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 ?
8751	2*F(328450)-1	68642	Henri Lifchitz	12/2009
8752	5^98201-34	68640	Lelio R Paula	06/2013
8753	(2^227993+1682)/2	68633	Stefano Morozzi	01/2020
8754	(2^227989+842)/2	68632	Stefano Morozzi	01/2020
8755	(2^227989+2010)/2	68632	Stefano Morozzi	01/2020
8756	(2^227959+3614)/2	68623	Stefano Morozzi	01/2020
8757	(2^227961+2054)/2	68623	Stefano Morozzi	01/2020
8758	9^71910+38^71910-24^71910-3*2^71910	68620	Mike Oakes	12/2010
8759	(2^227938+3678)/2	68616	Stefano Morozzi	01/2020
8760	18177^5948+5948^18177	68607	Hans Havermann	09/2019
8761	(2^227869+2822)/2	68596	Stefano Morozzi	01/2020
8762	(2^227813+666)/2	68579	Stefano Morozzi	01/2020
8763	7*2^227780-3	68570	Lelio R Paula	04/2014
8764	15327^16382-16382^15327	68567	Norbert Schneider	11/2018
8765	(2^227771+2730)/2	68566	Stefano Morozzi	01/2020
8766	2^227733-121	68555	Lelio R Paula	02/2012
8767	16460^14607+14607^16460	68549	Hans Havermann	09/2019
8768	2^227702-16967	68546	Enzo Doria	05/2013
8769	2^227689-111655	68542	Enzo Doria	05/2014
8770	gcd(V(823915),5F(164783)(F(164783)-1)+1)	68536	Serge Batalov	04/2015
8771	5^98051+2	68535	Ray Chandler	07/2011
8772	5*10^68524+51	68525	Robert Price	01/2017
8773	(11*10^68520-149)/3	68521	Robert Price	01/2017
8774	16624^13235+13235^16624	68520	Hans Havermann	09/2019
8775	16359^15430+15430^16359	68518	Hans Havermann	08/2019
8776	19^53573-78	68507	Lelio R Paula	09/2013
8777	(68*10^68504+13)/9	68505	Ray Chandler	10/2010
8778	9*5^98003+4	68503	Lelio R Paula	09/2014
8779	21121^1750+1750^21121	68497	Hans Havermann	10/2019
8780	2^227528+51	68493	Lelio R Paula	02/2012
8781	(146*28^47316+1)/3	68476	Karsten Bonath	06/2018
8782	(2^227462+3102)/2	68473	Stefano Morozzi	01/2020
8783	3^143497+8	68466	Lelio R Paula	04/2012
8784	2^227430-95	68464	Lelio R Paula	02/2012
8785	(8*10^68455+13)/3	68456	Robert Price	11/2017
8786	3*5^97934-2	68454	Lelio R Paula	09/2014
8787	20^52613+77	68452	Lelio R Paula	09/2013
8788	2^227371+32769	68446	Lelio R Paula	04/2012
8789	(3^143465+4)/21270420067	68440	Lelio R Paula	04/2012
8790	CopelandErdos(68433)	68433	Eric W. Weisstein	08/2013
8791	2^227323+75431	68432	Enzo Doria	04/2016
8792	2^227314-1965	68429	Lelio R Paula	04/2012
8793	2^227303-110617	68426	Enzo Doria	05/2014
8795	7^80963+66	68422	Lelio R Paula	07/2013
8794	2^227290+73849	68422	Enzo Doria	04/2016
8796	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
8797	2^227256-2786249	68411	Enzo Doria	03/2016
8799	8*10^68400-7	68401	Dmitry Domanov	11/2010
8798	(15*2^227228-1)/583	68401	Lelio R Paula	01/2014
8800	2^227210+1869169	68398	Enzo Doria	05/2016
8801	(2^227176+2958)/2	68387	Stefano Morozzi	01/2020
8802	2^227159-1838635	68382	Enzo Doria	05/2015
8803	44*10^68368+3	68370	Robert Price	08/2017
8804	2^227115-7807	68369	Lelio R Paula	10/2009
8805	18469^5032+5032^18469	68368	Hans Havermann	08/2019
8806	2^227078-47355	68358	Lelio R Paula	04/2012
8807	16927^10920+10920^16927	68355	Hans Havermann	10/2019
8808	(2^227063-1017)/349	68351	Lelio R Paula	04/2012
8809	2^227057+148091	68351	Lelio R Paula	04/2012
8810	2^227046+187	68348	Lelio R Paula	02/2012
8811	(2^227030+454)/2	68343	Stefano Morozzi	01/2020
8812	(2^227022+2950)/2	68341	Stefano Morozzi	01/2020
8814	2^227009-4693	68337	Yves Minet	05/2019
8813	(2^227010+3214)/2	68337	Stefano Morozzi	01/2020
8815	9*10^68331+59	68332	Robert Price	10/2017
8816	11^65608-720	68324	Enzo Doria	11/2012
8817	(32*10^68320+319)/9	68321	Robert Price	10/2017
8818	33408!2-2^33408-1	68315	Joe McLean	05/2017
8819	2^226894-123	68302	Lelio R Paula	02/2012
8820	10^68297+141559	68298	Patrick De Geest	05/2013
8821	10^68297-93	68297	Robert Price	05/2011
8822	680^24107-679^24107	68284	Jean-Louis Charton	07/2010
8823	12^63267+59	68277	Lelio R Paula	07/2013
8824	2^226785-1159	68270	Yves Minet	11/2012
8825	7^80769+90	68258	Lelio R Paula	07/2013
8826	(88*10^68256-1)/3	68258	Robert Price	10/2017
8827	2^226741+66587	68256	Yves Minet	10/2010
8828	2^226720-112403	68250	Enzo Doria	06/2014
8829	(78557*2^226694+1)/3	68247	Lelio R Paula	06/2014
8830	(2^226665+1674)/2	68233	Stefano Morozzi	01/2020
8831	(83*10^68231+7)/9	68232	Robert Price	10/2015
8832	65^37636+16	68231	Lelio R Paula	01/2016
8833	5^97615-4^(97615+1)	68230	Robert Price	04/2016
8834	(2^226634+2550)/2	68224	Stefano Morozzi	01/2020
8835	12^63200-43	68205	Lelio R Paula	07/2013
8836	-330*Bern(21940)/223790620733	68201	Serge Batalov	04/2015
8837	(2^226553+2246)/2	68199	Stefano Morozzi	01/2020
8838	3^142925+8680	68193	Lelio R Paula	06/2013
8839	3*2^226512-7	68188	Lelio R Paula	04/2014
8840	(2^226502+442)/2	68184	Stefano Morozzi	01/2020
8841	14^59484+57	68177	Lelio R Paula	08/2013
8842	(2^226452+406)/2	68169	Stefano Morozzi	01/2020
8843	11^65438-2190	68147	Enzo Doria	12/2012
8844	(2^226374+2814)/2	68146	Stefano Morozzi	01/2020
8845	91^34784-2	68144	Lelio R Paula	09/2013
8846	16589^12810+12810^16589	68141	Hans Havermann	10/2019
8847	(2^226356+2986)/2	68140	Stefano Morozzi	01/2020
8848	(2^226357+3702)/2	68140	Stefano Morozzi	01/2020
8850	(2^226336-3)*6-7	68135	Gilbert Mozzo	06/2016
8849	(2^226340+1878)/2	68135	Stefano Morozzi	01/2020
8851	(22*10^68133-37)/3	68134	Robert Price	05/2017
8852	5^97476+36	68133	Lelio R Paula	06/2013
8853	3*5^97474-2	68132	Lelio R Paula	09/2014
8854	12^63130+49	68129	Lelio R Paula	07/2013
8855	2^226281+5385	68118	Lelio R Paula	04/2012
8856	2^226257-3049	68111	Yves Minet	10/2014
8857	(28*10^68107-43)/3	68108	Robert Price	04/2016
8859	2^226243-2587	68106	Yves Minet	07/2014
8858	(2^226241+2570)/2	68106	Stefano Morozzi	01/2020
8860	20^52346-11	68104	Lelio R Paula	09/2013
8861	2^226205-99	68095	Lelio R Paula	02/2012
8862	2^226187-49	68090	Lelio R Paula	02/2012
8863	3^142708+76	68090	Lelio R Paula	06/2013
8864	7*10^68088-89	68089	Robert Price	01/2017
8865	18562^4653+4653^18562	68081	Hans Havermann	09/2019
8866	2^226154+71839	68080	Enzo Doria	04/2016
8867	(10^68078+59)/3	68078	Serge Batalov	12/2014
8868	(2^226121+2822)/2	68069	Stefano Morozzi	01/2020
8870	14^59387+69	68066	Lelio R Paula	08/2013
8869	2^226108-113429	68066	Enzo Doria	07/2014
8871	(62*10^68059-197)/9	68060	Robert Price	10/2017
8872	(24^49307-1)/23	68053	Robert Price	04/2012
8873	(2^226060+1842)/2	68051	Stefano Morozzi	01/2020
8874	15^57859-28	68048	Lelio R Paula	08/2013
8875	(2^226029+2802)/2	68042	Stefano Morozzi	01/2020
8876	(509203*2^226003-1)/13	68039	Lelio R Paula	04/2015
8877	2^226015-111361	68038	Enzo Doria	05/2014
8878	(10^(234016+1)+7210^34016-1)/9	68033	Robert Price	09/2017
8879	4*10^68020+91	68021	Robert Price	11/2017
8880	16181^15948+15948^16181	68004	Hans Havermann	09/2019
8881	156(10^(417000)-1)/101-1	68001	Robert Price	05/2014
8882	2^225878-1017	67997	Lelio R Paula	04/2012
8883	38^75289+5^75289-34^75289+3*2^75289	67994	Mike Oakes	11/2010
8884	3*2^225865+5	67993	Lelio R Paula	04/2014
8885	(2^225868+1662)/2	67993	Stefano Morozzi	01/2020
8886	11^65284-5820	67987	Enzo Doria	01/2013
8887	19^53166+70	67987	Lelio R Paula	08/2013
8888	2^225837+75407	67984	Enzo Doria	04/2016
8889	3^142464-112654	67973	Enzo Doria	06/2014
8890	16851^10802+10802^16851	67969	Hans Havermann	09/2019
8891	2^225777+95	67966	Lelio R Paula	02/2012
8892	(2^225643+1634)/2	67926	Stefano Morozzi	01/2020
8893	(2^225644+3606)/2	67926	Stefano Morozzi	01/2020
8894	(2^225642+1902)/2	67925	Stefano Morozzi	01/2020
8895	(2^225641-1017)/138815	67920	Lelio R Paula	04/2012
8896	2^225609-18445	67916	Enzo Doria	05/2013
8897	(2^225590+1414)/2	67910	Stefano Morozzi	01/2020
8898	2^225542-177	67895	Lelio R Paula	02/2012
8899	2^225536-29	67894	Henri Lifchitz	05/2005
8900	11^65190-3390	67889	Enzo Doria	12/2012
8901	62271!4-1024	67878	Robert Price	11/2019
8902	16971^9986+9986^16971	67874	Hans Havermann	09/2019
8903	3^142249-2^(142249-1)	67871	Robert Price	01/2016
8904	11^65168-4830	67866	Enzo Doria	01/2013
8905	10^67863+58627	67864	Patrick De Geest	01/2016
8906	16258^14933+14933^16258	67864	Hans Havermann	09/2019
8907	10^67863-11	67863	Robert Price	05/2011
8908	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
8909	(19*2^225357-1)/11	67840	Lelio R Paula	01/2014
8910	9*6^87164-7	67828	Lelio R Paula	09/2014
8911	131^32034+130	67825	Norbert Schneider	03/2015
8912	(29*2^225314+1)/10881	67824	Lelio R Paula	08/2012
8913	17761^6586+6586^17761	67823	Hans Havermann	09/2019
8914	(134*10^67816+7)/3	67818	Robert Price	02/2017
8915	2^225261+855	67811	Lelio R Paula	04/2012
8916	(29*2^225252-1)/2933	67806	Lelio R Paula	01/2014
8917	(4*10^67796+23)/9	67796	Robert Price	11/2014
8918	15477^16180-16180^15477	67790	Norbert Schneider	09/2018
8919	(2^225183+2318)/2	67787	Stefano Morozzi	01/2020
8920	(23*2^225177+1)/31	67785	Lelio R Paula	08/2012
8921	(4*10^67784+149)/9	67784	Robert Price	03/2017
8922	8177^17322+17322^8177	67774	Norbert Schneider	03/2019
8923	2^225120+151	67768	Lelio R Paula	02/2012
8924	(2^225109+3126)/2	67765	Stefano Morozzi	01/2020
8925	(44^41233+1)/45	67763	Robert Price	11/2013
8926	(2^225085+2610)/2	67758	Stefano Morozzi	01/2020
8927	89933!6-16	67747	Robert Price	08/2018
8928	8*10^67742+9	67743	Dmitry Domanov	11/2010
8929	(2^224979+3626)/2	67726	Stefano Morozzi	01/2020
8930	2^224977+1089	67725	Lelio R Paula	04/2012
8931	(2^224971+3678)/2	67723	Stefano Morozzi	01/2020
8932	(2^224950+5)/19509	67713	Lelio R Paula	04/2012
8933	11^65011-5970	67702	Enzo Doria	01/2013
8934	88*10^67691+7	67693	Robert Price	11/2016
8935	11^65000-7140	67691	Enzo Doria	01/2013
8936	2^224841+59	67684	Lelio R Paula	02/2012
8937	33129!2+2^33129	67684	Robert Price	09/2015
8938	2^224827+8415	67680	Lelio R Paula	02/2013
8939	(9913*2^224821-1)/19825	67678	Lelio R Paula	04/2015
8940	2^224815-49789	67677	Henri Lifchitz	04/2005
8941	7257^17528+17528^7257	67672	Norbert Schneider	08/2019
8942	(43*10^67664+11)/9	67665	Robert Price	06/2015
8943	(292*10^67659-1)/3	67661	Robert Price	01/2017
8944	(17*2^224766+1)/29007	67659	Lelio R Paula	06/2012
8945	2^224744+577294575	67655	Lelio R Paula	02/2016
8946	((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
8947	(2^224721+78557)/1739	67645	Lelio R Paula	05/2012
8948	2^224700+1915	67642	Lelio R Paula	04/2012
8949	(29*2^224694-1)/198905	67636	Lelio R Paula	01/2014
8950	(2^224679+2870)/2	67635	Stefano Morozzi	01/2020
8951	2^224658-93	67629	Lelio R Paula	02/2012
8952	2^224624-13077	67619	Enzo Doria	10/2012
8953	(2^224598+2910)/2	67611	Stefano Morozzi	01/2020
8954	18^53860-3319	67609	Enzo Doria	03/2013
8955	(21181*2^224570+1)/5	67606	Lelio R Paula	06/2014
8956	89762!6-3	67606	Robert Price	08/2018
8957	2^224578-111041	67605	Enzo Doria	05/2014
8958	2^224569-113233	67603	Enzo Doria	07/2014
8959	2^224562-113171	67600	Enzo Doria	07/2014
8960	2^224556-113129	67599	Enzo Doria	07/2014
8961	6*7^79980-5	67592	Lelio R Paula	09/2014
8962	(6883*2^224523-1)/16031	67588	Lelio R Paula	04/2015
8963	10^67579+164779	67580	Patrick De Geest	07/2017
8965	(52*10^67578-61)/9	67579	Robert Price	09/2015
8964	10^67579-401	67579	Robert Price	06/2017
8966	(17^54919-1)/16	67574	Paul Bourdelais	03/2010
8967	(2^224442+2314)/2	67564	Stefano Morozzi	01/2020
8968	22115^1134+1134^22115	67553	Hans Havermann	08/2019
8969	((10^33771-1)10000/9+6389)10^33771+(10^33771-1)/9	67546	Hans Havermann	05/2019
8970	(2^224363-9)/1951	67537	Lelio R Paula	04/2012
8971	(2^224327+2510)/2	67529	Stefano Morozzi	01/2020
8972	(2^224303+1458)/2	67522	Stefano Morozzi	01/2020
8973	(709*10^67517-7)/9	67519	Robert Price	09/2017
8974	(2^224289+1370)/2	67518	Stefano Morozzi	01/2020
8975	47719!3-59049	67516	Robert Price	12/2015
8976	16356^13411+13411^16356	67509	Hans Havermann	09/2019
8977	(22^50287+1)/23	67506	Robert Price	06/2013
8978	16671^11198+11198^16671	67504	Hans Havermann	09/2019
8979	3*10^67499+67	67500	Robert Price	11/2017
8980	11^64811-5820	67494	Enzo Doria	01/2013
8981	131^31870+31870^131	67478	Serge Batalov	05/2014
8982	9*10^67468+7	67469	Dmitry Domanov	11/2010
8983	(31*2^224115-1)/47723	67463	Lelio R Paula	01/2014
8984	(2^224108+1066)/2	67463	Stefano Morozzi	01/2020
8985	128^32001+32001^128	67433	Serge Batalov	05/2014
8986	(89*10^67431-17)/9	67432	Robert Price	11/2015
8987	2^223912-111059	67405	Enzo Doria	05/2014
8989	2^223913+73697	67405	Enzo Doria	04/2016
8988	(2*10^67405-23)/3	67405	Robert Price	09/2017
8990	(10^67404+179)/9	67404	Serge Batalov	12/2014
8991	18738^3955+3955^18738	67404	Hans Havermann	09/2016
8992	9*7^79728-2	67379	Lelio R Paula	09/2014
8993	(28*10^67378-43)/3	67379	Robert Price	04/2016
8994	(3^141234-7)/430241282	67378	Lelio R Paula	04/2012
8995	211^28988-2	67377	Lelio R Paula	09/2013
8996	4*10^67375+91	67376	Robert Price	11/2017
8997	2^223793-18069	67369	Enzo Doria	05/2013
8998	2^223777-2521	67364	Yves Minet	07/2014
8999	(15185*2^223775-1)/15183	67363	Lelio R Paula	04/2015
9000	(2^223759-lucasV(1,2,223759)+1)/2	67358	Mike Oakes	11/2016

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