PRP Records

Probable Primes Top 10000

(291192 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 ?
92512^300874+790573Lelio R Paula10/2012
925210^90567+948990568Patrick De Geest11/2018
925310^90567-23135390567Patrick De Geest07/2019
9254(2^300857+2214)/290567Stefano Morozzi01/2020
92555^129568-5690565Lelio R Paula04/2016
92562^300847-11283190564Enzo Doria06/2014
925710^90562+79019790563Patrick De Geest07/2019
925810^90562-298190562Patrick De Geest11/2018
9259(7796^23269-1)/779590557Serge Batalov08/2020
9260(31*10^90554+257)/990555Robert Price12/2021
926110^90549+381190550Patrick De Geest11/2018
926210^90549-63030390549Patrick De Geest07/2019
92632^300790-454190547Yves Minet03/2019
926410^90532+816990533Patrick De Geest11/2018
926510^90531+983190532Patrick De Geest11/2018
926610^90532-15488990532Patrick De Geest07/2019
926710^90531-106058990531Patrick De Geest07/2019
92692^300718+25525590526Lelio R Paula02/2016
9268(2^300719+938)/290526Stefano Morozzi01/2020
927010^90516+21591790517Patrick De Geest07/2019
927110^90516-678390516Patrick De Geest11/2018
927210^90511+3017790512Patrick De Geest07/2019
927310^90511-697790511Patrick De Geest11/2018
9274(8573^23011-1)/857290502Serge Batalov08/2020
92752^300637+9590501Lelio R Paula11/2012
92767^107087-2490500Lelio R Paula04/2016
927710^90499+19154790500Patrick De Geest07/2019
927810^90499-582390499Patrick De Geest11/2018
9280(10^90499+3^90499)/1390498Robert Price01/2013
927913^81241+9090498Lelio R Paula06/2016
9281(2^300600+1222)/290490Stefano Morozzi01/2020
928210^90480+513190481Patrick De Geest11/2018
928310^90480-8572190480Patrick De Geest07/2019
9284(34*10^90478-547)/990479Robert Price03/2021
92856^116273-8590478Lelio R Paula05/2016
928610^90473+313990474Patrick De Geest11/2018
928710^90473-15059990473Patrick De Geest07/2019
928810^90470+231990471Patrick De Geest11/2018
928910^90470-7163790470Patrick De Geest07/2019
92906^116256-1757390465Enzo Doria02/2013
92912^300502+5461590461Lelio R Paula02/2016
9292(13*2^300487+1)/4590456Lelio R Paula09/2013
929310^90453+14184390454Patrick De Geest07/2019
929510^90453-396990453Patrick De Geest11/2018
929410^90452+5931790453Patrick De Geest05/2021
929610^90452-8000000190452Robert Price04/2021
929710^90452-8471390452Patrick De Geest05/2021
929810^90440+135990441Patrick De Geest11/2018
929910^90440-1882190440Patrick De Geest07/2019
9300(3^189545-8)/590436Lelio R Paula01/2013
9301(7*2^300406-1)/390432Lelio R Paula02/2014
930210^90430+333990431Patrick De Geest11/2018
930310^90430-6347790430Patrick De Geest07/2019
9304(5408^24223-1)/540790422Serge Batalov08/2020
930510^90414+22959390415Patrick De Geest07/2019
930610^90414-154790414Patrick De Geest11/2018
930710^90404+4704190405Patrick De Geest07/2019
930810^90404-642990404Patrick De Geest11/2018
930910^90401+207790402Patrick De Geest11/2018
931010^90401-36863790401Patrick De Geest07/2019
931124900^4271+4271^2490090401Hans Havermann08/2020
93124*5^129332+390400Lelio R Paula10/2014
931410^90397+1978390398Patrick De Geest07/2019
931323380^7353+7353^2338090398Hans Havermann08/2020
931610^90397-32390397Patrick De Geest11/2018
9315(2^300293+2762)/290397Stefano Morozzi01/2020
931724058^5719+5719^2405890394Hans Havermann08/2020
93182^300249-1624590384Enzo Doria04/2013
931924414^5035+5035^2441490381Hans Havermann08/2020
9320(7*10^90371-313)/990371Robert Price11/2016
932110^90363+5867790364Patrick De Geest07/2019
932210^90363-355790363Patrick De Geest11/2018
932310^90358+10464190359Patrick De Geest07/2019
93262*6^116118+790358Lelio R Paula10/2014
932510^90358-497990358Patrick De Geest11/2018
932410^90357+11283790358Patrick De Geest07/2019
932710^90357-18959390357Patrick De Geest07/2019
932810^90356+5311390357Patrick De Geest07/2019
932910^90356-719790356Patrick De Geest11/2018
933010^90353+60321190354Patrick De Geest07/2019
933110^90353-108990353Patrick De Geest11/2018
9332(24737*2^300101+1)/2590343Lelio R Paula06/2014
93334*10^90334-2190335Robert Price04/2016
9334(4546^24697-1)/454590329Serge Batalov08/2020
933510^90322+13769190323Patrick De Geest07/2019
933610^90322-955190322Patrick De Geest11/2018
933710^90316+999190317Patrick De Geest11/2018
9338(4550^24691-1)/454990317Serge Batalov08/2020
933910^90316-4562790316Patrick De Geest07/2019
934010^90315+3288990316Patrick De Geest07/2019
93422^300019-11033590315Enzo Doria05/2014
934110^90315-856190315Patrick De Geest11/2018
9343FAB2(300001,5032)90310Robert Price05/2019
9344FAB2(300001,29405)90310Robert Price05/2019
9345(2^299965+2774)/290299Stefano Morozzi01/2020
934623679^6506+6506^2367990296Hans Havermann08/2020
93472^299949-100590294Lelio R Paula11/2013
9348(2^299947+2054)/290293Stefano Morozzi01/2020
934921740^14229+14229^2174090291Hans Havermann08/2020
935010^90279+6245790280Patrick De Geest07/2019
935110^90279-155190279Patrick De Geest09/2018
9352(2^299892+1986)/290277Stefano Morozzi01/2020
9353(2^299893+3866)/290277Stefano Morozzi01/2020
93542^299868-10961390270Enzo Doria04/2014
935510^90259+35929990260Patrick De Geest07/2019
935610^90259-944390259Patrick De Geest09/2018
9357(2^299831+3786)/290258Stefano Morozzi01/2020
935810^90252+10287390253Patrick De Geest07/2019
935910^90252-810390252Patrick De Geest09/2018
93605*2^299799-390250Lelio R Paula08/2014
9361(2^299803+3326)/290250Stefano Morozzi01/2020
936213^81008-290239Lelio R Paula09/2013
936380697!4-25690234Robert Price11/2019
936564^49957-63^4995790232Robert Price07/2013
9364(2^299745+2994)/290232Stefano Morozzi01/2020
936610^90227+5628190228Patrick De Geest06/2016
93702^299725+31590227Lelio R Paula11/2013
936710^90227-100000000190227Robert Price05/2016
936810^90227-6876390227Patrick De Geest06/2016
93699*10^90226+2990227Robert Price03/2022
93715^129082+4890225Lelio R Paula03/2016
93722^299699+19590219Lelio R Paula10/2012
9373(55*10^90211-1)/990212Ray Chandler02/2012
937422131^11918+11918^2213190211Hans Havermann08/2020
937510^90209+897190210Patrick De Geest09/2018
937610^90209-72479790209Patrick De Geest07/2019
937710^90208+18953190209Patrick De Geest07/2019
937810^90208-224790208Patrick De Geest09/2018
9379(629^32233-1)/62890207Michael Stocker05/2020
9380116^43693-11590203Norbert Schneider08/2018
938110^90202+355390203Patrick De Geest09/2018
93823^189053+28090202Lelio R Paula04/2016
938310^90202-6779390202Patrick De Geest07/2019
93842^299639-18790201Lelio R Paula10/2012
938510^90199+25403190200Patrick De Geest07/2019
938610^90199-289190199Patrick De Geest09/2018
93882^299631+18390198Lelio R Paula10/2012
938721567^15212+15212^2156790198Hans Havermann08/2020
938910^90196+18753990197Patrick De Geest07/2019
939110^90196-968390196Patrick De Geest09/2018
939021708^14287+14287^2170890196Hans Havermann08/2020
939210^90193+10497390194Patrick De Geest07/2019
939310^90193-980990193Patrick De Geest09/2018
9394(21*2^299611-1)/2990192Lelio R Paula02/2014
9395(2277^26863-1)/227690186Serge Batalov08/2020
93962^299567+11390179Lelio R Paula10/2012
93972^299550+18990174Lelio R Paula10/2012
939810^90170+37606390171Patrick De Geest07/2019
939910^90170-674990170Patrick De Geest09/2018
9400(2^299535+3)/2990168Lelio R Paula01/2013
9401(2^299521+13)/1590164Stefano Morozzi03/2020
940222316^10971+10971^2231690163Hans Havermann08/2020
940310^90160+27194790161Patrick De Geest07/2019
940410^90160-561390160Patrick De Geest09/2018
9405(97*10^90155-1)/390157Serge Batalov12/2014
9406(29*10^90153+583)/990154Robert Price06/2021
94083^188938+868090147Lelio R Paula04/2016
940710^90146+16020990147Patrick De Geest07/2019
940910^90146-202790146Patrick De Geest09/2018
94106^115840-5590142Lelio R Paula05/2016
9411(5*10^90142-473)/990142Robert Price12/2017
94128*7^106659+590139Lelio R Paula10/2014
94132^299406-1665390131Enzo Doria05/2013
9414(317057^16384+1)/290131Richard Fischer10/2019
9415(2^299409+834)/290131Stefano Morozzi01/2020
941610^90128+28867390129Patrick De Geest07/2019
9418208049#+(216091#)/(208049#)90128Makoto Morimoto04/2016
941710^90128-838790128Patrick De Geest09/2018
9420(F(5)^128941-F(4)^128941)/F(3)90126Wayne Halsdorf03/2012
9419(5^128941-3^128941)/290126Kellen Shenton05/2022
94216^115819-5390125Lelio R Paula05/2016
942210^90123+631390124Patrick De Geest09/2018
94236^115816-1685390123Enzo Doria02/2013
942410^90123-2261790123Patrick De Geest07/2019
94256^115813-2390121Lelio R Paula05/2016
94262^299351-93307590114Paul Bourdelais04/2021
9427(22*10^90110+161)/390111Robert Price02/2017
9429(2^299330-509203)/6990106Lelio R Paula01/2013
942810^90105+91575990106Patrick De Geest07/2019
943010^90105-76790105Patrick De Geest09/2018
943110^90104+4818990105Patrick De Geest07/2019
9432(6050^23827-1)/604990105Serge Batalov08/2020
943410^90104-770390104Patrick De Geest09/2018
943510^90103+915990104Patrick De Geest09/2018
9433(797*10^90102-23)/990104Robert Price01/2022
943610^90103-20845790103Patrick De Geest07/2019
943710^90102+7301190103Patrick De Geest07/2019
943810^90102-60243390102Patrick De Geest07/2019
943910^90101+122553790102Patrick De Geest07/2019
944110^90101-320790101Patrick De Geest09/2018
944021730^14007+14007^2173090101Hans Havermann08/2020
9442(29*10^90096-17)/390097Erik Branger09/2014
9443(49*10^90094+221)/990095Robert Price02/2022
944410^90089+14318190090Patrick De Geest07/2019
944510^90089-357390089Patrick De Geest09/2018
94462^299247+187052990083Enzo Doria05/2016
944710^90079+160990080Patrick De Geest09/2018
944810^90079-23004390079Patrick De Geest07/2019
94492^299229-279778390077Enzo Doria04/2016
94502^299220-1631790075Enzo Doria04/2013
945111^86491-135090072Enzo Doria12/2012
945210^90071+5233390072Patrick De Geest07/2019
945410^90071-123390071Patrick De Geest09/2018
9453(314401^16384+1)/290071Richard Fischer10/2019
945510^90069+15852790070Patrick De Geest07/2019
945610^90069-784190069Patrick De Geest09/2018
9457(31*10^90064-1)/390066Robert Price03/2017
945810^90060+14943190061Patrick De Geest07/2019
945910^90060-83990060Patrick De Geest09/2018
946010^90052+236190053Patrick De Geest09/2018
946110^90052-9092990052Patrick De Geest07/2019
946210^90047+61990048Patrick De Geest09/2018
946310^90047-15107190047Patrick De Geest07/2019
9464L(430949)/861899/144038756153990045Serge Batalov07/2017
946522996^8233+8233^2299690043Hans Havermann08/2020
94662^299112+7395190042Enzo Doria04/2016
94678^99702+7^(99702-1)90040Robert Price02/2016
946810^90038+15780390039Patrick De Geest07/2019
946910^90038-968790038Patrick De Geest09/2018
94715*10^90033+390034Dmitry Domanov11/2010
9470(17574^21211-1)/1757390034Serge Batalov08/2020
947210^90030+22581390031Patrick De Geest07/2019
947310^90030-146190030Patrick De Geest09/2018
9474243^37738+37738^24390029Norbert Schneider01/2015
947510^90025+7056990026Patrick De Geest07/2019
947610^90025-870390025Patrick De Geest09/2018
94772^299048-11329790023Enzo Doria07/2014
947810^90015+84990016Patrick De Geest09/2018
947910^90015-22838790015Patrick De Geest07/2019
948010^90010+681190011Patrick De Geest09/2018
948110^90010-18359790010Patrick De Geest11/2018
948210^90009+5832190010Patrick De Geest11/2018
948310^90008+84790009Patrick De Geest09/2018
948410^90009-35601390009Patrick De Geest11/2018
948525696^3183+3183^2569690009Hans Havermann08/2020
94873^188648+9290008Lelio R Paula12/2015
948610^90008-70604990008Patrick De Geest11/2018
94885*2^298991+790006Lelio R Paula08/2014
9489(25*2^298997+1)/326790005Lelio R Paula01/2013
949010^90000+886990001Patrick De Geest12/2009
949210^89999+8293990000Dirk Augustin04/2007
949110^90000-14034390000Patrick De Geest12/2009
949310^89999-19489189999Patrick De Geest11/2009
9494(2^298918+1798)/289983Stefano Morozzi01/2020
949519^70365-7889980Lelio R Paula12/2015
9496Phi(186062,10)/13460963248300334700445189977Makoto Kamada04/2021
9497NaturalLogarithmOf2(89973)89973Eric W. Weisstein10/2015
94982^298852-6487589964Lelio R Paula11/2013
9499(2^298825+1010)/289955Stefano Morozzi01/2020
950018^71659+3789952Lelio R Paula12/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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