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) !!!

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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 ?
7502	(8*10^81709-611)/9	81709	Robert Price	11/2017
7501	(2^271431+1790)/2	81709	Stefano Morozzi	01/2020
7503	19648^14399+14399^19648	81703	Hans Havermann	05/2020
7504	2^271382+12909	81695	Lelio R Paula	07/2013
7505	49^48334+48	81694	Norbert Schneider	07/2014
7506	7^96668+48	81694	Lelio R Paula	10/2015
7507	11^78435-1410	81682	Enzo Doria	12/2012
7508	19575^14882+14882^19575	81680	Hans Havermann	04/2020
7509	5*10^81653+9	81654	Dmitry Domanov	11/2010
7510	(2^271224+1230)/2	81647	Stefano Morozzi	01/2020
7511	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
7512	(2^271168+1806)/2	81630	Stefano Morozzi	01/2020
7513	3^171068+52	81621	Lelio R Paula	12/2015
7514	2^271115-110407	81614	Enzo Doria	05/2014
7515	2^271111-110635	81613	Enzo Doria	05/2014
7516	2^271098-111	81609	Lelio R Paula	06/2012
7517	(77*10^81606+13)/9	81607	Robert Price	10/2015
7518	2^271064-2790209	81599	Enzo Doria	03/2016
7519	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
7520	2^271040-57	81592	Lelio R Paula	06/2012
7521	(14*10^81585+73)/3	81586	Robert Price	04/2016
7522	127^38779+126	81584	Norbert Schneider	02/2015
7523	18^64966-43	81551	Lelio R Paula	11/2015
7524	19406^15909+15909^19406	81538	Hans Havermann	06/2020
7525	(2^270843+1074)/2	81532	Stefano Morozzi	01/2020
7526	(2^270840+47)/591	81529	Lelio R Paula	12/2012
7527	20^62654+87	81515	Lelio R Paula	01/2016
7528	20120^11241+11241^20120	81503	Hans Havermann	05/2020
7529	(19*10^81488+191)/3	81489	Robert Price	01/2017
7530	8*10^81487+21	81488	Robert Price	02/2017
7531	(73*10^81485+107)/9	81486	Robert Price	08/2016
7532	536^29847+29847^536	81458	Norbert Schneider	03/2017
7533	8*7^96378+9	81450	Lelio R Paula	10/2014
7534	(2^270560+3862)/2	81447	Stefano Morozzi	01/2020
7535	(5728^21673-1)/5727	81444	Serge Batalov	08/2020
7536	2^270546-110345	81443	Enzo Doria	05/2014
7537	13^73105-60	81435	Lelio R Paula	11/2015
7538	(2^270502+1518)/2	81429	Stefano Morozzi	01/2020
7539	(2^270479+2114)/2	81422	Stefano Morozzi	01/2020
7540	(2^270384+1218)/2	81394	Stefano Morozzi	01/2020
7541	44^49524+43	81391	Norbert Schneider	06/2014
7542	(3*2^270368-1)/13	81389	Lelio R Paula	02/2014
7543	19548^14563+14563^19548	81384	Hans Havermann	05/2020
7544	(2^270337+1130)/2	81380	Stefano Morozzi	01/2020
7545	27405^932+932^27405	81377	Hans Havermann	05/2020
7546	19396^15683+15683^19396	81375	Hans Havermann	05/2020
7548	(10^81363+719)/9	81363	Serge Batalov	12/2014
7547	(734^28393-1)/733	81363	Serge Batalov	08/2020
7549	(10^81353+449)/9	81353	Serge Batalov	12/2014
7550	14^70978-89	81350	Lelio R Paula	11/2015
7551	11^78108-2040	81342	Enzo Doria	12/2012
7552	7*10^81327-57	81328	Robert Price	06/2020
7553	19102^18065+18065^19102	81315	Hans Havermann	07/2020
7554	3^170400-58	81302	Lelio R Paula	12/2015
7555	(17*10^81300-131)/3	81301	Robert Price	12/2017
7556	10^81297+36991	81298	Patrick De Geest	06/2013
7557	10^81297-57	81297	Robert Price	05/2011
7558	(2^270063+3206)/2	81297	Stefano Morozzi	01/2020
7559	19359^15826+15826^19359	81296	Hans Havermann	06/2020
7560	2^270055-113047	81295	Enzo Doria	07/2014
7561	18^64759-55	81291	Lelio R Paula	11/2015
7562	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
7563	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
7564	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014
7565	(194^35521-1)/193	81263	Serge Batalov	08/2020
7566	20722^8343+8343^20722	81258	Hans Havermann	07/2020
7567	(2^269922+3574)/2	81255	Stefano Morozzi	01/2020
7568	21310^6497+6497^21310	81249	Hans Havermann	07/2020
7569	(16392^19273-1)/16391	81225	Serge Batalov	08/2020
7570	2^269819-4597	81224	Yves Minet	03/2019
7571	(2^269816+7)/424901	81218	Lelio R Paula	12/2012
7572	23470^2887+2887^23470	81217	Hans Havermann	05/2020
7573	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
7574	(2^269720+3778)/2	81194	Stefano Morozzi	01/2020
7575	(17*2^269720+1)/303	81193	Lelio R Paula	07/2012
7576	56^46441-55^46441	81188	Robert Price	10/2013
7577	2^269664+177	81177	Lelio R Paula	06/2012
7578	(13*2^269665-1)/185	81177	Lelio R Paula	02/2014
7579	21642^5615+5615^21642	81144	Hans Havermann	07/2020
7580	2^269539-112249	81140	Enzo Doria	06/2014
7581	((2170026-3)3^(170026-1)+1)/4	81128	Robert Price	01/2015
7583	(2^269495-5)/9	81126	Lelio R Paula	12/2012
7582	1239^26228+26228^1239	81126	Norbert Schneider	10/2019
7584	2^269490-3623	81125	Yves Minet	10/2009
7585	(55459*2^269444+1)/35	81114	Lelio R Paula	06/2014
7586	19554^14065+14065^19554	81113	Hans Havermann	06/2020
7587	(2^269417+78557)/5257	81099	Lelio R Paula	12/2012
7588	4*5^116011-7	81089	Lelio R Paula	10/2014
7589	(2^269349+2366)/2	81082	Stefano Morozzi	01/2020
7590	(2^269303+2946)/2	81068	Stefano Morozzi	01/2020
7591	6*10^81060+53	81061	Robert Price	05/2020
7592	7*10^81058+79	81059	Robert Price	02/2017
7593	2^269236-109907	81049	Enzo Doria	04/2014
7594	(2^269182+1870)/2	81032	Stefano Morozzi	01/2020
7595	(2^269179+3006)/2	81031	Stefano Morozzi	01/2020
7596	(8*10^81029-11)/3	81030	Erik Branger	03/2014
7597	19749^12668+12668^19749	81025	Hans Havermann	05/2020
7598	3*10^81021+7	81022	Erik Branger	11/2013
7599	6^104115+103	81018	Lelio R Paula	12/2015
7600	2^269120+1869151	81014	Enzo Doria	05/2016
7601	5^115901+12	81012	Lelio R Paula	10/2015
7602	(2^269072+3610)/2	80999	Stefano Morozzi	01/2020
7603	(2^269083-9)/320369	80997	Lelio R Paula	12/2012
7604	2*10^80981-49	80982	Robert Price	09/2020
7605	(2^269002+1614)/2	80978	Stefano Morozzi	01/2020
7606	17^65810-20	80976	Lelio R Paula	11/2015
7607	20^62236-23	80971	Lelio R Paula	01/2016
7608	2^268974-112181	80970	Enzo Doria	06/2014
7610	L(387433)	80969	Renaud Lifchitz	11/2003
7609	V(387433)	80969	Serge Batalov	03/2015
7611	22732^3645+3645^22732	80965	Hans Havermann	06/2020
7612	(2^268957+602)/2	80964	Stefano Morozzi	01/2020
7613	(2^268955-509203)/5	80963	Lelio R Paula	12/2012
7614	19485^14284+14284^19485	80958	Hans Havermann	05/2020
7615	(87398^16384+1)/65537	80957	Lelio R Paula	11/2011
7616	329^32160+32160^329	80954	Norbert Schneider	11/2014
7617	19678^12973+12973^19678	80937	Hans Havermann	02/2020
7618	(2^268864+3558)/2	80936	Stefano Morozzi	01/2020
7619	2^268859-159	80935	Lelio R Paula	05/2012
7620	(2^268841-lucasV(1,2,268841)+1)/2	80929	Mike Oakes	11/2016
7622	2^268827+5775	80925	Lelio R Paula	07/2013
7621	2^268824-110255	80925	Enzo Doria	05/2014
7623	(2^268824+1902)/2	80924	Stefano Morozzi	01/2020
7624	2^268798-1868321	80917	Enzo Doria	04/2016
7625	20613^8420+8420^20613	80913	Hans Havermann	03/2020
7626	2^268753-114621	80903	Enzo Doria	05/2015
7627	2^268743+1605	80900	Lelio R Paula	07/2013
7628	6^103954-139	80892	Lelio R Paula	12/2015
7629	10^80883+49	80884	Robert Price	03/2011
7630	10^80883-80327	80883	Patrick De Geest	07/2013
7631	6^103937+121	80879	Lelio R Paula	12/2015
7632	148^37266+147	80877	Norbert Schneider	12/2018
7633	(26*10^80875-119)/3	80876	Robert Price	07/2016
7634	(22699*2^268657+1)/6351	80875	Lelio R Paula	06/2014
7635	(2^268612+2530)/2	80860	Stefano Morozzi	01/2020
7636	2^268581-869688105	80851	Lelio R Paula	05/2016
7637	(11*2^268521-1)/3	80834	Lelio R Paula	02/2014
7638	2^268516-249	80832	Yves Minet	02/2012
7639	22259^4278+4278^22259	80828	Hans Havermann	03/2020
7640	2^268500+16095	80827	Lelio R Paula	07/2013
7641	3^169402+100	80826	Lelio R Paula	12/2015
7642	(2^268495+566)/2	80825	Stefano Morozzi	01/2020
7643	9^84698+8^(84698-1)	80823	Robert Price	03/2016
7644	2^268472-109739	80819	Enzo Doria	04/2014
7645	(9*2^268454+1)/37	80813	Lelio R Paula	12/2012
7646	(3*2^268502+1)/377902188435353647	80811	Lelio R Paula	12/2012
7647	(2^268441+3962)/2	80809	Stefano Morozzi	01/2020
7648	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
7649	15^68702-76	80800	Lelio R Paula	11/2015
7650	2^268408+7	80799	Lelio R Paula	05/2012
7651	(16095^19207-1)/16094	80794	Serge Batalov	08/2020
7652	2^268375+141	80789	Lelio R Paula	05/2012
7653	12^74856-47	80784	Lelio R Paula	11/2015
7654	2^268346+524287	80781	Paul Underwood	08/2018
7655	9*10^80777-41	80778	Robert Price	08/2020
7656	(10868^20011-1)/10867	80764	Serge Batalov	08/2020
7657	6^103770-107	80749	Lelio R Paula	12/2015
7658	(751^28081-1)/750	80748	Serge Batalov	08/2020
7659	3^169224-62	80741	Lelio R Paula	12/2015
7660	p(16866)#/2+64	80741	Robert Price	03/2017
7661	5^115502-72	80733	Lelio R Paula	10/2015
7662	(2^268154+2262)/2	80723	Stefano Morozzi	01/2020
7663	(2^268156+1290)/2	80723	Stefano Morozzi	01/2020
7665	2^268079-1927	80700	Yves Minet	10/2009
7664	(2^268078+2514)/2	80700	Stefano Morozzi	01/2020
7666	2^268028+117	80685	Lelio R Paula	05/2012
7667	121^38738+120	80683	Norbert Schneider	01/2015
7668	(3^169097-8)/835	80677	Lelio R Paula	12/2012
7669	(2^267956+1810)/2	80663	Stefano Morozzi	01/2020
7670	19359^14666+14666^19359	80656	Hans Havermann	12/2019
7671	2^267918+67	80652	Lelio R Paula	05/2012
7672	(89*10^80650-179)/9	80651	Robert Price	11/2017
7673	(2^267914+2094)/2	80650	Stefano Morozzi	01/2020
7674	(2^267894+2202)/2	80644	Stefano Morozzi	01/2020
7675	(302*10^80638+13)/9	80640	Robert Price	01/2017
7676	3^169004+2660	80636	Lelio R Paula	12/2015
7677	2^267860-112859	80634	Enzo Doria	06/2014
7678	2^267828-110705	80625	Enzo Doria	05/2014
7679	(2956^23227-1)/2955	80611	Serge Batalov	08/2020
7680	(2^267752+2602)/2	80602	Stefano Morozzi	01/2020
7681	2^267743+12705	80599	Lelio R Paula	07/2013
7682	(22*10^80595+23)/9	80596	Robert Price	03/2015
7683	(2^267712+2358)/2	80590	Stefano Morozzi	01/2020
7684	(2^267685+854)/2	80581	Stefano Morozzi	01/2020
7685	2^267674-51	80578	Lelio R Paula	05/2012
7686	(86*10^80571-41)/9	80572	Robert Price	11/2015
7687	(2^267637+2454)/2	80567	Stefano Morozzi	01/2020
7688	20452^8693+8693^20452	80564	Hans Havermann	02/2020
7689	2^267612-1965	80560	Lelio R Paula	07/2013
7690	2^267553+4097	80542	Lelio R Paula	07/2013
7691	7^95276-8	80518	Robert Price	01/2014
7692	(15185*2^267457-1)/47829	80513	Lelio R Paula	04/2015
7693	6^103467+163	80513	Lelio R Paula	12/2015
7694	20283^9314+9314^20283	80506	Hans Havermann	02/2020
7695	(2^267387+2294)/2	80492	Stefano Morozzi	01/2020
7696	(7*10^80490+143)/3	80491	Robert Price	04/2016
7697	19887^11152+11152^19887	80490	Hans Havermann	01/2020
7698	(2^267348+3810)/2	80480	Stefano Morozzi	01/2020
7699	86^41597-85^41597	80470	Robert Price	04/2015
7700	13^72237+30	80468	Lelio R Paula	11/2015
7701	17^65389+14	80458	Lelio R Paula	11/2015
7702	423^30634+30634^423	80456	Norbert Schneider	05/2017
7703	(2^267257+470)/2	80453	Stefano Morozzi	01/2020
7704	2^267232+105	80445	Lelio R Paula	05/2012
7705	22101^4360+4360^22101	80437	Hans Havermann	02/2020
7706	11^77237-3072000	80435	Enzo Doria	01/2013
7707	20696^7689+7689^20696	80422	Hans Havermann	01/2020
7708	(2^267149+2562)/2	80420	Stefano Morozzi	01/2020
7709	21321^5908+5908^21321	80411	Hans Havermann	02/2020
7710	(13100^19531-1)/13099	80411	Serge Batalov	08/2020
7711	2^267116-459959	80410	Enzo Doria	06/2015
7712	38715!2+8	80406	Robert Price	01/2015
7713	19579^12786+12786^19579	80406	Hans Havermann	02/2020
7714	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
7715	(2^267006+1134)/2	80377	Stefano Morozzi	01/2020
7716	24273^2048+2048^24273	80376	Hans Havermann	01/2020
7717	(2^266989+734)/2	80372	Stefano Morozzi	01/2020
7718	(2^266989+1850)/2	80372	Stefano Morozzi	01/2020
7719	(13427^19471-1)/13426	80372	Serge Batalov	08/2020
7720	2^266968-45	80366	Lelio R Paula	05/2012
7721	(2^266967+3974)/2	80365	Stefano Morozzi	01/2020
7722	20^61768-63	80363	Lelio R Paula	01/2016
7723	(6253^21169-1)/6252	80356	Serge Batalov	08/2020
7724	(14005^19381-1)/14004	80355	Serge Batalov	08/2020
7725	2^266920-112967	80351	Enzo Doria	06/2014
7726	(2^266910+2394)/2	80348	Stefano Morozzi	01/2020
7727	(2^266899+1994)/2	80345	Stefano Morozzi	01/2020
7728	8*10^80342+87	80343	Robert Price	10/2017
7729	(2^266861+890)/2	80333	Stefano Morozzi	01/2020
7730	12^74428-13	80322	Lelio R Paula	11/2015
7731	(2^266810+2718)/2	80318	Stefano Morozzi	01/2020
7732	(2^266800+2886)/2	80315	Stefano Morozzi	01/2020
7733	(6163^21187-1)/6162	80291	Serge Batalov	08/2020
7734	2^266680+27	80279	Lelio R Paula	05/2012
7735	2^266630-131	80264	Lelio R Paula	05/2012
7736	(2^266627+1278)/2	80263	Stefano Morozzi	01/2020
7737	2^266598+76819	80254	Enzo Doria	05/2016
7738	24463^1908+1908^24463	80253	Hans Havermann	01/2020
7739	2^266587+1880633	80251	Enzo Doria	10/2016
7740	(2^266570+3942)/2	80246	Stefano Morozzi	01/2020
7741	2^266541-110049	80237	Enzo Doria	04/2014
7742	38635!2-8	80222	Robert Price	06/2015
7743	(2^266465+986)/2	80214	Stefano Morozzi	01/2020
7744	3^168111+168111^3-1	80210	Robert Price	04/2014
7745	(2^266447+758)/2	80209	Stefano Morozzi	01/2020
7746	2^266443+513	80208	Lelio R Paula	07/2013
7747	(26*10^80200+61)/3	80201	Robert Price	06/2017
7748	2^266412-109913	80199	Enzo Doria	04/2014
7749	(10223*2^266417+1)/45091	80199	Lelio R Paula	06/2014
7750	2^266413-4693	80199	Yves Minet	05/2019

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Probable Primes Top 10000

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