Henri & Renaud Lifchitz's PRP Top records

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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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 ?
8501	(5728^21673-1)/5727	81444	Serge Batalov	08/2020
8502	2^270546-110345	81443	Enzo Doria	05/2014
8503	13^73105-60	81435	Lelio R Paula	11/2015
8504	(2^270502+1518)/2	81429	Stefano Morozzi	01/2020
8505	(2^270479+2114)/2	81422	Stefano Morozzi	01/2020
8506	(2^270384+1218)/2	81394	Stefano Morozzi	01/2020
8507	44^49524+43	81391	Norbert Schneider	06/2014
8508	(3*2^270368-1)/13	81389	Lelio R Paula	02/2014
8509	96*10^81387-7	81389	Robert Price	03/2021
8510	19548^14563+14563^19548	81384	Hans Havermann	05/2020
8511	(2^270337+1130)/2	81380	Stefano Morozzi	01/2020
8512	27405^932+932^27405	81377	Hans Havermann	05/2020
8513	19396^15683+15683^19396	81375	Hans Havermann	05/2020
8515	(10^81363+719)/9	81363	Serge Batalov	12/2014
8514	(734^28393-1)/733	81363	Serge Batalov	08/2020
8516	(10^81353+449)/9	81353	Serge Batalov	12/2014
8517	14^70978-89	81350	Lelio R Paula	11/2015
8518	11^78108-2040	81342	Enzo Doria	12/2012
8519	7*10^81327-57	81328	Robert Price	06/2020
8520	(7*10^81328-79)/9	81328	Robert Price	01/2021
8521	19102^18065+18065^19102	81315	Hans Havermann	07/2020
8522	3^170400-58	81302	Lelio R Paula	12/2015
8523	(17*10^81300-131)/3	81301	Robert Price	12/2017
8524	10^81297+36991	81298	Patrick De Geest	06/2013
8525	10^81297-57	81297	Robert Price	05/2011
8526	(2^270063+3206)/2	81297	Stefano Morozzi	01/2020
8527	19359^15826+15826^19359	81296	Hans Havermann	06/2020
8528	2^270055-113047	81295	Enzo Doria	07/2014
8529	18^64759-55	81291	Lelio R Paula	11/2015
8530	3*10^81290-17	81291	Robert Price	03/2021
8531	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
8532	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
8533	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014
8534	(194^35521-1)/193	81263	Serge Batalov	08/2020
8535	20722^8343+8343^20722	81258	Hans Havermann	07/2020
8536	(2^269922+3574)/2	81255	Stefano Morozzi	01/2020
8537	21310^6497+6497^21310	81249	Hans Havermann	07/2020
8538	(16392^19273-1)/16391	81225	Serge Batalov	08/2020
8539	2^269819-4597	81224	Yves Minet	03/2019
8540	(2^269816+7)/424901	81218	Lelio R Paula	12/2012
8541	23470^2887+2887^23470	81217	Hans Havermann	05/2020
8542	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
8543	(2^269720+3778)/2	81194	Stefano Morozzi	01/2020
8544	(17*2^269720+1)/303	81193	Lelio R Paula	07/2012
8545	56^46441-55^46441	81188	Robert Price	10/2013
8546	2^269664+177	81177	Lelio R Paula	06/2012
8547	(13*2^269665-1)/185	81177	Lelio R Paula	02/2014
8548	21642^5615+5615^21642	81144	Hans Havermann	07/2020
8549	2^269539-112249	81140	Enzo Doria	06/2014
8550	((2170026-3)3^(170026-1)+1)/4	81128	Robert Price	01/2015
8552	(2^269495-5)/9	81126	Lelio R Paula	12/2012
8551	1239^26228+26228^1239	81126	Norbert Schneider	10/2019
8553	2^269490-3623	81125	Yves Minet	10/2009
8554	(55459*2^269444+1)/35	81114	Lelio R Paula	06/2014
8555	19554^14065+14065^19554	81113	Hans Havermann	06/2020
8556	(2^269417+78557)/5257	81099	Lelio R Paula	12/2012
8557	4*5^116011-7	81089	Lelio R Paula	10/2014
8558	(2^269349+2366)/2	81082	Stefano Morozzi	01/2020
8559	(2^269303+2946)/2	81068	Stefano Morozzi	01/2020
8560	6*10^81060+53	81061	Robert Price	05/2020
8561	7*10^81058+79	81059	Robert Price	02/2017
8562	2^269236-109907	81049	Enzo Doria	04/2014
8563	(2^269182+1870)/2	81032	Stefano Morozzi	01/2020
8564	(2^269179+3006)/2	81031	Stefano Morozzi	01/2020
8565	(8*10^81029-11)/3	81030	Erik Branger	03/2014
8566	19749^12668+12668^19749	81025	Hans Havermann	05/2020
8567	3*10^81021+7	81022	Erik Branger	11/2013
8568	6^104115+103	81018	Lelio R Paula	12/2015
8569	2^269120+1869151	81014	Enzo Doria	05/2016
8570	5^115901+12	81012	Lelio R Paula	10/2015
8571	(2^269072+3610)/2	80999	Stefano Morozzi	01/2020
8572	(2^269083-9)/320369	80997	Lelio R Paula	12/2012
8573	(5*10^80992-179)/3	80993	Robert Price	10/2020
8574	2*10^80981-49	80982	Robert Price	09/2020
8575	(2^269002+1614)/2	80978	Stefano Morozzi	01/2020
8576	17^65810-20	80976	Lelio R Paula	11/2015
8577	20^62236-23	80971	Lelio R Paula	01/2016
8578	2^268974-112181	80970	Enzo Doria	06/2014
8580	L(387433)	80969	Renaud Lifchitz	11/2003
8579	V(387433)	80969	Serge Batalov	03/2015
8581	22732^3645+3645^22732	80965	Hans Havermann	06/2020
8582	(2^268957+602)/2	80964	Stefano Morozzi	01/2020
8583	(2^268955-509203)/5	80963	Lelio R Paula	12/2012
8584	19485^14284+14284^19485	80958	Hans Havermann	05/2020
8585	(87398^16384+1)/65537	80957	Lelio R Paula	11/2011
8586	329^32160+32160^329	80954	Norbert Schneider	11/2014
8587	19678^12973+12973^19678	80937	Hans Havermann	02/2020
8588	(2^268864+3558)/2	80936	Stefano Morozzi	01/2020
8589	2^268859-159	80935	Lelio R Paula	05/2012
8590	(2^268841-lucasV(1,2,268841)+1)/2	80929	Mike Oakes	11/2016
8592	2^268827+5775	80925	Lelio R Paula	07/2013
8591	2^268824-110255	80925	Enzo Doria	05/2014
8593	(2^268824+1902)/2	80924	Stefano Morozzi	01/2020
8594	2^268798-1868321	80917	Enzo Doria	04/2016
8595	20613^8420+8420^20613	80913	Hans Havermann	03/2020
8596	2^268753-114621	80903	Enzo Doria	05/2015
8597	2^268743+1605	80900	Lelio R Paula	07/2013
8598	6^103954-139	80892	Lelio R Paula	12/2015
8599	10^80883+49	80884	Robert Price	03/2011
8600	10^80883-80327	80883	Patrick De Geest	07/2013
8601	6^103937+121	80879	Lelio R Paula	12/2015
8602	148^37266+147	80877	Norbert Schneider	12/2018
8603	(26*10^80875-119)/3	80876	Robert Price	07/2016
8604	(22699*2^268657+1)/6351	80875	Lelio R Paula	06/2014
8605	(2^268612+2530)/2	80860	Stefano Morozzi	01/2020
8606	2^268581-869688105	80851	Lelio R Paula	05/2016
8607	(11*2^268521-1)/3	80834	Lelio R Paula	02/2014
8608	2^268516-249	80832	Yves Minet	02/2012
8609	22259^4278+4278^22259	80828	Hans Havermann	03/2020
8610	2^268500+16095	80827	Lelio R Paula	07/2013
8611	3^169402+100	80826	Lelio R Paula	12/2015
8612	(2^268495+566)/2	80825	Stefano Morozzi	01/2020
8613	9^84698+8^(84698-1)	80823	Robert Price	03/2016
8614	2^268472-109739	80819	Enzo Doria	04/2014
8615	(9*2^268454+1)/37	80813	Lelio R Paula	12/2012
8616	(3*2^268502+1)/377902188435353647	80811	Lelio R Paula	12/2012
8617	(2^268441+3962)/2	80809	Stefano Morozzi	01/2020
8618	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
8619	15^68702-76	80800	Lelio R Paula	11/2015
8620	2^268408+7	80799	Lelio R Paula	05/2012
8621	(16095^19207-1)/16094	80794	Serge Batalov	08/2020
8622	2^268375+141	80789	Lelio R Paula	05/2012
8623	12^74856-47	80784	Lelio R Paula	11/2015
8624	2^268346+524287	80781	Paul Underwood	08/2018
8625	9*10^80777-41	80778	Robert Price	08/2020
8626	(10868^20011-1)/10867	80764	Serge Batalov	08/2020
8627	6^103770-107	80749	Lelio R Paula	12/2015
8628	(751^28081-1)/750	80748	Serge Batalov	08/2020
8629	3^169224-62	80741	Lelio R Paula	12/2015
8630	p(16866)#/2+64	80741	Robert Price	03/2017
8631	5^115502-72	80733	Lelio R Paula	10/2015
8632	(2^268154+2262)/2	80723	Stefano Morozzi	01/2020
8633	(2^268156+1290)/2	80723	Stefano Morozzi	01/2020
8635	2^268079-1927	80700	Yves Minet	10/2009
8634	(2^268078+2514)/2	80700	Stefano Morozzi	01/2020
8636	2^268028+117	80685	Lelio R Paula	05/2012
8637	121^38738+120	80683	Norbert Schneider	01/2015
8638	(3^169097-8)/835	80677	Lelio R Paula	12/2012
8639	(2^267956+1810)/2	80663	Stefano Morozzi	01/2020
8640	19359^14666+14666^19359	80656	Hans Havermann	12/2019
8641	2^267918+67	80652	Lelio R Paula	05/2012
8642	(89*10^80650-179)/9	80651	Robert Price	11/2017
8643	(2^267914+2094)/2	80650	Stefano Morozzi	01/2020
8644	(2^267894+2202)/2	80644	Stefano Morozzi	01/2020
8645	(302*10^80638+13)/9	80640	Robert Price	01/2017
8646	3^169004+2660	80636	Lelio R Paula	12/2015
8647	2^267860-112859	80634	Enzo Doria	06/2014
8648	96*10^80624-7	80626	Robert Price	03/2021
8649	2^267828-110705	80625	Enzo Doria	05/2014
8650	(2956^23227-1)/2955	80611	Serge Batalov	08/2020
8651	(2^267752+2602)/2	80602	Stefano Morozzi	01/2020
8652	2^267743+12705	80599	Lelio R Paula	07/2013
8653	(22*10^80595+23)/9	80596	Robert Price	03/2015
8654	(2^267712+2358)/2	80590	Stefano Morozzi	01/2020
8655	(2^267685+854)/2	80581	Stefano Morozzi	01/2020
8656	2^267674-51	80578	Lelio R Paula	05/2012
8657	(86*10^80571-41)/9	80572	Robert Price	11/2015
8658	(2^267637+2454)/2	80567	Stefano Morozzi	01/2020
8659	20452^8693+8693^20452	80564	Hans Havermann	02/2020
8660	2^267612-1965	80560	Lelio R Paula	07/2013
8661	2^267553+4097	80542	Lelio R Paula	07/2013
8662	7^95276-8	80518	Robert Price	01/2014
8663	(15185*2^267457-1)/47829	80513	Lelio R Paula	04/2015
8664	6^103467+163	80513	Lelio R Paula	12/2015
8665	20283^9314+9314^20283	80506	Hans Havermann	02/2020
8666	(2^267387+2294)/2	80492	Stefano Morozzi	01/2020
8667	(7*10^80490+143)/3	80491	Robert Price	04/2016
8668	19887^11152+11152^19887	80490	Hans Havermann	01/2020
8669	(2^267348+3810)/2	80480	Stefano Morozzi	01/2020
8670	86^41597-85^41597	80470	Robert Price	04/2015
8671	13^72237+30	80468	Lelio R Paula	11/2015
8672	17^65389+14	80458	Lelio R Paula	11/2015
8673	423^30634+30634^423	80456	Norbert Schneider	05/2017
8674	(2^267257+470)/2	80453	Stefano Morozzi	01/2020
8675	2^267232+105	80445	Lelio R Paula	05/2012
8676	(298*10^80442+11)/3	80444	Robert Price	11/2020
8677	22101^4360+4360^22101	80437	Hans Havermann	02/2020
8678	11^77237-3072000	80435	Enzo Doria	01/2013
8679	20696^7689+7689^20696	80422	Hans Havermann	01/2020
8680	(2^267149+2562)/2	80420	Stefano Morozzi	01/2020
8681	21321^5908+5908^21321	80411	Hans Havermann	02/2020
8682	(13100^19531-1)/13099	80411	Serge Batalov	08/2020
8683	2^267116-459959	80410	Enzo Doria	06/2015
8684	38715!2+8	80406	Robert Price	01/2015
8685	19579^12786+12786^19579	80406	Hans Havermann	02/2020
8686	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
8687	(2^267006+1134)/2	80377	Stefano Morozzi	01/2020
8688	24273^2048+2048^24273	80376	Hans Havermann	01/2020
8689	(2^266989+734)/2	80372	Stefano Morozzi	01/2020
8690	(2^266989+1850)/2	80372	Stefano Morozzi	01/2020
8691	(13427^19471-1)/13426	80372	Serge Batalov	08/2020
8692	2^266968-45	80366	Lelio R Paula	05/2012
8693	(2^266967+3974)/2	80365	Stefano Morozzi	01/2020
8694	20^61768-63	80363	Lelio R Paula	01/2016
8695	(6253^21169-1)/6252	80356	Serge Batalov	08/2020
8696	(14005^19381-1)/14004	80355	Serge Batalov	08/2020
8697	2^266920-112967	80351	Enzo Doria	06/2014
8698	(2^266910+2394)/2	80348	Stefano Morozzi	01/2020
8699	(2^266899+1994)/2	80345	Stefano Morozzi	01/2020
8700	8*10^80342+87	80343	Robert Price	10/2017
8701	(10^80363+1)/11866136004174221950876906463	80335	Anonymous	10/2020
8702	(2^266861+890)/2	80333	Stefano Morozzi	01/2020
8703	12^74428-13	80322	Lelio R Paula	11/2015
8704	(2^266810+2718)/2	80318	Stefano Morozzi	01/2020
8705	(2^266800+2886)/2	80315	Stefano Morozzi	01/2020
8706	(6163^21187-1)/6162	80291	Serge Batalov	08/2020
8707	2^266680+27	80279	Lelio R Paula	05/2012
8708	(232*10^80264+17)/3	80266	Robert Price	04/2021
8709	2^266630-131	80264	Lelio R Paula	05/2012
8710	(2^266627+1278)/2	80263	Stefano Morozzi	01/2020
8711	2^266598+76819	80254	Enzo Doria	05/2016
8712	24463^1908+1908^24463	80253	Hans Havermann	01/2020
8713	2^266587+1880633	80251	Enzo Doria	10/2016
8714	(2^266570+3942)/2	80246	Stefano Morozzi	01/2020
8715	2^266541-110049	80237	Enzo Doria	04/2014
8716	38635!2-8	80222	Robert Price	06/2015
8717	(2^266465+986)/2	80214	Stefano Morozzi	01/2020
8718	3^168111+168111^3-1	80210	Robert Price	04/2014
8719	(2^266447+758)/2	80209	Stefano Morozzi	01/2020
8720	2^266443+513	80208	Lelio R Paula	07/2013
8721	(26*10^80200+61)/3	80201	Robert Price	06/2017
8722	2^266412-109913	80199	Enzo Doria	04/2014
8723	(10223*2^266417+1)/45091	80199	Lelio R Paula	06/2014
8724	2^266413-4693	80199	Yves Minet	05/2019
8725	(13737^19381-1)/13736	80193	Serge Batalov	08/2020
8726	13^71988+66	80191	Lelio R Paula	11/2015
8727	11^77002-4320	80190	Enzo Doria	01/2013
8728	19839^11012+11012^19839	80187	Hans Havermann	03/2020
8730	18^63879-13	80186	Lelio R Paula	11/2015
8729	(2^266371+1814)/2	80186	Stefano Morozzi	01/2020
8731	2^266368-112295	80185	Enzo Doria	06/2014
8732	19217^14880+14880^19217	80185	Hans Havermann	03/2020
8733	(3^168050+5)/1021454	80175	Lelio R Paula	10/2012
8734	(2^266324+1386)/2	80172	Stefano Morozzi	01/2020
8735	(22*10^80167+41)/9	80168	Robert Price	02/2015
8736	(2^266308+1618)/2	80167	Stefano Morozzi	01/2020
8737	(34*10^80162-43)/9	80163	Ray Chandler	12/2010
8738	(2^266276+762)/2	80157	Stefano Morozzi	01/2020
8740	(38*10^80150-11)/9	80151	Robert Price	05/2015
8739	(598*10^80149-31)/9	80151	Robert Price	02/2017
8741	19^62678-80	80150	Lelio R Paula	12/2015
8742	(559^29173-1)/558	80148	Serge Batalov	08/2020
8743	10^80139+32343	80140	Patrick De Geest	02/2011
8744	10^80139-9	80139	Alexander Gramolin	01/2011
8745	3^167955-106	80135	Lelio R Paula	12/2015
8746	20545^7944+7944^20545	80127	Hans Havermann	04/2020
8747	18876^17569+17569^18876	80124	Hans Havermann	03/2020
8748	(2^266137+3782)/2	80115	Stefano Morozzi	01/2020
8749	(2^266121+3846)/2	80111	Stefano Morozzi	01/2020
8750	22752^3313+3313^22752	80093	Hans Havermann	03/2020

Find by discoverer :

PRP Records

Probable Primes Top 10000

(280932 PRPs in the top)