PRP Records

Probable Primes Top 10000

(288949 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 ?
5251(3*29^72089-1075)/4105423Curtis Bright05/2015
5252(2^350187+2658)/2105417Stefano Morozzi09/2020
52532^350139-109009105403Enzo Doria04/2014
5254(2^350129+3026)/2105400Stefano Morozzi09/2020
5255(2^350097+2070)/2105390Stefano Morozzi09/2020
52563*5^150763+4105380Lelio R Paula11/2014
525712^97643+91105375Lelio R Paula02/2017
52586*5^150744-7105367Lelio R Paula11/2014
5259(2^350018+2074)/2105366Stefano Morozzi09/2020
52604*10^105364-39105365Robert Price09/2020
52622^349996-112169105360Enzo Doria06/2014
5261(2^349997+3702)/2105360Stefano Morozzi09/2020
5263(418*10^105343+23)/9105345Robert Price02/2020
526425490^13563+13563^25490105334Hans Havermann10/2020
526511^101142-1080105329Enzo Doria12/2012
5266(68*10^105320-41)/9105321Robert Price10/2013
526724800^17649+17649^24800105319Hans Havermann09/2020
52683^220712-9934105307Enzo Doria05/2014
52697*10^105296+9105297Robert Price09/2015
527089*10^105284-7105286Robert Price04/2020
52712^349739+1873373105282Enzo Doria06/2016
52727^124574+24105278Lelio R Paula11/2016
52732^349708-20957105273Enzo Doria06/2013
527434115^1218+1218^34115105267Hans Havermann09/2020
52752^349649-20469105255Enzo Doria06/2013
52762^349607-20109105243Enzo Doria06/2013
5277(85*10^105242+473)/9105243Robert Price01/2020
52782^349594-19085105239Enzo Doria05/2013
52792^349530+1874479105220Enzo Doria06/2016
5280(3^220528+8)/8081105215Lelio R Paula12/2013
5281(106*10^105199+17)/3105201Robert Price04/2021
5282(2^349452+3570)/2105196Stefano Morozzi09/2020
52833^220464-112852105189Enzo Doria07/2014
52842^349419-17349105186Enzo Doria05/2013
52852^349400-2579105180Yves Minet07/2014
52868*5^150471+3105176Lelio R Paula11/2014
5287(2^349359+2298)/2105168Stefano Morozzi02/2021
5288655^37342+37342^655105165Norbert Schneider08/2018
528913^94403+94105160Lelio R Paula12/2016
52902^349301-112309105151Enzo Doria06/2014
529130291^2960+2960^30291105149Hans Havermann09/2020
529227350^6981+6981^27350105132Hans Havermann09/2020
52949*2^349220+5105127Lelio R Paula09/2014
5293(2^349225+3122)/2105127Stefano Morozzi09/2020
52957*3^220317+8105119Lelio R Paula09/2014
52967^124386+88105119Lelio R Paula11/2016
5297(2^349197+570)/2105119Stefano Morozzi09/2020
52982^349171-19657105111Enzo Doria06/2013
5299(2^349115+590)/2105094Stefano Morozzi09/2020
5300(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
5301(2^349111-5)/3105093Lelio R Paula12/2013
5302675^37142+37142^675105087Norbert Schneider08/2018
53032^348981-2797573105054Enzo Doria04/2016
53042^348869-6555105021Lelio R Paula01/2017
53055^150217+78104998Lelio R Paula11/2016
5306(88*10^104989-1)/3104991Robert Price04/2020
5307(28*10^104972+149)/3104973Robert Price12/2019
530824927^16262+16262^24927104972Hans Havermann10/2020
53092^348703-113005104971Enzo Doria06/2014
5310(191*10^104956-17)/3104958Robert Price11/2021
53122^348612-809104943Yves Minet05/2013
5311(73*10^104942-1)/9104943Robert Price01/2015
53132^348583-350407104934Enzo Doria06/2015
53142^348531-949104919Yves Minet05/2012
531520^80636-59104910Lelio R Paula12/2016
53168*10^104893-13104894Robert Price08/2019
53182^348437+35104890Lelio R Paula09/2011
531725208^14487+14487^25208104890Hans Havermann09/2020
53192^348348+135104864Lelio R Paula09/2011
5320(29*10^104858+349)/9104859Robert Price06/2021
53216*10^104852-31104853Robert Price07/2020
5323(2^348284+9)/25104843Lelio R Paula12/2013
532275^55914-74104843Norbert Schneider01/2015
53242^348268+255255104840Lelio R Paula01/2017
532535540^891+891^35540104839Hans Havermann09/2020
53265^149985-52104836Lelio R Paula11/2016
53272^348224-20249104826Enzo Doria06/2013
5328(2^348217+2522)/2104824Stefano Morozzi09/2020
53292^348212-20105104823Enzo Doria06/2013
533024647^17898+17898^24647104819Hans Havermann10/2020
533120^80562+19104814Lelio R Paula12/2016
53322*10^104811-87104812Robert Price04/2018
53332^348149-20053104804Enzo Doria06/2013
53342^348095-171104788Lelio R Paula09/2011
533525383^13412+13412^25383104769Hans Havermann09/2020
53362^348003-20377104760Enzo Doria06/2013
53372^347994-741104757Lelio R Paula12/2016
5338(2^347993+2234)/2104757Stefano Morozzi01/2021
5339(2^347990+790)/2104756Stefano Morozzi09/2020
534025137^14702+14702^25137104756Hans Havermann09/2020
5341(13*2^347972-1)/282309104746Lelio R Paula03/2014
53422^347910-109937104732Enzo Doria04/2014
5343(88*10^104709-637)/9104710Robert Price11/2020
5344(13*10^104702+71)/3104703Robert Price06/2021
53455^149794+28104702Lelio R Paula11/2016
5346105^51800-2104698Lelio R Paula10/2017
5347(16^86939+3^86939)/19104684Robert Price06/2013
5348(15^89009-1)/14104682Paul Bourdelais03/2010
53492^347731-18609104678Enzo Doria05/2013
53504*6^134519+7104677Lelio R Paula11/2014
5351(34*10^104672-259)/9104673Robert Price12/2021
535225321^13588+13588^25321104656Hans Havermann09/2020
53532^347612-18545104642Enzo Doria05/2013
53566^134465+95104635Lelio R Paula11/2016
5354(2^347588+3718)/2104635Stefano Morozzi09/2020
5355(166*10^104633-7)/3104635Robert Price11/2020
53572^347517-17301104614Enzo Doria05/2013
5358(2^347493+3186)/2104606Stefano Morozzi09/2020
5359(2^347490+2574)/2104605Stefano Morozzi09/2020
53603^219222-310104596Lelio R Paula11/2016
536125993^10554+10554^25993104581Hans Havermann09/2020
5362(15*2^347399-1)/13104578Lelio R Paula03/2014
53632^347372-17853104570Enzo Doria05/2013
53642^347314+99104552Lelio R Paula09/2011
53652^347300-22233104548Enzo Doria06/2013
53662^347287-19845104544Enzo Doria06/2013
5367(31*2^347254-1)/891104533Lelio R Paula03/2014
53685*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
53697*2^347239-3104531Lelio R Paula09/2014
5370(3^219098-8)/514147439969104525Lelio R Paula12/2013
53715*3^219047+8104513Lelio R Paula09/2014
53722^347148-109073104502Enzo Doria04/2014
53732^347129-20145104497Enzo Doria06/2013
53744*10^104461-57104462Robert Price10/2018
5375(2^346989+590)/2104454Stefano Morozzi09/2020
53762^346923-19585104435Enzo Doria05/2013
5377(11*2^346864-1)/175104416Lelio R Paula03/2014
53782^346854+346854^2+1104414Robert Price06/2014
53792^346834+11715104408Lelio R Paula04/2015
538024276^19961+19961^24276104392Hans Havermann09/2020
538179^55009+78104387Norbert Schneider02/2015
53823^218744+58104368Lelio R Paula11/2016
53839*10^104361+89104362Robert Price11/2019
538425048^14665+14665^25048104358Hans Havermann09/2020
53852^346649+65104352Lelio R Paula09/2011
53862^346638-17265104349Enzo Doria05/2013
5387(2^346606+2082)/2104339Stefano Morozzi09/2020
5388(2^346607+2070)/2104339Stefano Morozzi09/2020
5389(2^346582+3202)/2104332Stefano Morozzi09/2020
539026092^9967+9967^26092104331Hans Havermann09/2020
53915*10^104326+77104327Robert Price12/2018
5392(2^346564+2026)/2104326Stefano Morozzi09/2020
53942^346527-111817104316Enzo Doria05/2014
53936^134055+101104316Lelio R Paula11/2016
539592105!4+8104312Robert Price09/2019
53966^134013+163104283Lelio R Paula11/2016
5397(2^346318+862)/2104252Stefano Morozzi02/2021
539918^83049-89104250Lelio R Paula01/2017
5398(2^346311+606)/2104250Stefano Morozzi09/2020
5400(166*10^104230+11)/3104232Robert Price03/2021
54012^346213+484049104221Enzo Doria04/2017
540218^83021-91104214Lelio R Paula01/2017
540310^104212+128779104213Patrick De Geest05/2016
540410^104212+237447104213Patrick De Geest05/2016
540510^104212+242139104213Patrick De Geest05/2016
540610^104212+269199104213Patrick De Geest05/2016
540724254^19803+19803^24254104213Hans Havermann09/2020
5408(10^104212-71)/1104212Serge Batalov12/2014
540923678^23821-23821^23678104202Norbert Schneider01/2020
54102^346078+7695104180Lelio R Paula12/2016
54112^346055-19537104173Enzo Doria05/2013
5412(3*2^346057+1)/77104173Lelio R Paula12/2013
54132^346037-20125104168Enzo Doria06/2013
5414(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
54156^133854-17993104159Enzo Doria03/2013
54162^345990+1874239104154Enzo Doria06/2016
54172^345988-20373104153Enzo Doria06/2013
5418(2^345965+2214)/2104146Stefano Morozzi09/2020
5419(26*10^104132-503)/9104133Robert Price07/2018
54203*5^148968+8104125Lelio R Paula11/2014
5421(7*10^104113+53)/3104114Robert Price05/2018
5422p(21253)#/2+8104113Robert Price01/2017
542333582^1259+1259^33582104106Hans Havermann09/2020
542432958^1441+1441^32958104104Hans Havermann09/2020
542529127^3748+3748^29127104095Hans Havermann09/2020
5426322^41507+41507^322104094Norbert Schneider12/2014
54276^133768-17423104092Enzo Doria03/2013
54282^345786-19557104092Enzo Doria05/2013
5430171^46606-2104072Lelio R Paula10/2017
5429(29*10^104071+91)/3104072Robert Price04/2020
54312^345704-149104068Lelio R Paula09/2011
543225821^10712+10712^25821104056Hans Havermann09/2020
5433(2^345662+2038)/2104055Stefano Morozzi09/2020
54346^133704-17273104042Enzo Doria02/2013
5435(3*2^345590-1)/23104033Lelio R Paula03/2014
5436(19*2^345590+1)/33859104030Lelio R Paula12/2013
54372^345547+11104021Lelio R Paula09/2011
5438(19*10^104014-49)/3104015Robert Price05/2019
5439(2^345519+1794)/2104012Stefano Morozzi01/2021
54402^345504+723104008Lelio R Paula09/2011
54412^345498-20037104006Enzo Doria06/2013
544218^82854-37104005Lelio R Paula01/2017
5443(2^345497+2070)/2104005Stefano Morozzi09/2020
54442^345486-109065104002Enzo Doria04/2014
54452^345487-1851507104002Enzo Doria08/2015
54462^345476+777103999Lelio R Paula09/2011
5447(2^345477+1554)/2103999Stefano Morozzi09/2020
54484*10^103981-83103982Robert Price10/2018
5449(2^345327+3206)/2103954Stefano Morozzi09/2020
5450(5*2^345321-1)/3103953Lelio R Paula03/2014
5451(2^345267-9)/539049127103927Lelio R Paula12/2013
5452(19*10^103907+77)/3103908Robert Price05/2019
5453(78557*2^345163+1)/78589103905Lelio R Paula07/2014
54542^345106-112181103888Enzo Doria06/2014
5455(2^345105+1326)/2103887Stefano Morozzi02/2021
54562^345079+99103880Lelio R Paula09/2011
5457(2^345034+1198)/2103866Stefano Morozzi09/2020
545811^99736-1500103865Enzo Doria12/2012
5459(2^345010+2082)/2103859Stefano Morozzi09/2020
546023263^23784-23784^23263103857Norbert Schneider01/2020
54613*10^103844+31103845Robert Price06/2021
546223927^21814+21814^23927103813Hans Havermann09/2020
54632^344842-20157103808Enzo Doria06/2013
5464(47*2^344822+1)/1071103801Lelio R Paula05/2015
54652^344802-20765103796Enzo Doria06/2013
54662^344794-3821103794Yves Minet05/2011
54672^344782-109103103790Enzo Doria04/2014
54683^217521-112292103784Enzo Doria06/2014
54692^344759-3505103783Lelio R Paula11/2016
54702^344735-147103776Lelio R Paula09/2011
5471L(496533)-p(496533)103770Robert Price02/2018
54722*10^103749-69103750Robert Price03/2018
5473(55459*2^344617+1)/3103745Lelio R Paula07/2014
54742^344607-108891103738Enzo Doria03/2014
5475(2^344608+3798)/2103738Stefano Morozzi02/2021
5476(148*10^103718-1)/3103720Robert Price03/2020
54772^344541-19561103718Enzo Doria05/2013
5478(1017*2^344529-1)/569103714Lelio R Paula05/2015
5479(2^344503+1758)/2103706Stefano Morozzi09/2020
5480(4*10^103703-1)/3103704Serge Batalov08/2009
54812^344444-455103688Yves Minet03/2012
5482(4*10^103678-43)/3103679Robert Price01/2022
5483(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
5484(2^344367+2738)/2103665Stefano Morozzi01/2021
54862^344317-109933103650Enzo Doria04/2014
548526055^9508+9508^26055103650Hans Havermann09/2020
54872^344309-1852033103648Enzo Doria08/2015
548825729^10672+10672^25729103643Hans Havermann09/2020
5489(2^344289+1166)/2103642Stefano Morozzi09/2020
54903*10^103637+61103638Robert Price09/2020
5491(2^344246+1614)/2103629Stefano Morozzi09/2020
54922^344213-21253103619Enzo Doria06/2013
54932^344196-465103614Lelio R Paula11/2016
54942^344187-20001103611Enzo Doria06/2013
5495(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
549620^79621-19^79621103590Jean-Louis Charton03/2011
5497Phi(155391,10)/1243129103586Maksym Voznyy09/2015
54982^344085-20365103580Enzo Doria06/2013
54995^148169+54103566Lelio R Paula11/2016
55002^344017-108795103560Enzo Doria03/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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