 19514276 19810832 19916902 20109598 20317650 20338906 20338564 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 22740816 22738600 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 27548300 27625562 27639120 27678634 27738902 27768276 28027008 28099080 27441534 28413758 28487278 28580718 28768058 29048042 29097708 29202654 29247740 29340732 29350290 29500622 29509260 29501096 29585874 29723118 29863462 30046920 30101988 30216696 30250088 30328508 30376064 30799220 30813412 30877996 30946880 31125356 31154730 31380744 31342854 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 38670832 38659632 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 271018852 * 1814570322977518 * 1814570322984178 *	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer, finding 988 primes. 7 primes (*) were reported by independent searchers. As of 18th January 2021, all b up to 102143724 have been checked.
	Starting in December 2015, PrimeGrid is running a two-pass search on BOINC using Genefer. As of 18th January 2021, the leading edge is b=102575326.

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GFN Prime Search Status: n=17

As of 18th January 2021, there are 298 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	PrimeGrid is running a two-pass search of this range on BOINC using Genefer starting in October 2015, finding 103 primes.
	PrimeGrid is currently running a two-pass search on BOINC using Genefer. As of 18th January 2021, the trailing edge is b=14686990 and the leading edge is b=22292134.
	Between the leading edge of the previous range and b=42658772, no organised testing has been carried out, and no primes are known.
42654182 43163894 43165206 44049878 44085096 44330870 44438760 44919410 45315256 45570624 46077492 46371508 46385310 46413358 46730280 46736070 46776558 47090246 48273828 48370248 48643706 49038514 49090565 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 271643232 *	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 18th January 2021, all b up to 22173002 have been checked and 183 primes have been found. 1 prime (*) was reported by independent searchers
	As of 18th January 2021, the leading edge of this search is 82357564.

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GFN Prime Search Status: n=18

As of 18th January 2021, there are 44 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	PrimeGrid ran a two-pass search of this range on BOINC using Genefer starting in November 2015, finding 37 primes.
	PrimeGrid is currently running a two-pass search on BOINC using Genefer. As of 18th January 2021, the trailing edge is b=12031136 and the leading edge is b=12867308.

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GFN Prime Search Status: n=19

As of 18th January 2021, there are 13 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	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 12 primes. As of 18th January 2021, all candidates up to b=4095136 have been double-checked.
	A two-pass search on BOINC using Genefer is currently running. As of 18th January 2021, the trailing edge is b=4095148 and the leading edge is b=4251974.

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GFN Prime Search Status: n=20

As of 18th January 2021, 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 18th January 2021, all b up to 1497744 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 18th January 2021, 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 18th January 2021, the leading edge is b=654346.

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GFN Prime Search Status: n=22

As of 18th January 2021, 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 18th January 2021, the trailing edge is b=176740 and the leading edge is b=189586.
	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 18th January 2021, all b up to 918690 have been checked and no primes have been found.
	As of 18th January 2021, the leading edge of this search is 926670.

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