PRP Records

Probable Primes Top 10000

(294113 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 ?
95012^321716-278693996847Enzo Doria03/2016
950222496^20181+20181^2249696844Hans Havermann03/2020
95032^321701-11305396842Enzo Doria07/2014
95042^321700-2863596842Lelio R Paula06/2016
9505(5*2^321691-1)/2796838Lelio R Paula02/2014
95066*10^96835+1396836Robert Price10/2021
95076^124433-12443396828Robert Price01/2014
95082^321631+6996821Lelio R Paula12/2012
9509(27109^21841-1)/2710896820Serge Batalov06/2022
9510(13*2^321606+1)/11996813Lelio R Paula11/2013
9511(5052^26141-1)/505196809Serge Batalov06/2022
9512(46*10^96798-1)/996799Serge Batalov10/2014
9513(59*10^96798+31)/996799Robert Price09/2015
9514(2^321536+2062)/296792Stefano Morozzi09/2020
9515223319#+23122396790Makoto Morimoto02/2016
95162^321519-2863596787Lelio R Paula06/2016
95172^321487-186723796778Enzo Doria03/2016
95182^321461-6396770Lelio R Paula12/2012
9519(16053^23011-1)/1605296770Serge Batalov06/2022
95202^321439+12396763Lelio R Paula12/2012
95212^321434+70996762Lelio R Paula02/2013
95222^321419+2270396757Enzo Doria09/2023
9523(2^321415+554)/296756Stefano Morozzi09/2020
952414^84413+8996749Lelio R Paula07/2016
9525(28*10^96743+71)/996744Serge Batalov12/2008
952613^86847+9696743Lelio R Paula06/2016
95279*2^321336-796733Lelio R Paula08/2014
9528(209*10^96722-17)/396724Robert Price05/2017
9529(54163^20431-1)/5416296710Serge Batalov06/2022
95302^321237-461596702Yves Minet05/2019
9531(27273^21799-1)/2727296691Serge Batalov06/2022
95322^321187-115996687Yves Minet11/2012
95332^321182-185008196686Enzo Doria08/2015
953523359^13768+13768^2335996680Hans Havermann06/2020
9534(65630^20071-1)/6562996680Serge Batalov06/2022
95362^321116-11282996666Enzo Doria06/2014
95372^321108-10949996664Enzo Doria04/2014
95382^321098+279385996661Enzo Doria03/2016
9539(2^321100+1170)/296661Stefano Morozzi09/2020
95402^321057+409796648Lelio R Paula06/2016
9541(4435*29^66081-4)/796640Curtis Bright05/2015
954222743^17750+17750^2274396640Hans Havermann04/2020
954322882^16679+16679^2288296612Hans Havermann02/2020
954423452^13163+13163^2345296608Hans Havermann02/2020
9545(1042^32009-1)/104196596Serge Batalov06/2022
9546(85*10^96594-373)/996595Robert Price05/2021
9547(2^320863+666)/296590Stefano Morozzi09/2020
9548p(19849)#/2-6496581Robert Price04/2017
95492^320817+18996576Lelio R Paula12/2012
95502^320816-468596576Yves Minet05/2019
9552(361*10^96567-163)/996569Robert Price10/2017
9551(19*10^96568+137)/396569Robert Price03/2022
95532^320788-11032796567Enzo Doria05/2014
9554(3065^27697-1)/306496561Serge Batalov06/2022
95552^320764+79396560Lelio R Paula02/2013
9556(2^320752+1842)/296556Stefano Morozzi02/2021
9557(48331^20611-1)/4833096542Serge Batalov06/2022
9558(107746^19321-1)/(107746^139-1)96532Ryan Propper11/2023
9559(50595^20521-1)/5059496529Serge Batalov06/2022
9560(9179*2^320652-1)/22196528Lelio R Paula05/2015
956123288^13947+13947^2328896517Hans Havermann07/2020
95632^320616-7879596516Lelio R Paula03/2016
9562(19*10^96520+287)/9/109/40996516Alfred Reich11/2022
95642^320612-46193996514Enzo Doria07/2015
9565(21245^22303-1)/2124496507Serge Batalov06/2022
956610^96504+98765432196505Robert Price12/2019
956710^96504+7188796505Patrick De Geest02/2020
956822654^18195+18195^2265496505Hans Havermann07/2020
956910^96504-13927796504Patrick De Geest02/2020
9570(218^41263-1)/21796490Serge Batalov06/2022
9571(47220^20641-1)/4721996474Serge Batalov06/2022
95725*2^320431+796461Lelio R Paula08/2014
957319^75431-9096458Lelio R Paula06/2016
9574(11853^23677-1)/1185296452Serge Batalov06/2022
9575(2^320386+2814)/296446Stefano Morozzi02/2021
9576(2^320370+3)/6796440Lelio R Paula10/2013
95773*10^96431-1796432Robert Price03/2021
95782^320309+187147796423Enzo Doria05/2016
9579(10412^24001-1)/1041196421Serge Batalov06/2022
9580tau(809^6028)96410Nik Lygeros / Olivier Rozier / LR team10/2013
9581(29*10^96407-23)/396408Robert Price03/2022
9582(21*2^320252-1)/189596404Lelio R Paula02/2014
95832^320232-17396400Lelio R Paula12/2012
9584175^42975-296395Lelio R Paula10/2017
9585(2^320170+2718)/296381Stefano Morozzi09/2020
958610^96377+19991196378Patrick De Geest12/2016
958710^96377-2000196377Robert Price11/2016
9588(18079^22639-1)/1807896374Serge Batalov06/2022
95902^320124-279044996367Enzo Doria03/2016
958910^96366+1919796367Patrick De Geest08/2021
959210^96366-1000000000196366Robert Price04/2021
959110^96366-28736796366Patrick De Geest08/2021
9593(26351^21799-1)/2635096365Serge Batalov06/2022
959422488^19255+19255^2248896351Hans Havermann11/2019
959523248^13939+13939^2324896346Hans Havermann11/2019
9596(5928^25537-1)/592796345Serge Batalov06/2022
95982^320043-10877596343Enzo Doria04/2014
959724989^7168+7168^2498996343Hans Havermann11/2019
959910^96338+42493996339Patrick De Geest03/2016
960010^96338-928196338Robert Price09/2015
9601(8527^24509-1)/852696336Serge Batalov06/2022
9602(3*2^320008+1)/796332Lelio R Paula09/2013
9603(2444^28433-1)/244396331Serge Batalov06/2022
9604(48690^20551-1)/4868996327Serge Batalov06/2022
9605(61935^20101-1)/6193496318Serge Batalov06/2022
960625699^5596+5596^2569996317Hans Havermann07/2020
9607(7*10^96312+83)/996312Tyler Busby01/2023
9608(11*10^96298+529)/996299Robert Price09/2021
961026502^4297+4297^2650296287Hans Havermann07/2020
9609(54180^20341-1)/5417996287Serge Batalov06/2022
96112^319838+425796281Lelio R Paula03/2016
96122^319830-1699596279Lelio R Paula03/2016
96136^123713+14396268Lelio R Paula05/2016
9614(28*10^96265-97)/396266Robert Price07/2016
9615(3799^26893-1)/379896265Serge Batalov06/2022
9617103^47825-10296264Norbert Schneider10/2016
9616(54041^20341-1)/5404096264Serge Batalov06/2022
9618(2^319777+2082)/296263Stefano Morozzi09/2020
9619(2^319771+3686)/296261Stefano Morozzi09/2020
96202^319713-8196244Lelio R Paula11/2012
96212^319711+21341396243Enzo Doria09/2023
9622(55459*2^319706+1)/2016796242Lelio R Paula07/2014
962322834^16393+16393^2283496238Hans Havermann05/2020
96248*10^96236+2796237Robert Price09/2021
962512^89153-4396213Lelio R Paula06/2016
9626(25048^21871-1)/2504796202Serge Batalov06/2022
9628(2*10^96195-59)/396195Robert Price05/2017
96279*10^96194-7796195Robert Price08/2020
96292^319545+14796193Lelio R Paula11/2012
963023357^13128+13128^2335796189Hans Havermann02/2020
9631(19838^22381-1)/1983796179Serge Batalov06/2022
9632(221^41023-1)/22096172Serge Batalov06/2022
963325952^5073+5073^2595296160Hans Havermann12/2019
9634(50891^20431-1)/5089096157Serge Batalov06/2022
9635(50^56597+1)/5196155Robert Price03/2014
963622313^20374+20374^2231396149Hans Havermann12/2019
963722279^20668+20668^2227996141Hans Havermann11/2019
9638(41*10^96137-59)/996138Robert Price10/2017
96392^319353-11034396135Enzo Doria05/2014
964011^92309-4296130Lelio R Paula05/2016
9641(21675^22171-1)/2167496129Serge Batalov06/2022
964214^83869-13^8386996125Jean-Louis Charton01/2009
9643(7*10^96112+143)/396113Robert Price04/2016
964426731^3940+3940^2673196112Hans Havermann07/2020
964522640^17583+17583^2264096109Hans Havermann07/2020
9646(19178^22441-1)/1917796107Serge Batalov06/2022
96472^319237+6583596100Lelio R Paula03/2016
96482^319194-184196087Yves Minet03/2013
964923949^10280+10280^2394996084Hans Havermann07/2020
9650(1927^29251-1)/192696083Serge Batalov06/2022
965120^73847-3196078Lelio R Paula05/2016
9652(60229^20101-1)/6022896075Serge Batalov06/2022
9653(28044^21601-1)/2804396074Serge Batalov06/2022
965450^56543-4996065Norbert Schneider09/2018
96552^319107-10955596061Enzo Doria04/2014
9656(3*2^319114-1)/262796060Lelio R Paula02/2014
96572^319098-11215796059Enzo Doria06/2014
965815^81673+9496055Lelio R Paula07/2016
9659(85761^19471-1)/8576096052Serge Batalov06/2022
96602^319074+187174996051Enzo Doria05/2016
966125670^5517+5517^2567096050Hans Havermann06/2020
96626*10^96037+1996038Robert Price11/2021
96632^319007-11211196031Enzo Doria06/2014
9664(57987^20161-1)/5798696029Serge Batalov06/2022
96662^318946-142196013Yves Minet01/2013
9665(68310^19861-1)/6830996013Serge Batalov06/2022
9667(20294^22291-1)/2029396012Serge Batalov06/2022
9668(304^38669-1)/30396008Serge Batalov06/2022
9669(1840^29401-1)/183995986Serge Batalov06/2022
967022830^16003+16003^2283095982Hans Havermann02/2020
96712^318834-11041195979Enzo Doria05/2014
96722^318831-196595978Lelio R Paula03/2016
9673(5*10^95976+7)/395977Erik Branger03/2014
9674(12797^23369-1)/1279695975Serge Batalov06/2022
9675(10534^23857-1)/1053395963Serge Batalov06/2022
967622871^15696+15696^2287195962Hans Havermann01/2020
9677(2^318760+858)/295957Stefano Morozzi02/2021
967823167^13860+13860^2316795953Hans Havermann01/2020
9679(823^32911-1)/82295946Serge Batalov06/2022
96815*3^201089-895945Lelio R Paula08/2014
9680(81783^19531-1)/8178295945Serge Batalov06/2022
96822^318711-13995942Lelio R Paula11/2012
96832^318635-116795919Lelio R Paula03/2016
968415^81555+1695917Lelio R Paula07/2016
9685(37*10^95895+377)/995896Robert Price10/2017
9686(22699*2^318527+1)/2195890Lelio R Paula07/2014
968745^57997+19607295882Enzo Doria10/2023
96882^318496-9730595877Lelio R Paula03/2016
968922129^21496+21496^2212995871Hans Havermann07/2020
96912^318466+1501595868Lelio R Paula03/2016
969024847^7216+7216^2484795868Hans Havermann07/2020
969223706^11065+11065^2370695866Hans Havermann07/2020
9693(2863^27733-1)/286295865Serge Batalov06/2022
96946^123187-17312995859Mike Oakes04/2011
96952^318423-48795855Yves Minet03/2012
969610^95848+44370995849Patrick De Geest10/2022
969710^95848-500000000195848Robert Price09/2022
969810^95848-6197195848Patrick De Geest10/2022
9699(2^318359+678)/295836Stefano Morozzi09/2020
9700(10223*2^318350+1)/156395834Lelio R Paula07/2014
9701(8060^24533-1)/805995831Serge Batalov06/2022
9702(9853^23993-1)/985295814Serge Batalov06/2022
9704(2^318267+2550)/295808Stefano Morozzi09/2020
9703(5048^25873-1)/504795808Serge Batalov06/2022
97064*10^95799+1395800Robert Price02/2021
9705(65533^19891-1)/6553295800Serge Batalov06/2022
97072^318203+21134395789Enzo Doria08/2023
970845369!2+102495787Robert Price02/2015
97093^200758-8695786Lelio R Paula05/2016
9710(2^318271+1)/(3*46031404238891*654090604244843)95781Gord Palameta12/2018
9711(2^318171+2030)/295779Stefano Morozzi09/2020
97123*10^95776-5995777Robert Price10/2017
9713(82970^19471-1)/8296995772Serge Batalov06/2022
9714193^41901-295768Lelio R Paula10/2017
9715(2^318124+2502)/295765Stefano Morozzi09/2020
9716(12900^23297-1)/1289995761Serge Batalov06/2022
97174*10^95752-7195753Robert Price11/2017
9718(16955^22639-1)/1695495743Serge Batalov06/2022
9719(81795^19489-1)/8179495740Serge Batalov06/2022
9720(2742^27847-1)/274195737Serge Batalov06/2022
9721(6072^25303-1)/607195726Serge Batalov06/2022
972223640^11197+11197^2364095721Hans Havermann12/2019
972310^95712+8932995713Patrick De Geest09/2022
972510^95712-400000195712Robert Price07/2021
972410^95712-98931395712Patrick De Geest09/2022
9726(60657^20011-1)/6065695706Serge Batalov06/2022
9727((10^47850-1)*10000/9+6421)*10^47850+(10^47850-1)/995704Hans Havermann05/2019
9728(509203*2^317881-1)/5280595693Lelio R Paula04/2015
9729(26161^21661-1)/2616095687Serge Batalov06/2022
9730(2^317853+1086)/295683Stefano Morozzi09/2020
97314*10^95672+9195673Robert Price11/2017
97326*10^95665+4395666Robert Price07/2020
9733(20819^22153-1)/2081895663Serge Batalov06/2022
9734(64464^19891-1)/6446395658Serge Batalov06/2022
9735(934^32203-1)/93395652Serge Batalov06/2022
9736(11*10^95641-113)/395642Robert Price01/2017
9737(72330^19681-1)/7232995632Serge Batalov06/2022
9738(13224^23203-1)/1322395624Serge Batalov06/2022
9739(18211^22441-1)/1821095602Serge Batalov06/2022
9740(71975^19681-1)/7197495590Serge Batalov06/2022
9741(13*10^95588+11)/395589Robert Price05/2015
9742Phi(191188,10)/19118995587Maksym Voznyy11/2015
9743(13368^23167-1)/1336795585Serge Batalov06/2022
9744(25874^21661-1)/2587395583Serge Batalov06/2022
97453^200325+7095580Lelio R Paula05/2016
9746(25*10^95574-7)/995575Robert Price12/2014
9747(2^317485-3)/2131395569Lelio R Paula06/2013
97482^317464+3195567Lelio R Paula11/2012
9749(2^317451+2114)/295562Stefano Morozzi09/2020
97507^113073+8295558Lelio R Paula04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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