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 ?
6501	2^272907-111439	82154	Enzo Doria	05/2014
6502	(67607*2^272901+1)/50790115	82149	Lelio R Paula	06/2014
6503	2^272875-69	82144	Lelio R Paula	06/2012
6504	7^97197+4	82141	Robert Price	01/2014
6505	(4*6^105554+1)/5	82137	Serge Batalov	10/2014
6506	2^272826-4433	82129	Yves Minet	03/2019
6507	6^105531-109	82120	Lelio R Paula	12/2015
6508	2^272766-65	82111	Lelio R Paula	06/2012
6509	19^64205-78	82103	Lelio R Paula	12/2015
6510	2^272702+1869979	82092	Enzo Doria	05/2016
6511	(29*2^272687-1)/9	82088	Lelio R Paula	02/2014
6512	(5*10^82085-119)/3	82086	Robert Price	04/2016
6513	(2^272665+1334)/2	82081	Stefano Morozzi	01/2020
6514	2^272660-110049	82079	Enzo Doria	04/2014
6515	6^105474+67	82075	Lelio R Paula	12/2015
6516	2^272637+82875	82072	Lelio R Paula	07/2013
6517	2^272587-31	82057	Lelio R Paula	06/2012
6518	(41*10^82044-59)/9	82045	Robert Price	10/2017
6519	8*5^117368+9	82038	Lelio R Paula	10/2014
6520	(101525^16384+1)/131074	82023	Lelio R Paula	11/2011
6521	4*5^117343-7	82020	Lelio R Paula	10/2014
6522	(2^272381+506)/2	81995	Stefano Morozzi	01/2020
6523	(265*10^81990+17)/3	81992	Robert Price	05/2016
6524	3^171843+10	81990	Robert Price	10/2013
6525	(2^272361+3762)/2	81989	Stefano Morozzi	01/2020
6526	(7*10^81985+107)/3	81986	Robert Price	02/2017
6527	(3*2^272356+1)/177163	81983	Lelio R Paula	12/2012
6528	2^272296-111149	81970	Enzo Doria	05/2014
6529	(2^272293+2810)/2	81969	Stefano Morozzi	01/2020
6530	(2^272278+2118)/2	81964	Stefano Morozzi	01/2020
6531	(9*2^272243-1)/7	81954	Lelio R Paula	02/2014
6532	2^272177-111223	81934	Enzo Doria	05/2014
6533	(2^272127+3878)/2	81919	Stefano Morozzi	01/2020
6535	(151009^15817+1)/151010	81912	Faysal YAtim	06/2017
6534	(2^272104+1950)/2	81912	Stefano Morozzi	01/2020
6536	(16*10^81896-19)/3	81897	Robert Price	03/2016
6537	(2^271922+78557)/63	81855	Lelio R Paula	12/2012
6538	(10^81848+77)/3	81848	Robert Price	01/2017
6539	(24737*2^271883+1)/3757	81846	Lelio R Paula	06/2014
6540	(2^271885+1670)/2	81846	Stefano Morozzi	01/2020
6541	18813^19144-19144^18813	81831	Norbert Schneider	02/2020
6542	(2^271734+3942)/2	81800	Stefano Morozzi	01/2020
6543	10^81778+39	81779	Robert Price	03/2011
6544	10^81778-171999	81778	Patrick De Geest	07/2013
6545	(2^271652+2886)/2	81776	Stefano Morozzi	01/2020
6546	(14*10^81767-11)/3	81768	Erik Branger	09/2014
6547	(2^271546+610)/2	81744	Stefano Morozzi	01/2020
6548	2^271541+1868417	81742	Enzo Doria	04/2016
6549	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
6550	2^271484-167	81725	Lelio R Paula	06/2012
6551	(8*10^81709-611)/9	81709	Robert Price	11/2017
6552	(2^271431+1790)/2	81709	Stefano Morozzi	01/2020
6553	2^271382+12909	81695	Lelio R Paula	07/2013
6554	49^48334+48	81694	Norbert Schneider	07/2014
6555	7^96668+48	81694	Lelio R Paula	10/2015
6556	11^78435-1410	81682	Enzo Doria	12/2012
6557	5*10^81653+9	81654	Dmitry Domanov	11/2010
6558	(2^271224+1230)/2	81647	Stefano Morozzi	01/2020
6559	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
6560	(2^271168+1806)/2	81630	Stefano Morozzi	01/2020
6561	3^171068+52	81621	Lelio R Paula	12/2015
6562	2^271115-110407	81614	Enzo Doria	05/2014
6563	2^271111-110635	81613	Enzo Doria	05/2014
6564	2^271098-111	81609	Lelio R Paula	06/2012
6565	(77*10^81606+13)/9	81607	Robert Price	10/2015
6566	2^271064-2790209	81599	Enzo Doria	03/2016
6567	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
6568	2^271040-57	81592	Lelio R Paula	06/2012
6569	(14*10^81585+73)/3	81586	Robert Price	04/2016
6570	127^38779+126	81584	Norbert Schneider	02/2015
6571	18^64966-43	81551	Lelio R Paula	11/2015
6572	(2^270843+1074)/2	81532	Stefano Morozzi	01/2020
6573	(2^270840+47)/591	81529	Lelio R Paula	12/2012
6574	20^62654+87	81515	Lelio R Paula	01/2016
6575	(19*10^81488+191)/3	81489	Robert Price	01/2017
6576	8*10^81487+21	81488	Robert Price	02/2017
6577	(73*10^81485+107)/9	81486	Robert Price	08/2016
6578	536^29847+29847^536	81458	Norbert Schneider	03/2017
6579	8*7^96378+9	81450	Lelio R Paula	10/2014
6580	(2^270560+3862)/2	81447	Stefano Morozzi	01/2020
6581	2^270546-110345	81443	Enzo Doria	05/2014
6582	13^73105-60	81435	Lelio R Paula	11/2015
6583	(2^270502+1518)/2	81429	Stefano Morozzi	01/2020
6584	(2^270479+2114)/2	81422	Stefano Morozzi	01/2020
6585	(2^270384+1218)/2	81394	Stefano Morozzi	01/2020
6586	44^49524+43	81391	Norbert Schneider	06/2014
6587	(3*2^270368-1)/13	81389	Lelio R Paula	02/2014
6588	(2^270337+1130)/2	81380	Stefano Morozzi	01/2020
6589	(10^81363+719)/9	81363	Serge Batalov	12/2014
6590	(10^81353+449)/9	81353	Serge Batalov	12/2014
6591	14^70978-89	81350	Lelio R Paula	11/2015
6592	11^78108-2040	81342	Enzo Doria	12/2012
6593	3^170400-58	81302	Lelio R Paula	12/2015
6594	(17*10^81300-131)/3	81301	Robert Price	12/2017
6595	10^81297+36991	81298	Patrick De Geest	06/2013
6596	10^81297-57	81297	Robert Price	05/2011
6597	(2^270063+3206)/2	81297	Stefano Morozzi	01/2020
6598	2^270055-113047	81295	Enzo Doria	07/2014
6599	18^64759-55	81291	Lelio R Paula	11/2015
6600	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
6601	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
6602	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014
6603	(2^269922+3574)/2	81255	Stefano Morozzi	01/2020
6604	2^269819-4597	81224	Yves Minet	03/2019
6605	(2^269816+7)/424901	81218	Lelio R Paula	12/2012
6606	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
6607	(2^269720+3778)/2	81194	Stefano Morozzi	01/2020
6608	(17*2^269720+1)/303	81193	Lelio R Paula	07/2012
6609	56^46441-55^46441	81188	Robert Price	10/2013
6610	2^269664+177	81177	Lelio R Paula	06/2012
6611	(13*2^269665-1)/185	81177	Lelio R Paula	02/2014
6612	2^269539-112249	81140	Enzo Doria	06/2014
6613	((2170026-3)3^(170026-1)+1)/4	81128	Robert Price	01/2015
6615	(2^269495-5)/9	81126	Lelio R Paula	12/2012
6614	1239^26228+26228^1239	81126	Norbert Schneider	10/2019
6616	2^269490-3623	81125	Yves Minet	10/2009
6617	(55459*2^269444+1)/35	81114	Lelio R Paula	06/2014
6618	(2^269417+78557)/5257	81099	Lelio R Paula	12/2012
6619	4*5^116011-7	81089	Lelio R Paula	10/2014
6620	(2^269349+2366)/2	81082	Stefano Morozzi	01/2020
6621	(2^269303+2946)/2	81068	Stefano Morozzi	01/2020
6622	7*10^81058+79	81059	Robert Price	02/2017
6623	2^269236-109907	81049	Enzo Doria	04/2014
6624	(2^269182+1870)/2	81032	Stefano Morozzi	01/2020
6625	(2^269179+3006)/2	81031	Stefano Morozzi	01/2020
6626	(8*10^81029-11)/3	81030	Erik Branger	03/2014
6627	3*10^81021+7	81022	Erik Branger	11/2013
6628	6^104115+103	81018	Lelio R Paula	12/2015
6629	2^269120+1869151	81014	Enzo Doria	05/2016
6630	5^115901+12	81012	Lelio R Paula	10/2015
6631	(2^269072+3610)/2	80999	Stefano Morozzi	01/2020
6632	(2^269083-9)/320369	80997	Lelio R Paula	12/2012
6633	(2^269002+1614)/2	80978	Stefano Morozzi	01/2020
6634	17^65810-20	80976	Lelio R Paula	11/2015
6635	20^62236-23	80971	Lelio R Paula	01/2016
6636	2^268974-112181	80970	Enzo Doria	06/2014
6638	L(387433)	80969	Renaud Lifchitz	11/2003
6637	V(387433)	80969	Serge Batalov	03/2015
6639	(2^268957+602)/2	80964	Stefano Morozzi	01/2020
6640	(2^268955-509203)/5	80963	Lelio R Paula	12/2012
6641	(87398^16384+1)/65537	80957	Lelio R Paula	11/2011
6642	329^32160+32160^329	80954	Norbert Schneider	11/2014
6643	19678^12973+12973^19678	80937	Hans Havermann	02/2020
6644	(2^268864+3558)/2	80936	Stefano Morozzi	01/2020
6645	2^268859-159	80935	Lelio R Paula	05/2012
6646	(2^268841-lucasV(1,2,268841)+1)/2	80929	Mike Oakes	11/2016
6648	2^268827+5775	80925	Lelio R Paula	07/2013
6647	2^268824-110255	80925	Enzo Doria	05/2014
6649	(2^268824+1902)/2	80924	Stefano Morozzi	01/2020
6650	2^268798-1868321	80917	Enzo Doria	04/2016
6651	20613^8420+8420^20613	80913	Hans Havermann	03/2020
6652	2^268753-114621	80903	Enzo Doria	05/2015
6653	2^268743+1605	80900	Lelio R Paula	07/2013
6654	6^103954-139	80892	Lelio R Paula	12/2015
6655	10^80883+49	80884	Robert Price	03/2011
6656	10^80883-80327	80883	Patrick De Geest	07/2013
6657	6^103937+121	80879	Lelio R Paula	12/2015
6658	148^37266+147	80877	Norbert Schneider	12/2018
6659	(26*10^80875-119)/3	80876	Robert Price	07/2016
6660	(22699*2^268657+1)/6351	80875	Lelio R Paula	06/2014
6661	(2^268612+2530)/2	80860	Stefano Morozzi	01/2020
6662	2^268581-869688105	80851	Lelio R Paula	05/2016
6663	(11*2^268521-1)/3	80834	Lelio R Paula	02/2014
6664	2^268516-249	80832	Yves Minet	02/2012
6665	22259^4278+4278^22259	80828	Hans Havermann	03/2020
6666	2^268500+16095	80827	Lelio R Paula	07/2013
6667	3^169402+100	80826	Lelio R Paula	12/2015
6668	(2^268495+566)/2	80825	Stefano Morozzi	01/2020
6669	9^84698+8^(84698-1)	80823	Robert Price	03/2016
6670	2^268472-109739	80819	Enzo Doria	04/2014
6671	(9*2^268454+1)/37	80813	Lelio R Paula	12/2012
6672	(3*2^268502+1)/377902188435353647	80811	Lelio R Paula	12/2012
6673	(2^268441+3962)/2	80809	Stefano Morozzi	01/2020
6674	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
6675	15^68702-76	80800	Lelio R Paula	11/2015
6676	2^268408+7	80799	Lelio R Paula	05/2012
6677	2^268375+141	80789	Lelio R Paula	05/2012
6678	12^74856-47	80784	Lelio R Paula	11/2015
6679	2^268346+524287	80781	Paul Underwood	08/2018
6680	6^103770-107	80749	Lelio R Paula	12/2015
6681	3^169224-62	80741	Lelio R Paula	12/2015
6682	p(16866)#/2+64	80741	Robert Price	03/2017
6683	5^115502-72	80733	Lelio R Paula	10/2015
6684	(2^268154+2262)/2	80723	Stefano Morozzi	01/2020
6685	(2^268156+1290)/2	80723	Stefano Morozzi	01/2020
6687	2^268079-1927	80700	Yves Minet	10/2009
6686	(2^268078+2514)/2	80700	Stefano Morozzi	01/2020
6688	2^268028+117	80685	Lelio R Paula	05/2012
6689	121^38738+120	80683	Norbert Schneider	01/2015
6690	(3^169097-8)/835	80677	Lelio R Paula	12/2012
6691	(2^267956+1810)/2	80663	Stefano Morozzi	01/2020
6692	19359^14666+14666^19359	80656	Hans Havermann	12/2019
6693	2^267918+67	80652	Lelio R Paula	05/2012
6694	(89*10^80650-179)/9	80651	Robert Price	11/2017
6695	(2^267914+2094)/2	80650	Stefano Morozzi	01/2020
6696	(2^267894+2202)/2	80644	Stefano Morozzi	01/2020
6697	(302*10^80638+13)/9	80640	Robert Price	01/2017
6698	3^169004+2660	80636	Lelio R Paula	12/2015
6699	2^267860-112859	80634	Enzo Doria	06/2014
6700	2^267828-110705	80625	Enzo Doria	05/2014
6701	(2^267752+2602)/2	80602	Stefano Morozzi	01/2020
6702	2^267743+12705	80599	Lelio R Paula	07/2013
6703	(22*10^80595+23)/9	80596	Robert Price	03/2015
6704	(2^267712+2358)/2	80590	Stefano Morozzi	01/2020
6705	(2^267685+854)/2	80581	Stefano Morozzi	01/2020
6706	2^267674-51	80578	Lelio R Paula	05/2012
6707	(86*10^80571-41)/9	80572	Robert Price	11/2015
6708	(2^267637+2454)/2	80567	Stefano Morozzi	01/2020
6709	20452^8693+8693^20452	80564	Hans Havermann	02/2020
6710	2^267612-1965	80560	Lelio R Paula	07/2013
6711	2^267553+4097	80542	Lelio R Paula	07/2013
6712	7^95276-8	80518	Robert Price	01/2014
6713	(15185*2^267457-1)/47829	80513	Lelio R Paula	04/2015
6714	6^103467+163	80513	Lelio R Paula	12/2015
6715	20283^9314+9314^20283	80506	Hans Havermann	02/2020
6716	(2^267387+2294)/2	80492	Stefano Morozzi	01/2020
6717	(7*10^80490+143)/3	80491	Robert Price	04/2016
6718	19887^11152+11152^19887	80490	Hans Havermann	01/2020
6719	(2^267348+3810)/2	80480	Stefano Morozzi	01/2020
6720	86^41597-85^41597	80470	Robert Price	04/2015
6721	13^72237+30	80468	Lelio R Paula	11/2015
6722	17^65389+14	80458	Lelio R Paula	11/2015
6723	423^30634+30634^423	80456	Norbert Schneider	05/2017
6724	(2^267257+470)/2	80453	Stefano Morozzi	01/2020
6725	2^267232+105	80445	Lelio R Paula	05/2012
6726	22101^4360+4360^22101	80437	Hans Havermann	02/2020
6727	11^77237-3072000	80435	Enzo Doria	01/2013
6728	20696^7689+7689^20696	80422	Hans Havermann	01/2020
6729	(2^267149+2562)/2	80420	Stefano Morozzi	01/2020
6730	21321^5908+5908^21321	80411	Hans Havermann	02/2020
6731	2^267116-459959	80410	Enzo Doria	06/2015
6732	38715!2+8	80406	Robert Price	01/2015
6733	19579^12786+12786^19579	80406	Hans Havermann	02/2020
6734	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
6735	(2^267006+1134)/2	80377	Stefano Morozzi	01/2020
6736	24273^2048+2048^24273	80376	Hans Havermann	01/2020
6737	(2^266989+734)/2	80372	Stefano Morozzi	01/2020
6738	(2^266989+1850)/2	80372	Stefano Morozzi	01/2020
6739	2^266968-45	80366	Lelio R Paula	05/2012
6740	(2^266967+3974)/2	80365	Stefano Morozzi	01/2020
6741	20^61768-63	80363	Lelio R Paula	01/2016
6742	2^266920-112967	80351	Enzo Doria	06/2014
6743	(2^266910+2394)/2	80348	Stefano Morozzi	01/2020
6744	(2^266899+1994)/2	80345	Stefano Morozzi	01/2020
6745	8*10^80342+87	80343	Robert Price	10/2017
6746	(2^266861+890)/2	80333	Stefano Morozzi	01/2020
6747	12^74428-13	80322	Lelio R Paula	11/2015
6748	(2^266810+2718)/2	80318	Stefano Morozzi	01/2020
6749	(2^266800+2886)/2	80315	Stefano Morozzi	01/2020
6750	2^266680+27	80279	Lelio R Paula	05/2012

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