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 ?
7501	(19*10^84409-61)/3	84410	Robert Price	04/2017
7502	2^280388+117	84406	Lelio R Paula	08/2012
7503	2^280389-566533	84406	Paul Bourdelais	03/2013
7504	23423^4008+4008^23423	84392	Hans Havermann	07/2020
7505	(2^280340+3322)/2	84391	Stefano Morozzi	01/2020
7506	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
7507	(1897^25741-1)/1896	84378	Serge Batalov	08/2020
7509	119^40652+118	84376	Norbert Schneider	09/2018
7508	(2^280291+2274)/2	84376	Stefano Morozzi	01/2020
7510	2^280240-173	84361	Lelio R Paula	08/2012
7511	(184*10^84348-1)/3	84350	Robert Price	02/2017
7512	21068^10083+10083^21068	84348	Hans Havermann	07/2020
7513	4*10^84346+93	84347	Robert Price	01/2017
7514	7*2^280156-5	84337	Lelio R Paula	08/2014
7515	(8760^21391-1)/8759	84331	Serge Batalov	08/2020
7516	8*7^99782-3	84327	Lelio R Paula	10/2014
7517	2^280116+133	84324	Lelio R Paula	08/2012
7518	2^280118+54615	84324	Lelio R Paula	09/2013
7519	(509203*2^280090-1)/3	84321	Lelio R Paula	04/2015
7520	6^108354+47	84316	Lelio R Paula	12/2015
7521	(2^280069+462)/2	84309	Stefano Morozzi	01/2020
7522	20657^12058+12058^20657	84307	Hans Havermann	07/2020
7523	10^84305+141963	84306	Patrick De Geest	07/2013
7524	10^84305-57	84305	Robert Price	05/2011
7525	9^88339+38^88339-24^88339-3*2^88339	84297	Mike Oakes	01/2011
7526	75843!4-32	84295	Robert Price	11/2019
7527	3^176648-112804	84283	Enzo Doria	06/2014
7528	6^108310+115	84282	Lelio R Paula	12/2015
7529	(11*2^279968-1)/5	84280	Lelio R Paula	02/2014
7530	6^108288-16643	84265	Enzo Doria	02/2013
7531	2^279917-58695	84264	Lelio R Paula	08/2013
7532	65^46477+36	84259	Lelio R Paula	01/2016
7533	(2^279883+3230)/2	84253	Stefano Morozzi	01/2020
7534	(2^279876+1422)/2	84251	Stefano Morozzi	01/2020
7535	2^279866-1907	84249	Yves Minet	05/2013
7536	23140^4373+4373^23140	84248	Hans Havermann	07/2020
7537	19736^18567+18567^19736	84248	Hans Havermann	07/2020
7539	(3^176580-5)/28076	84246	Lelio R Paula	12/2012
7538	(p(17530)#+4)/2	84246	Robert Price	09/2017
7540	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
7541	18^67103-41	84233	Lelio R Paula	11/2015
7542	20^64743-43	84233	Lelio R Paula	01/2016
7543	(2^279807+2454)/2	84230	Stefano Morozzi	01/2020
7544	19717^18672+18672^19717	84216	Hans Havermann	07/2020
7545	(2^279754+3574)/2	84215	Stefano Morozzi	01/2020
7546	143^39070+39070^143	84209	Serge Batalov	05/2014
7547	11^80857-5400	84204	Enzo Doria	01/2013
7548	(2^279642+3130)/2	84181	Stefano Morozzi	01/2020
7549	(13*10^84179+161)/3	84180	Robert Price	04/2017
7550	2^279634-110405	84179	Enzo Doria	05/2014
7551	(74*10^84170+313)/9	84171	Robert Price	11/2017
7552	2^279582-1017	84163	Lelio R Paula	08/2013
7553	(22*10^84159-19)/3	84160	Robert Price	02/2017
7554	p(17513)#/2+512	84156	Robert Price	05/2017
7555	(19*10^84144-43)/3	84145	Robert Price	10/2017
7556	(9*2^279507-1)/137	84139	Lelio R Paula	02/2014
7557	11^80792-810	84137	Enzo Doria	11/2012
7558	(97*10^84134-1)/3	84136	Serge Batalov	12/2014
7559	p(17507)#/2+32	84125	Robert Price	12/2016
7560	(1750^25939-1)/1749	84118	Serge Batalov	08/2020
7561	21485^8224+8224^21485	84116	Hans Havermann	04/2017
7562	3^176294-340	84114	Lelio R Paula	12/2015
7563	(3^176287+4)/2191	84107	Lelio R Paula	12/2012
7564	2^279388-719	84105	Yves Minet	05/2012
7565	(22699*2^279378+1)/221	84104	Lelio R Paula	06/2014
7566	(28*10^84095-67)/3	84096	Robert Price	10/2020
7567	(2^279343+578)/2	84091	Stefano Morozzi	01/2020
7568	2^279332-110447	84088	Enzo Doria	05/2014
7569	2^279320+7	84084	Lelio R Paula	06/2012
7570	127^39966-2	84081	Lelio R Paula	10/2017
7571	(2^279299+2490)/2	84078	Stefano Morozzi	01/2020
7572	(2^279301+1694)/2	84078	Stefano Morozzi	01/2020
7573	(2^279285+962)/2	84073	Stefano Morozzi	01/2020
7574	(2^279269+1122)/2	84069	Stefano Morozzi	01/2020
7575	(11*2^279240-1)/95	84059	Lelio R Paula	02/2014
7576	2^279218-111347	84053	Enzo Doria	05/2014
7577	35^54435+2	84052	Lelio R Paula	05/2013
7578	(2^279176+2998)/2	84041	Stefano Morozzi	01/2020
7579	(31*2^279191-1)/12511523	84040	Lelio R Paula	02/2014
7580	20996^10059+10059^20996	84038	Hans Havermann	05/2017
7581	97*10^84033-3	84035	Robert Price	01/2017
7582	(2^279153+1326)/2	84034	Stefano Morozzi	01/2020
7583	(2^279155+3534)/2	84034	Stefano Morozzi	01/2020
7584	21234^9067+9067^21234	84033	Hans Havermann	05/2017
7585	(134569^16384+1)/2	84033	Richard Fischer	06/2018
7586	(5858^22303-1)/5857	84029	Serge Batalov	08/2020
7587	2^279095-109717	84016	Enzo Doria	04/2014
7588	(2^279054+1438)/2	84004	Stefano Morozzi	01/2020
7589	10^83997-40001	83997	Robert Price	01/2021
7590	14^73282-99	83991	Lelio R Paula	11/2015
7591	21457^8200+8200^21457	83979	Hans Havermann	06/2017
7592	89*10^83976-7	83978	Robert Price	03/2017
7593	2^278955+173	83974	Lelio R Paula	06/2012
7594	(7*2^278851+1)/39	83942	Lelio R Paula	12/2012
7595	(9913*2^278844-1)/40803	83940	Lelio R Paula	04/2015
7596	5^120076-14846	83930	Enzo Doria	02/2013
7597	(85*10^83921-1)/3	83923	Robert Price	07/2017
7598	(2^278770-3)/23	83917	Lelio R Paula	12/2012
7599	(10^83916+449)/9	83916	Serge Batalov	12/2014
7601	2^278715+99	83902	Lelio R Paula	06/2012
7600	(132109^16384+1)/2	83902	Richard Fischer	05/2018
7602	40235!2-2^40235	83899	Robert Price	09/2015
7603	2^278698-171	83897	Lelio R Paula	06/2012
7604	(19*10^83894-43)/3	83895	Robert Price	10/2017
7605	6^107802+25	83887	Lelio R Paula	12/2015
7606	8*10^83880+39	83881	Robert Price	01/2017
7607	(58*10^83878+23)/9	83879	Robert Price	09/2015
7608	7^99244-90	83871	Lelio R Paula	10/2015
7609	(2^278601+1674)/2	83867	Stefano Morozzi	01/2020
7610	2^278554+4257	83854	Lelio R Paula	08/2013
7611	2^278504-109619	83839	Enzo Doria	04/2014
7612	2^278499+1870433	83837	Enzo Doria	05/2016
7613	(2^278487+570)/2	83833	Stefano Morozzi	01/2020
7614	105^41475+104	83829	Norbert Schneider	11/2016
7615	15^71276-68	83828	Lelio R Paula	11/2015
7616	2^278464-216413	83827	Enzo Doria	04/2013
7617	(2^278440+1602)/2	83819	Stefano Morozzi	01/2020
7618	(76*10^83816-211)/9	83817	Robert Price	10/2017
7619	(2^278429+1950)/2	83816	Stefano Morozzi	01/2020
7620	(2^278428+1750)/2	83815	Stefano Morozzi	01/2020
7621	(8*10^83811-101)/3	83812	Robert Price	10/2017
7622	2^278400+40755	83807	Lelio R Paula	08/2013
7623	(2^278394+3718)/2	83805	Stefano Morozzi	01/2020
7624	(2^278388+3586)/2	83803	Stefano Morozzi	01/2020
7625	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
7626	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
7627	19551^19268+19268^19551	83773	Hans Havermann	05/2017
7628	20625^11522+11522^20625	83770	Hans Havermann	05/2017
7629	(44*10^83768-791)/9	83769	Robert Price	10/2017
7630	(87^43189+1)/88	83764	Paul Bourdelais	08/2017
7631	2^278235-49	83758	Lelio R Paula	06/2012
7632	23543^3610+3610^23543	83755	Hans Havermann	05/2017
7634	18^66711-91	83741	Lelio R Paula	11/2015
7633	4*10^83740-89	83741	Robert Price	08/2017
7635	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
7636	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
7637	4*7^99059-9	83716	Lelio R Paula	10/2014
7638	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
7639	2^278077+1867211	83710	Enzo Doria	03/2016
7640	(85*10^83708+203)/9	83709	Robert Price	09/2020
7641	2^278059-27	83705	Lelio R Paula	06/2012
7642	214^35917+35917^214	83702	Norbert Schneider	12/2014
7643	(23*10^83693+7)/3	83694	Robert Price	10/2015
7644	85^43375-2	83689	Lelio R Paula	09/2013
7645	5*3^175360+4	83669	Lelio R Paula	07/2014
7646	(23^61441-1)/22	83665	Robert Price	01/2012
7647	20091^14596+14596^20091	83664	Hans Havermann	03/2017
7648	2^277907-110629	83659	Enzo Doria	05/2014
7649	19522^19283+19283^19522	83656	Hans Havermann	04/2017
7650	(2^277881+2570)/2	83651	Stefano Morozzi	01/2020
7651	8*5^119664-3	83643	Lelio R Paula	10/2014
7652	8*3^175299-7	83640	Lelio R Paula	07/2014
7653	(26*10^83638-413)/9	83639	Robert Price	10/2017
7654	(197*10^83636+7)/3	83638	Robert Price	12/2020
7655	3^175250+22	83616	Robert Price	12/2013
7656	11^80285+30	83609	Lelio R Paula	10/2015
7657	26870^1293+1293^26870	83609	Hans Havermann	03/2017
7658	(6730^21841-1)/6729	83604	Serge Batalov	08/2020
7659	(2828^24223-1)/2827	83602	Serge Batalov	08/2020
7660	2^277691+1874423	83594	Enzo Doria	06/2016
7661	13^75022-60	83571	Lelio R Paula	11/2015
7662	(2^277593+2622)/2	83564	Stefano Morozzi	01/2020
7663	14^72905-51	83559	Lelio R Paula	11/2015
7664	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
7665	5^119532-12	83550	Lelio R Paula	10/2015
7666	6^107358-16253	83541	Enzo Doria	02/2013
7667	2^277478-460211	83530	Enzo Doria	06/2015
7668	(2^277474+814)/2	83528	Stefano Morozzi	01/2020
7669	(22*10^83525-7)/3	83526	Erik Branger	09/2014
7670	(30^56543+1)/31	83520	Robert Price	07/2013
7671	2^277417-460783	83511	Paul Bourdelais	04/2013
7672	(2^277404+3582)/2	83507	Stefano Morozzi	01/2020
7673	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
7674	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
7675	21368^8085+8085^21368	83500	Hans Havermann	04/2017
7676	(2^277353+3750)/2	83492	Stefano Morozzi	01/2020
7677	(2^277348+3538)/2	83490	Stefano Morozzi	01/2020
7678	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
7679	5^119439-66	83485	Lelio R Paula	10/2015
7680	(14*10^83471-101)/3	83472	Robert Price	04/2017
7681	5*6^107263+7	83468	Lelio R Paula	10/2014
7682	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
7683	2^277244-175709	83459	Hans Havermann	10/2018
7684	(2^277230+1450)/2	83455	Stefano Morozzi	01/2020
7685	(2^277232+3658)/2	83455	Stefano Morozzi	01/2020
7686	17^67796-92	83420	Lelio R Paula	11/2015
7687	2^277106-110057	83418	Enzo Doria	04/2014
7688	6^107200-19	83418	Lelio R Paula	12/2015
7689	11^80096-1830	83412	Enzo Doria	12/2012
7690	3^174801+56	83402	Lelio R Paula	12/2015
7691	2^277033-111973	83396	Enzo Doria	05/2014
7692	120^40105-119	83386	Norbert Schneider	09/2018
7693	(2^276992+2046)/2	83383	Stefano Morozzi	01/2020
7694	(2^276990+474)/2	83382	Stefano Morozzi	01/2020
7695	20519^11572+11572^20519	83378	Hans Havermann	03/2017
7696	20850^9971+9971^20850	83374	Hans Havermann	03/2017
7699	6^107122-18863	83358	Enzo Doria	03/2013
7697	(2^276908+2322)/2	83358	Stefano Morozzi	01/2020
7698	(2^276910+2734)/2	83358	Stefano Morozzi	01/2020
7700	4*10^83354-89	83355	Robert Price	08/2017
7701	3^174697-34	83352	Robert Price	11/2013
7703	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
7702	(2^276860+1678)/2	83343	Stefano Morozzi	01/2020
7704	(2^276841+3354)/2	83338	Stefano Morozzi	01/2020
7706	2^276825+75227	83333	Enzo Doria	04/2016
7705	34*10^83331-9	83333	Robert Price	06/2020
7707	5^119214+84	83328	Lelio R Paula	10/2015
7708	2^276803-159	83327	Lelio R Paula	06/2012
7709	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
7710	7*10^83297-39	83298	Robert Price	07/2020
7711	114^40495+40495^114	83295	Norbert Schneider	12/2014
7712	39967!2+1024	83282	Robert Price	02/2015
7713	(1894^25411-1)/1893	83279	Serge Batalov	08/2020
7715	2^276641+57	83278	Lelio R Paula	06/2012
7716	35^53934-3414	83278	Enzo Doria	03/2013
7714	21777^6670+6670^21777	83278	Hans Havermann	06/2020
7717	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
7718	2^276615-4035	83270	Lelio R Paula	08/2013
7719	2^276588+1155	83262	Lelio R Paula	08/2013
7720	2^276587-937	83261	Yves Minet	10/2009
7721	2^276584-113183	83261	Enzo Doria	07/2014
7722	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
7723	2^276547-109591	83249	Enzo Doria	04/2014
7724	13^74733-32	83249	Lelio R Paula	11/2015
7725	2^276523-2587	83242	Yves Minet	07/2014
7726	18^66311-43	83239	Lelio R Paula	11/2015
7727	11^79919-1530	83228	Enzo Doria	12/2012
7728	2^276468-109745	83226	Enzo Doria	04/2014
7729	2^276462+5385	83224	Lelio R Paula	08/2013
7730	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
7732	2^276391-15	83202	Lelio R Paula	06/2012
7731	(4*10^83201+173)/3	83202	Robert Price	01/2017
7733	(259*10^83186-1)/3	83188	Robert Price	12/2020
7734	(2^276327+534)/2	83183	Stefano Morozzi	01/2020
7735	2^276316-109655	83180	Enzo Doria	04/2014
7736	2^276305-112063	83177	Enzo Doria	06/2014
7737	(2^276296+3406)/2	83174	Stefano Morozzi	01/2020
7738	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
7739	(2^276277+3254)/2	83168	Stefano Morozzi	01/2020
7740	74913!4-2	83161	Robert Price	07/2017
7741	(3023^23893-1)/3022	83155	Serge Batalov	08/2020
7742	2^276227-1837207	83153	Enzo Doria	05/2015
7744	(2^276227+3)/7	83152	Lelio R Paula	12/2012
7743	(2^276229+12)/28	83152	Stefano Morozzi	03/2020
7745	(2^276205+1190)/2	83146	Stefano Morozzi	01/2020
7746	2^276184-63389	83140	Paul Bourdelais	02/2012
7747	(2^276165+2046)/2	83134	Stefano Morozzi	01/2020
7748	(2^276105+1274)/2	83116	Stefano Morozzi	01/2020
7749	2^276066-111603	83105	Enzo Doria	05/2014
7750	19438^18837+18837^19438	83098	Hans Havermann	07/2020

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Probable Primes Top 10000

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