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	2^229305-1868533	69028	Enzo Doria	04/2016
7502	2^229297+1385	69026	Lelio R Paula	04/2012
7503	18^54986-2441	69023	Enzo Doria	03/2013
7504	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
7505	5^98736-14636	69014	Enzo Doria	02/2013
7506	(13^61949-5^61949)/8	69007	Robert Price	03/2013
7507	(2^229227+5)/611	69002	Lelio R Paula	04/2012
7508	2^229216-113279	69001	Enzo Doria	07/2014
7509	10^68994+51913	68995	Patrick De Geest	03/2016
7511	10^68994-10^5814-1	68994	Serge Batalov	01/2011
7510	10^68994-82947	68994	Patrick De Geest	03/2016
7512	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
7513	2^229113+107	68970	Lelio R Paula	02/2012
7514	11^66202-4410	68943	Enzo Doria	01/2013
7515	12^63883+5	68942	Lelio R Paula	07/2013
7516	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
7517	2^228962-111581	68925	Enzo Doria	05/2014
7518	2^228944+81	68920	Henri Lifchitz	01/2007
7519	11^66174-54	68914	Lelio R Paula	09/2013
7520	2^228913-111265	68910	Enzo Doria	05/2014
7521	2^228902+73519	68907	Enzo Doria	04/2016
7522	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
7523	2^228821+76427	68882	Enzo Doria	05/2016
7524	3^144340+50	68868	Lelio R Paula	09/2013
7525	2^228758-112967	68864	Enzo Doria	06/2014
7526	2^228743-111379	68859	Enzo Doria	05/2014
7527	2^228741-110911	68858	Enzo Doria	05/2014
7529	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
7528	3*5^98511-8	68857	Lelio R Paula	09/2014
7530	2^228717+467	68851	Lelio R Paula	02/2011
7531	Phi(153218,10)/2211855049/23592660859/497714117291	68849	Maksym Voznyy	10/2011
7532	(509203*2^228665-1)/35	68840	Lelio R Paula	04/2015
7533	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
7534	11^66074-1050	68809	Enzo Doria	11/2012
7535	(68*10^68798-11)/3	68800	Robert Price	10/2017
7536	2^228484+181	68781	Lelio R Paula	02/2012
7537	2^228479-58695	68780	Lelio R Paula	04/2012
7538	2^228465-15853	68775	Enzo Doria	04/2013
7539	11^66040-5400	68774	Enzo Doria	01/2013
7540	(13*2^228441-1)/575	68766	Lelio R Paula	01/2014
7541	(17*2^228393+1)/295	68752	Lelio R Paula	08/2012
7542	2*10^68744+41	68745	Robert Price	01/2017
7543	11^66011-150	68744	Enzo Doria	08/2012
7544	(13*2^228304-1)/81	68726	Lelio R Paula	01/2014
7545	2^228295-111079	68724	Enzo Doria	05/2014
7547	(3^144039+7)/22	68723	Lelio R Paula	04/2012
7546	(8*10^68722+49)/3	68723	Robert Price	03/2016
7548	(35*10^68718+1)/9	68719	Serge Batalov	11/2010
7549	2^228271-228271	68717	Henri Lifchitz	11/2004
7550	2^228257+82875	68713	Lelio R Paula	02/2013
7551	3^144013+40	68712	Lelio R Paula	09/2013
7552	13^61671-86	68699	Lelio R Paula	09/2013
7553	(46*10^68698+683)/9	68699	Robert Price	12/2017
7554	17^55828-72	68694	Lelio R Paula	09/2013
7555	6^88259+61	68679	Lelio R Paula	09/2013
7556	18^54699-5	68663	Lelio R Paula	09/2013
7557	33^45216+2	68662	Lelio R Paula	05/2013
7559	(2^228073-5)/3	68657	Lelio R Paula	04/2012
7558	(2^(6*38012+1)-5)/3	68657	Kevin Acres	11/2013
7560	2^228055-111607	68652	Enzo Doria	05/2014
7561	2^228054-114761	68652	Enzo Doria	05/2015
7562	2^228041+1185	68648	Lelio R Paula	04/2012
7563	2^228040-1037	68647	Yves Minet	11/2012
7564	2*F(328450)-1	68642	Henri Lifchitz	12/2009
7565	5^98201-34	68640	Lelio R Paula	06/2013
7566	9^71910+38^71910-24^71910-3*2^71910	68620	Mike Oakes	12/2010
7567	7*2^227780-3	68570	Lelio R Paula	04/2014
7568	15327^16382-16382^15327	68567	Norbert Schneider	11/2018
7569	2^227733-121	68555	Lelio R Paula	02/2012
7570	2^227702-16967	68546	Enzo Doria	05/2013
7571	2^227689-111655	68542	Enzo Doria	05/2014
7572	gcd(V(823915),5F(164783)(F(164783)-1)+1)	68536	Serge Batalov	04/2015
7573	5^98051+2	68535	Ray Chandler	07/2011
7574	5*10^68524+51	68525	Robert Price	01/2017
7575	(11*10^68520-149)/3	68521	Robert Price	01/2017
7576	19^53573-78	68507	Lelio R Paula	09/2013
7577	(68*10^68504+13)/9	68505	Ray Chandler	10/2010
7578	9*5^98003+4	68503	Lelio R Paula	09/2014
7579	2^227528+51	68493	Lelio R Paula	02/2012
7580	(146*28^47316+1)/3	68476	Karsten Bonath	06/2018
7581	3^143497+8	68466	Lelio R Paula	04/2012
7582	2^227430-95	68464	Lelio R Paula	02/2012
7583	(8*10^68455+13)/3	68456	Robert Price	11/2017
7584	3*5^97934-2	68454	Lelio R Paula	09/2014
7585	20^52613+77	68452	Lelio R Paula	09/2013
7586	2^227371+32769	68446	Lelio R Paula	04/2012
7587	(3^143465+4)/21270420067	68440	Lelio R Paula	04/2012
7588	CopelandErdos(68433)	68433	Eric W. Weisstein	08/2013
7589	2^227323+75431	68432	Enzo Doria	04/2016
7590	2^227314-1965	68429	Lelio R Paula	04/2012
7591	2^227303-110617	68426	Enzo Doria	05/2014
7592	7^80963+66	68422	Lelio R Paula	07/2013
7593	2^227290+73849	68422	Enzo Doria	04/2016
7594	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
7595	2^227256-2786249	68411	Enzo Doria	03/2016
7597	8*10^68400-7	68401	Dmitry Domanov	11/2010
7596	(15*2^227228-1)/583	68401	Lelio R Paula	01/2014
7598	2^227210+1869169	68398	Enzo Doria	05/2016
7599	2^227159-1838635	68382	Enzo Doria	05/2015
7600	44*10^68368+3	68370	Robert Price	08/2017
7601	2^227115-7807	68369	Lelio R Paula	10/2009
7602	2^227078-47355	68358	Lelio R Paula	04/2012
7603	(2^227063-1017)/349	68351	Lelio R Paula	04/2012
7604	2^227057+148091	68351	Lelio R Paula	04/2012
7605	2^227046+187	68348	Lelio R Paula	02/2012
7606	2^227009-4693	68337	Yves Minet	05/2019
7607	9*10^68331+59	68332	Robert Price	10/2017
7608	11^65608-720	68324	Enzo Doria	11/2012
7609	(32*10^68320+319)/9	68321	Robert Price	10/2017
7610	33408!2-2^33408-1	68315	Joe McLean	05/2017
7611	2^226894-123	68302	Lelio R Paula	02/2012
7612	10^68297+141559	68298	Patrick De Geest	05/2013
7613	10^68297-93	68297	Robert Price	05/2011
7614	680^24107-679^24107	68284	Jean-Louis Charton	07/2010
7615	12^63267+59	68277	Lelio R Paula	07/2013
7616	2^226785-1159	68270	Yves Minet	11/2012
7617	7^80769+90	68258	Lelio R Paula	07/2013
7618	(88*10^68256-1)/3	68258	Robert Price	10/2017
7619	2^226741+66587	68256	Yves Minet	10/2010
7620	2^226720-112403	68250	Enzo Doria	06/2014
7621	(78557*2^226694+1)/3	68247	Lelio R Paula	06/2014
7622	(83*10^68231+7)/9	68232	Robert Price	10/2015
7623	65^37636+16	68231	Lelio R Paula	01/2016
7624	5^97615-4^(97615+1)	68230	Robert Price	04/2016
7625	12^63200-43	68205	Lelio R Paula	07/2013
7626	-330*Bern(21940)/223790620733	68201	Serge Batalov	04/2015
7627	3^142925+8680	68193	Lelio R Paula	06/2013
7628	3*2^226512-7	68188	Lelio R Paula	04/2014
7629	14^59484+57	68177	Lelio R Paula	08/2013
7630	11^65438-2190	68147	Enzo Doria	12/2012
7631	91^34784-2	68144	Lelio R Paula	09/2013
7632	(2^226336-3)*6-7	68135	Gilbert Mozzo	06/2016
7633	(22*10^68133-37)/3	68134	Robert Price	05/2017
7634	5^97476+36	68133	Lelio R Paula	06/2013
7635	3*5^97474-2	68132	Lelio R Paula	09/2014
7636	12^63130+49	68129	Lelio R Paula	07/2013
7637	2^226281+5385	68118	Lelio R Paula	04/2012
7638	2^226257-3049	68111	Yves Minet	10/2014
7639	(28*10^68107-43)/3	68108	Robert Price	04/2016
7640	2^226243-2587	68106	Yves Minet	07/2014
7641	20^52346-11	68104	Lelio R Paula	09/2013
7642	2^226205-99	68095	Lelio R Paula	02/2012
7643	2^226187-49	68090	Lelio R Paula	02/2012
7644	3^142708+76	68090	Lelio R Paula	06/2013
7645	7*10^68088-89	68089	Robert Price	01/2017
7646	2^226154+71839	68080	Enzo Doria	04/2016
7647	(10^68078+59)/3	68078	Serge Batalov	12/2014
7649	14^59387+69	68066	Lelio R Paula	08/2013
7648	2^226108-113429	68066	Enzo Doria	07/2014
7650	(62*10^68059-197)/9	68060	Robert Price	10/2017
7651	(24^49307-1)/23	68053	Robert Price	04/2012
7652	15^57859-28	68048	Lelio R Paula	08/2013
7653	(509203*2^226003-1)/13	68039	Lelio R Paula	04/2015
7654	2^226015-111361	68038	Enzo Doria	05/2014
7655	(10^(234016+1)+7210^34016-1)/9	68033	Robert Price	09/2017
7656	4*10^68020+91	68021	Robert Price	11/2017
7657	156(10^(417000)-1)/101-1	68001	Robert Price	05/2014
7658	2^225878-1017	67997	Lelio R Paula	04/2012
7659	38^75289+5^75289-34^75289+3*2^75289	67994	Mike Oakes	11/2010
7660	3*2^225865+5	67993	Lelio R Paula	04/2014
7662	11^65284-5820	67987	Enzo Doria	01/2013
7661	19^53166+70	67987	Lelio R Paula	08/2013
7663	2^225837+75407	67984	Enzo Doria	04/2016
7664	3^142464-112654	67973	Enzo Doria	06/2014
7665	2^225777+95	67966	Lelio R Paula	02/2012
7666	(2^225641-1017)/138815	67920	Lelio R Paula	04/2012
7667	2^225609-18445	67916	Enzo Doria	05/2013
7668	2^225542-177	67895	Lelio R Paula	02/2012
7669	2^225536-29	67894	Henri Lifchitz	05/2005
7670	11^65190-3390	67889	Enzo Doria	12/2012
7671	3^142249-2^(142249-1)	67871	Robert Price	01/2016
7672	11^65168-4830	67866	Enzo Doria	01/2013
7673	10^67863+58627	67864	Patrick De Geest	01/2016
7674	10^67863-11	67863	Robert Price	05/2011
7675	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
7676	(19*2^225357-1)/11	67840	Lelio R Paula	01/2014
7677	9*6^87164-7	67828	Lelio R Paula	09/2014
7678	131^32034+130	67825	Norbert Schneider	03/2015
7679	(29*2^225314+1)/10881	67824	Lelio R Paula	08/2012
7680	(134*10^67816+7)/3	67818	Robert Price	02/2017
7681	2^225261+855	67811	Lelio R Paula	04/2012
7682	(29*2^225252-1)/2933	67806	Lelio R Paula	01/2014
7683	(4*10^67796+23)/9	67796	Robert Price	11/2014
7684	15477^16180-16180^15477	67790	Norbert Schneider	09/2018
7685	(23*2^225177+1)/31	67785	Lelio R Paula	08/2012
7686	(4*10^67784+149)/9	67784	Robert Price	03/2017
7687	8177^17322+17322^8177	67774	Norbert Schneider	03/2019
7688	2^225120+151	67768	Lelio R Paula	02/2012
7689	(44^41233+1)/45	67763	Robert Price	11/2013
7690	89933!6-16	67747	Robert Price	08/2018
7691	8*10^67742+9	67743	Dmitry Domanov	11/2010
7692	2^224977+1089	67725	Lelio R Paula	04/2012
7693	(2^224950+5)/19509	67713	Lelio R Paula	04/2012
7694	11^65011-5970	67702	Enzo Doria	01/2013
7695	88*10^67691+7	67693	Robert Price	11/2016
7696	11^65000-7140	67691	Enzo Doria	01/2013
7698	2^224841+59	67684	Lelio R Paula	02/2012
7697	33129!2+2^33129	67684	Robert Price	09/2015
7699	2^224827+8415	67680	Lelio R Paula	02/2013
7700	(9913*2^224821-1)/19825	67678	Lelio R Paula	04/2015
7701	2^224815-49789	67677	Henri Lifchitz	04/2005
7702	(43*10^67664+11)/9	67665	Robert Price	06/2015
7703	(292*10^67659-1)/3	67661	Robert Price	01/2017
7704	(17*2^224766+1)/29007	67659	Lelio R Paula	06/2012
7705	2^224744+577294575	67655	Lelio R Paula	02/2016
7706	((1+sqrt(7)+sqrt(6))^45863-1)((1+sqrt(7)-sqrt(6))^45863-1)((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(7	67653	Mike Oakes	05/2009
7707	(2^224721+78557)/1739	67645	Lelio R Paula	05/2012
7708	2^224700+1915	67642	Lelio R Paula	04/2012
7709	(29*2^224694-1)/198905	67636	Lelio R Paula	01/2014
7710	2^224658-93	67629	Lelio R Paula	02/2012
7711	2^224624-13077	67619	Enzo Doria	10/2012
7712	18^53860-3319	67609	Enzo Doria	03/2013
7713	(21181*2^224570+1)/5	67606	Lelio R Paula	06/2014
7714	89762!6-3	67606	Robert Price	08/2018
7715	2^224578-111041	67605	Enzo Doria	05/2014
7716	2^224569-113233	67603	Enzo Doria	07/2014
7717	2^224562-113171	67600	Enzo Doria	07/2014
7718	2^224556-113129	67599	Enzo Doria	07/2014
7719	6*7^79980-5	67592	Lelio R Paula	09/2014
7720	(6883*2^224523-1)/16031	67588	Lelio R Paula	04/2015
7721	10^67579+164779	67580	Patrick De Geest	07/2017
7723	(52*10^67578-61)/9	67579	Robert Price	09/2015
7722	10^67579-401	67579	Robert Price	06/2017
7724	(17^54919-1)/16	67574	Paul Bourdelais	03/2010
7725	((10^33771-1)10000/9+6389)10^33771+(10^33771-1)/9	67546	Hans Havermann	05/2019
7726	(2^224363-9)/1951	67537	Lelio R Paula	04/2012
7727	(709*10^67517-7)/9	67519	Robert Price	09/2017
7728	47719!3-59049	67516	Robert Price	12/2015
7729	(22^50287+1)/23	67506	Robert Price	06/2013
7730	3*10^67499+67	67500	Robert Price	11/2017
7731	11^64811-5820	67494	Enzo Doria	01/2013
7732	131^31870+31870^131	67478	Serge Batalov	05/2014
7733	9*10^67468+7	67469	Dmitry Domanov	11/2010
7734	(31*2^224115-1)/47723	67463	Lelio R Paula	01/2014
7735	128^32001+32001^128	67433	Serge Batalov	05/2014
7736	(89*10^67431-17)/9	67432	Robert Price	11/2015
7737	2^223912-111059	67405	Enzo Doria	05/2014
7739	2^223913+73697	67405	Enzo Doria	04/2016
7738	(2*10^67405-23)/3	67405	Robert Price	09/2017
7741	(10^67404+179)/9	67404	Serge Batalov	12/2014
7740	18738^3955+3955^18738	67404	Hans Havermann	09/2016
7742	9*7^79728-2	67379	Lelio R Paula	09/2014
7743	(28*10^67378-43)/3	67379	Robert Price	04/2016
7744	(3^141234-7)/430241282	67378	Lelio R Paula	04/2012
7745	211^28988-2	67377	Lelio R Paula	09/2013
7746	4*10^67375+91	67376	Robert Price	11/2017
7747	2^223793-18069	67369	Enzo Doria	05/2013
7748	2^223777-2521	67364	Yves Minet	07/2014
7749	(15185*2^223775-1)/15183	67363	Lelio R Paula	04/2015
7750	(2^223759-lucasV(1,2,223759)+1)/2	67358	Mike Oakes	11/2016

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Probable Primes Top 10000

(253466 PRPs in the top)