PRP Records

Probable Primes Top 10000

(293510 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
55012^365838-461267110129Enzo Doria07/2015
550230152^4491+4491^30152110126Hans Havermann11/2020
550310^110111+464019110112Patrick De Geest05/2021
550410^110111-40001110111Robert Price01/2021
55052^365763-6555110106Lelio R Paula04/2017
5506(2^365689+2^182845+1)/511008311/2006
55072^365666-459161110077Enzo Doria05/2015
55083*10^110076-7110077Robert Price08/2015
550913^98785-72110041Lelio R Paula03/2017
5510(25^78707+1)/26110027Robert Price06/2013
5511(7*10^110027-277)/9110027Robert Price02/2022
5512(16*10^110014-73)/3110015Robert Price07/2020
5513(7*10^110006-151)/9110006Robert Price02/2018
55146^141361-7110001Lelio R Paula11/2014
551520^84536+81109984Lelio R Paula03/2017
55165*2^365347-9109982Lelio R Paula09/2014
55179*6^141303+7109957Lelio R Paula11/2014
551827635^9522+9522^27635109953Hans Havermann11/2020
551978^58099+77109929Norbert Schneider02/2015
55202*10^109928-7109929Robert Price10/2015
552130580^3933+3933^30580109927Hans Havermann11/2020
552226380^14689+14689^26380109926Hans Havermann11/2020
5523(2^365161+1130)/2109925Stefano Morozzi09/2020
5524(27*2^365137-1)/2021109916Lelio R Paula03/2014
5525(4441*29^75152-24)/7109905Curtis Bright05/2015
5526(2^365087+7)/6015109899Lelio R Paula01/2014
5527(2^365069+3774)/2109897Stefano Morozzi02/2021
552829652^5083+5083^29652109894Mark Rodenkirch10/2020
5529(2^365049+722)/2109891Stefano Morozzi09/2020
5530(35*10^109888-89)/9109889Robert Price02/2022
553118^87533-11109878Lelio R Paula04/2017
55322^364982-5109871Henri Lifchitz04/2006
55333*10^109861+59109862Robert Price08/2018
55345*10^109860-69109861Robert Price02/2021
55352^364936-1867979109857Enzo Doria04/2016
553627013^11652+11652^27013109846Hans Havermann10/2020
55372^364867-112087109836Enzo Doria06/2014
55384^182415-85061109825Mike Oakes06/2011
5539(2^364809+1034)/2109819Stefano Morozzi09/2020
5540(53*10^109809-287)/9109810Robert Price02/2022
5541(52*10^109807-133)/9109808Robert Price09/2021
554225708^18675+18675^25708109806Hans Havermann10/2020
5543(17^89227+16^89227)/33109788Robert Price08/2013
55442^364687-187109782Lelio R Paula01/2012
55452^364644+67109769Lelio R Paula01/2012
5546(9787*2^364625-1)/24947109763Lelio R Paula05/2015
5547(2^364616+5)/9109760Lelio R Paula01/2014
5548(55*10^109759+89)/9109760Robert Price03/2019
5549(14*32^72921+4171)/31109757Eric Chen04/2023
555012^101694+73109747Lelio R Paula03/2017
555113^98518-66109744Lelio R Paula03/2017
5552(8*10^109721-269)/9109721Robert Price09/2021
55532^364478-113261109719Enzo Doria07/2014
5554(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
5555(24737*2^364454+1)/3109716Lelio R Paula07/2014
555627814^8777+8777^27814109681Hans Havermann10/2020
5557(62*10^109673+1)/9109674Serge Batalov11/2010
55583^229824+340109654Lelio R Paula03/2017
5559(16623*33^72206-8095)/16109649Eric Chen05/2023
5560(2*10^109645-71)/3109645Robert Price12/2017
55612^364169-112813109626Enzo Doria06/2014
556228822^6359+6359^28822109622Hans Havermann11/2020
556310^109615+21109616Lelio R Paula03/2017
556410^109615-456267109615Patrick De Geest03/2017
55652^364094-113109604Lelio R Paula01/2012
556625251^21898+21898^25251109600Hans Havermann11/2020
5567(4^182026+11)/3109591Robert Price02/2017
55682^364041-6883109588Lelio R Paula09/2011
556912^101545+11109586Lelio R Paula03/2017
557026536^13475+13475^26536109582Hans Havermann11/2020
55712^363842-2787101109528Enzo Doria03/2016
5572(2^363812+3570)/2109519Stefano Morozzi09/2020
5573(22699*2^363782+1)/763109511Lelio R Paula07/2014
55742^363769+5711109506Lelio R Paula04/2017
5575(31*2^363748+1)/49109499Lelio R Paula03/2014
5576(2^363670+100280245065)109476Paul Bourdelais05/2022
5577p(22245)#/2-8109462Robert Price01/2017
55782^363556+55109442Lelio R Paula01/2012
5579(509*10^109414+31)/9109416Robert Price08/2022
5580(2^363437+1682)/2109406Stefano Morozzi09/2020
5581(55459*2^363411+1)/81109401Lelio R Paula07/2014
55822^363406+1871569109397Enzo Doria05/2016
5583(2^363370+1338)/2109385Stefano Morozzi02/2021
5584(2^363349+7)/9109378Lelio R Paula01/2014
55853^229236+100109374Lelio R Paula03/2017
5586(2^363315+3258)/2109369Stefano Morozzi02/2021
55872^363268-58695109355Lelio R Paula04/2017
55882^363191-112321109332Enzo Doria06/2014
558926231^14718+14718^26231109327Hans Havermann10/2020
559025461^19672+19672^25461109326Hans Havermann10/2020
55914*10^109316-63109317Robert Price10/2018
55922^363120+3109311Donovan Johnson04/2006
5593(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
55942^363042-114641109287Enzo Doria04/2015
55952^363020-112793109280Enzo Doria06/2014
5596(85*10^109253+203)/9109254Robert Price09/2020
559724990^23431+23431^24990109202Hans Havermann10/2020
5598(2^362746+3738)/2109198Stefano Morozzi09/2020
5599(2^362716+1282)/2109189Stefano Morozzi01/2021
5600(67607*2^362695+1)/70499109183Lelio R Paula07/2014
560125060^22737+22737^25060109180Hans Havermann10/2020
5602(9*2^362644+1)/5109167Lelio R Paula03/2014
56035^156181+38109166Lelio R Paula02/2017
5604(2^362623+3618)/2109161Stefano Morozzi09/2020
560525138^21993+21993^25138109157Hans Havermann10/2020
56064*10^109142+91109143Robert Price08/2018
56073^228750+68109142Lelio R Paula03/2017
5608(2^362561+786)/2109142Stefano Morozzi09/2020
5609(23*10^109113+61)/3109114Robert Price01/2022
56102*10^109100-49109101Robert Price09/2020
5611(10223*2^362376+1)/9109090Lelio R Paula07/2014
561265^60167-64^60167109078Robert Price08/2013
56137*3^228589-2109066Lelio R Paula09/2014
561424874^24243+24243^24874109063Hans Havermann11/2020
5615(17*10^109059-161)/9109060Robert Price02/2021
561629158^5495+5495^29158109050Hans Havermann11/2020
5617(78557*2^362188+1)/189109033Lelio R Paula07/2014
56182*7^129008+9109025Lelio R Paula11/2014
561988*10^109022+7109024Robert Price03/2020
562028194^7337+7337^28194108985Hans Havermann10/2020
5621(5*10^108960+91)/3108961Robert Price04/2018
56222^361957+76367108960Enzo Doria05/2016
56232^361873-1411108935Yves Minet01/2013
5624(24737*2^361857+1)/35108933Lelio R Paula07/2014
5625115^52842-114108892Norbert Schneider07/2018
562613^97745-24108883Lelio R Paula03/2017
5627(2^361696+2562)/2108882Stefano Morozzi09/2020
562817^88475+8108864Lelio R Paula04/2017
56292^361567+51108843Lelio R Paula01/2012
56302^361563-109501108842Enzo Doria04/2014
563112^100852+83108838Lelio R Paula03/2017
56322^361497+767108822Lelio R Paula01/2012
563328019^7630+7630^28019108785Hans Havermann10/2020
563424723^24758-24758^24723108765Norbert Schneider11/2020
56352^361280-112349108757Enzo Doria06/2014
56362^361271-5955108754Lelio R Paula04/2017
563712^100757+19108736Lelio R Paula03/2017
563825368^19333+19333^25368108735Hans Havermann11/2020
5639(2^361195+3618)/2108731Stefano Morozzi09/2020
56402^361153-111546435108718Paul Bourdelais10/2021
564114^94849-61108710Lelio R Paula05/2017
564227267^9700+9700^27267108708Hans Havermann11/2020
5643(19^85009-5^85009)/14108705Robert Price07/2013
564424832^23853+23853^24832108704Hans Havermann11/2020
564527502^8963+8963^27502108701Hans Havermann11/2020
564625807^16278+16278^25807108689Hans Havermann11/2020
5647(11*2^361027+1)/40463108677Lelio R Paula03/2014
56482^360973+1299108664Lelio R Paula04/2017
56492^360959-109101108660Enzo Doria04/2014
56506*5^155454+7108659Lelio R Paula11/2014
565110^108656+79108657Lelio R Paula02/2017
565210^108656-50001108656Patrick De Geest03/2017
56532^360918-35108648Lelio R Paula01/2012
56544*10^108646-47108647Robert Price10/2021
5655(11*2^360886-1)/7108638Lelio R Paula03/2014
56563*10^108624-49108625Robert Price07/2018
5657(2^360831+666)/2108621Stefano Morozzi09/2020
5658(134*10^108610+7)/3108612Robert Price02/2020
56592*10^108609+29108610Robert Price02/2021
5660(10^108604+7)/71/191108600Alfred Reich06/2021
5661(2^360742+3222)/2108594Stefano Morozzi09/2020
56622^360706-458903108584Enzo Doria04/2015
566331112^3087+3087^31112108567Hans Havermann11/2020
56642^360641-113185108564Enzo Doria07/2014
5665(29*10^108559-71)/3108560Robert Price07/2021
56662^360618+75019108557Enzo Doria04/2016
56672^360607-216367108554Harrison Mesh06/2022
5668(14*10^108545-221)/9108546Robert Price04/2018
5669(44*10^108544-233)/9108545Robert Price01/2019
56703*5^155286+2108541Lelio R Paula11/2014
56717^128422+4108530Lelio R Paula11/2014
56727^128421-80108529Lelio R Paula03/2017
56732^360497+53807108521Yves Minet07/2010
56742^360468-4559108512Yves Minet03/2019
5675(2^360451+578)/2108507Stefano Morozzi09/2020
56762^360366+1459108481Lelio R Paula09/2011
56772^360364-1499108481Yves Minet05/2013
567825662^16871+16871^25662108477Hans Havermann10/2020
567925009^21748+21748^25009108475Hans Havermann10/2020
568014^94642-23108472Lelio R Paula05/2017
5681(197*10^108446-11)/3108448Robert Price03/2020
5682(2^360229+1290)/2108440Stefano Morozzi01/2021
56834*10^108412+9108413Robert Price05/2015
5684(259*10^108409-1)/3108411Robert Price12/2020
5685(2^360122+1194)/2108408Stefano Morozzi09/2020
5686133^51042-132108406Norbert Schneider02/2019
56872^360093-351103108399Enzo Doria06/2015
56882^360042+723108384Lelio R Paula01/2012
568985^56164-2108364Lelio R Paula10/2013
56902^359937-29323108352Enzo Doria07/2015
5691(2^359922+1762)/2108348Stefano Morozzi09/2020
5692(2^359903+758)/2108342Stefano Morozzi09/2020
56932^359898-19997108341Enzo Doria06/2013
5694(2^359886+2122)/2108337Stefano Morozzi09/2020
56952*5^154948-7108305Lelio R Paula11/2014
569610^108303+13108304Lelio R Paula02/2017
569710^108303-207959108303Patrick De Geest03/2017
56987*10^108300+69108301Robert Price07/2019
56992^359730+753108290Lelio R Paula12/2011
5700(8*10^108273+13)/3108274Robert Price06/2018
57012^359650-19797108266Enzo Doria06/2013
5702(47*10^108261+259)/9108262Robert Price03/2022
570391^55259-90^55259108255Robert Price07/2015
570410^108251+85749108252Patrick De Geest02/2021
570510^108251-50000000001108251Robert Price12/2020
570610^108251-252081108251Patrick De Geest02/2021
57074*10^108238-71108239Robert Price12/2018
57083^226845+68108233Lelio R Paula03/2017
570931836^2509+2509^31836108227Hans Havermann10/2020
57105^154822-12866108216Enzo Doria05/2014
5711(9*2^359480+1)/5108215Lelio R Paula03/2014
57122^359454-177108207Lelio R Paula12/2011
5713(19*10^108184+191)/3108185Robert Price05/2019
57146^139022-59108181Lelio R Paula02/2017
5715(19*10^108176-43)/3108177Robert Price05/2019
57162^359352-179108176Lelio R Paula12/2011
57172^359338-1858781108172Enzo Doria04/2016
571812^100230-97108167Lelio R Paula03/2017
571927028^10043+10043^27028108163Hans Havermann11/2020
5720(25*2^359297-1)/137108159Lelio R Paula03/2014
5721(2^359262-509203)/9108148Lelio R Paula12/2013
572226583^11702+11702^26583108147Hans Havermann11/2020
5723(3^226648-8)/352715633108131Lelio R Paula12/2013
57246^138956-59108129Lelio R Paula02/2017
57252^359184+30285108126Lelio R Paula04/2017
572613^97059+10108119Lelio R Paula03/2017
57272^359137-81108112Lelio R Paula12/2011
5729(15185*2^359105-1)/567108103Lelio R Paula05/2015
57282^359110-11655108103Lelio R Paula04/2017
57302^359069-933075108091Paul Bourdelais06/2021
573126227^13222+13222^26227108090Hans Havermann10/2020
57328*6^138875+5108067Lelio R Paula11/2014
57332^358987-216919108066Enzo Doria05/2014
5734(2^358977+2714)/2108063Stefano Morozzi09/2020
573539^67918-67918^39108062Norbert Schneider02/2017
573624^78283-1*78283^24108048Dylan Delgado12/2019
573725282^18767+18767^25282108040Hans Havermann11/2020
57382^358785-16933108006Enzo Doria05/2013
5739(2^358783+5)/33383108000Lelio R Paula12/2013
57406^138770-77107985Lelio R Paula02/2017
5741(2^358727-1017)/94178479107980Lelio R Paula12/2013
574210^107976+19107977Lelio R Paula02/2017
574310^107976-202103107976Patrick De Geest03/2017
57442^358684+75781107975Enzo Doria04/2016
574524928^21411+21411^24928107955Hans Havermann10/2020
574699^54094+2107952Lelio R Paula06/2013
5747(2^358583-9)/391107942Lelio R Paula12/2013
5748(2^358562+838)/2107938Stefano Morozzi02/2021
57492^358538+55107931Lelio R Paula12/2011
57502^358517-109009107925Enzo Doria03/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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