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 ?
4751	22971^21692+21692^22971	99610	Hans Havermann	03/2018
4752	2^330845+71687	99595	Enzo Doria	04/2016
4753	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
4754	24494^11613+11613^24494	99567	Hans Havermann	03/2018
4755	2^330735+8415	99562	Lelio R Paula	09/2016
4756	2^330720+74071	99557	Enzo Doria	04/2016
4757	31^66738-2	99531	Lelio R Paula	09/2013
4758	7*3^208567+4	99513	Lelio R Paula	08/2014
4759	(13*10^99508+47)/3	99509	Robert Price	01/2017
4760	2^330553+779	99507	Lelio R Paula	01/2013
4761	15^84606-94	99505	Lelio R Paula	08/2016
4762	6^127858+47	99493	Lelio R Paula	08/2016
4763	5^142337+48	99490	Lelio R Paula	08/2016
4764	7^117724-20	99489	Lelio R Paula	08/2016
4765	(29*10^99474-17)/3	99475	Erik Branger	09/2014
4766	(2^330410+2038)/2	99464	Stefano Morozzi	09/2020
4767	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
4768	(2^330373+2114)/2	99452	Stefano Morozzi	09/2020
4769	(68*10^99441+7)/3	99443	Robert Price	03/2016
4770	10^99434+155571	99435	Patrick De Geest	04/2020
4771	10^99434-123456789	99434	Robert Price	02/2020
4772	10^99434-191237	99434	Patrick De Geest	04/2020
4773	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
4774	23839^14802+14802^23839	99417	Hans Havermann	02/2018
4775	(2*10^99408+529)/9	99408	Robert Price	01/2017
4776	(2^330216+3510)/2	99405	Stefano Morozzi	09/2020
4777	53^57646-2	99398	Lelio R Paula	09/2013
4778	2^330165+1870025	99390	Enzo Doria	05/2016
4779	2^330142-155	99383	Lelio R Paula	12/2012
4780	2^330088-115259	99367	Enzo Doria	06/2015
4781	24216^12671+12671^24216	99354	Hans Havermann	01/2018
4782	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
4783	(746*10^99303+1)/9	99305	Robert Price	02/2017
4784	3^208107+40	99293	Lelio R Paula	08/2016
4785	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
4786	8*3^208093+5	99287	Lelio R Paula	08/2014
4787	5^142043+56	99284	Lelio R Paula	08/2016
4788	22*10^99275+7	99277	Robert Price	04/2016
4789	2^329778+1876189	99274	Enzo Doria	07/2016
4790	(10^99239-13)/3	99239	Robert Price	02/2017
4791	3^207987+62	99236	Lelio R Paula	08/2016
4792	2^329638+49	99231	Lelio R Paula	12/2012
4793	7^117413-18	99226	Lelio R Paula	08/2016
4794	2^329586-458903	99216	Enzo Doria	04/2015
4795	2^329553+101	99206	Lelio R Paula	12/2012
4796	2^329551-112897	99205	Enzo Doria	06/2014
4797	(3^207925+7)/50	99204	Lelio R Paula	09/2013
4798	6^127458-17993	99182	Enzo Doria	03/2013
4799	27197^4428+4428^27197	99166	Hans Havermann	10/2017
4800	(46*10^99143-1)/9	99144	Robert Price	12/2014
4801	7*10^99133+69	99134	Robert Price	10/2017
4802	18^78968-3065	99127	Enzo Doria	03/2013
4803	25927^6654+6654^25927	99122	Hans Havermann	10/2017
4804	87915!4+16	99122	Robert Price	09/2019
4805	2^329259+189	99117	Lelio R Paula	12/2012
4806	8*10^99113+39	99114	Robert Price	01/2017
4807	6^127364+77	99109	Lelio R Paula	08/2016
4808	(2^329135+1110)/2	99080	Stefano Morozzi	09/2020
4809	6^127285+13	99047	Lelio R Paula	08/2016
4810	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
4811	2^329007+73283	99041	Enzo Doria	04/2016
4812	5*3^207543-8	99024	Lelio R Paula	08/2014
4813	(2^328930+570)/2	99018	Stefano Morozzi	09/2020
4814	2^328885+149	99005	Lelio R Paula	12/2012
4815	23392^17075+17075^23392	99004	Hans Havermann	09/2017
4816	(2^328879-9)/119	99001	Lelio R Paula	10/2013
4817	5^141618+54	98987	Lelio R Paula	08/2016
4818	8*10^98982+51	98983	Robert Price	05/2017
4819	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
4820	2^328794-2797601	98977	Enzo Doria	04/2016
4821	6^127176+5	98963	Lelio R Paula	11/2014
4822	2*10^98961-21	98962	Robert Price	09/2020
4823	24262^11989+11989^24262	98960	Hans Havermann	09/2017
4824	2^328700-109709	98949	Enzo Doria	04/2014
4825	87771!4-128	98944	Robert Price	11/2019
4826	(2^328658+3042)/2	98936	Stefano Morozzi	09/2020
4827	46711!2-2^46711	98916	Robert Price	09/2015
4828	9*7^117037+4	98909	Lelio R Paula	11/2014
4829	127^47012+126	98905	Norbert Schneider	01/2019
4830	(2^328525+1250)/2	98896	Stefano Morozzi	09/2020
4831	(10^98890+149)/3	98890	Serge Batalov	12/2014
4832	22775^21978+21978^22775	98889	Hans Havermann	08/2017
4833	2^328497-216933	98888	Enzo Doria	05/2014
4834	2^328487+32769	98885	Lelio R Paula	08/2016
4835	3^207250-112358	98884	Enzo Doria	06/2014
4836	13^88754-90	98867	Lelio R Paula	08/2016
4838	2^328406+709	98861	Lelio R Paula	02/2013
4837	2*10^98860-21	98861	Robert Price	09/2020
4839	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
4840	7^116976+76	98857	Lelio R Paula	08/2016
4841	(2^328378+2710)/2	98852	Stefano Morozzi	09/2020
4842	2^328335+1155	98839	Lelio R Paula	08/2016
4844	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
4843	287^40210+40210^287	98832	Norbert Schneider	11/2014
4845	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
4846	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
4847	24746^9825+9825^24746	98795	Hans Havermann	07/2020
4848	26620^5143+5143^26620	98793	Hans Havermann	07/2020
4849	65^54491+48	98788	Lelio R Paula	04/2016
4850	3^207042+98	98785	Lelio R Paula	08/2016
4851	(2^328121+3110)/2	98774	Stefano Morozzi	09/2020
4853	3^206977-112756	98754	Enzo Doria	07/2014
4852	10^98754-40000000001	98754	Robert Price	09/2020
4854	7^116846-50	98747	Lelio R Paula	08/2016
4855	23267^17512+17512^23267	98730	Hans Havermann	04/2020
4856	2^327967-28635	98728	Lelio R Paula	08/2016
4857	707^34642+34642^707	98710	Norbert Schneider	12/2017
4858	6^126850-47	98709	Lelio R Paula	08/2016
4859	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
4860	8*6^126830-7	98694	Lelio R Paula	11/2014
4861	11^94770-270	98693	Enzo Doria	08/2012
4862	2^327832+43	98688	Lelio R Paula	12/2012
4863	2^327795+761	98677	Lelio R Paula	02/2013
4864	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
4865	10^98669+147411	98670	Patrick De Geest	11/2016
4867	10^98669-9^(98669-1)	98669	Robert Price	05/2016
4866	10^98669-105249	98669	Patrick De Geest	11/2016
4868	2^327671-109801	98639	Enzo Doria	04/2014
4869	24398^11037+11037^24398	98638	Hans Havermann	10/2019
4870	5^141090-14	98618	Lelio R Paula	08/2016
4871	20^75799+47	98617	Lelio R Paula	08/2016
4872	28101^3226+3226^28101	98597	Hans Havermann	07/2020
4873	2^327515-1017	98592	Lelio R Paula	08/2016
4874	6^126692+97681	98586	Mike Oakes	04/2011
4875	2^327467-741	98578	Lelio R Paula	08/2016
4876	22713^21800+21800^22713	98540	Hans Havermann	05/2020
4877	(2^327329+9)/19	98535	Lelio R Paula	10/2013
4878	7^116577-66	98519	Lelio R Paula	08/2016
4880	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
4879	23220^17479+17479^23220	98512	Hans Havermann	03/2020
4881	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
4882	2^327162-66945	98486	Lelio R Paula	08/2016
4883	30139^1852+1852^30139	98484	Hans Havermann	02/2020
4884	23182^17703+17703^23182	98479	Hans Havermann	01/2020
4885	4*10^98472-3	98473	Erik Branger	11/2013
4886	26167^5794+5794^26167	98466	Hans Havermann	01/2020
4887	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
4888	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
4889	13^88363+94	98432	Lelio R Paula	08/2016
4890	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
4891	6^126481+41	98422	Lelio R Paula	08/2016
4892	78*10^98413-7	98415	Robert Price	05/2017
4893	22634^22263+22263^22634	98404	Hans Havermann	07/2020
4894	7^116416+46	98383	Lelio R Paula	08/2016
4895	7^116407-24	98376	Lelio R Paula	07/2016
4896	439^37228+37228^439	98374	Norbert Schneider	08/2018
4898	2^326782-1860671	98372	Enzo Doria	03/2016
4897	17^79948+58	98372	Lelio R Paula	08/2016
4899	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
4900	3^206143-98	98356	Lelio R Paula	08/2016
4901	8*5^140705+7	98350	Lelio R Paula	11/2014
4902	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020
4903	2^326585+11	98312	Lelio R Paula	12/2012
4904	2^326582-459161	98311	Enzo Doria	05/2015
4906	(2^326548+9)/5	98301	Lelio R Paula	10/2013
4905	(2^326549+18)/10	98301	Stefano Morozzi	03/2020
4907	2^326538+71659	98298	Enzo Doria	04/2016
4908	(2^326520+2082)/2	98293	Stefano Morozzi	09/2020
4909	(2^326521+1002)/2	98293	Stefano Morozzi	09/2020
4910	15^83575-58	98292	Lelio R Paula	08/2016
4911	10^98288+3	98289	Robert Price	03/2011
4912	10^98288-117017	98288	Patrick De Geest	11/2011
4913	(44*10^98284-719)/9	98285	Robert Price	12/2017
4914	23466^15419+15419^23466	98277	Hans Havermann	02/2020
4915	2^326421-2797573	98263	Enzo Doria	04/2016
4916	2^326401+16095	98257	Lelio R Paula	07/2016
4917	7^116240-116240^7	98235	Norbert Schneider	05/2017
4918	17^79826-78	98222	Lelio R Paula	08/2016
4919	2^326268-809	98217	Yves Minet	04/2011
4920	22659^21590+21590^22659	98210	Hans Havermann	10/2019
4921	22268^22587-22587^22268	98202	Norbert Schneider	08/2020
4922	(418*10^98199+23)/9	98201	Robert Price	08/2017
4923	12*10^98198-7	98200	Robert Price	11/2017
4924	15^83496-76	98199	Lelio R Paula	08/2016
4925	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
4926	9*5^140471-4	98186	Lelio R Paula	11/2014
4927	22774^20455+20455^22774	98175	Hans Havermann	07/2020
4928	2^326069-2383	98157	Yves Minet	10/2013
4929	2^325973+1185	98128	Lelio R Paula	07/2016
4930	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
4931	2^325945-1847269	98120	Enzo Doria	07/2015
4932	8*10^98111-67	98112	Robert Price	10/2017
4933	(2^325902+1138)/2	98106	Stefano Morozzi	09/2020
4934	2^325866+15	98096	Lelio R Paula	12/2012
4935	22591^21952+21952^22591	98079	Hans Havermann	02/2020
4936	2^325765+1974305	98066	Enzo Doria	06/2016
4937	2^325733-58695	98056	Lelio R Paula	07/2016
4938	2^325717-3645	98051	Lelio R Paula	07/2016
4939	(2^325704+718)/2	98047	Stefano Morozzi	09/2020
4940	23968^12293+12293^23968	98021	Hans Havermann	11/2019
4941	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
4942	(7*10^98007-13)/3	98008	Robert Price	06/2016
4943	(2^325544+1110)/2	97999	Stefano Morozzi	09/2020
4944	2^325512-459959	97989	Enzo Doria	05/2015
4945	(2^325492+682)/2	97983	Stefano Morozzi	09/2020
4946	(3^205354-8)/17	97978	Lelio R Paula	09/2013
4947	2^325433+76817	97966	Enzo Doria	05/2016
4948	5*10^97963+81	97964	Robert Price	08/2017
4949	2^325390-109061	97953	Enzo Doria	04/2014
4950	13^87921+24	97940	Lelio R Paula	08/2016
4951	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
4952	22600^21499+21499^22600	97913	Hans Havermann	05/2020
4953	2^325215+12909	97900	Lelio R Paula	07/2016
4954	22619^21286+21286^22619	97898	Hans Havermann	04/2020
4955	7*10^97874-69	97875	Robert Price	01/2017
4957	(17^79537+5^79537)/22	97865	Robert Price	06/2013
4956	15^83212+22	97865	Lelio R Paula	08/2016
4958	2^325087-109057	97861	Enzo Doria	04/2014
4959	2^325074+1870657	97858	Enzo Doria	05/2016
4961	2^325066-2111	97855	Yves Minet	08/2013
4960	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
4962	26660^4677+4677^26660	97842	Hans Havermann	12/2019
4963	18^77944-89	97841	Lelio R Paula	07/2016
4964	119^47136+118	97833	Norbert Schneider	09/2018
4965	6^125720-17663	97830	Enzo Doria	02/2013
4966	2^324972-2069	97827	Yves Minet	05/2013
4967	2^324958-4691	97823	Yves Minet	05/2019
4968	2^324944-2788319	97818	Enzo Doria	03/2016
4969	22845^19112+19112^22845	97807	Hans Havermann	10/2019
4970	(2^324898+1270)/2	97804	Stefano Morozzi	09/2020
4972	4*10^97799-9	97800	Erik Branger	11/2013
4971	2^324882+577294575	97800	Lelio R Paula	09/2016
4973	2^324863-1867921	97794	Enzo Doria	04/2016
4974	6^125662-18473	97785	Enzo Doria	03/2013
4975	12^90604+11	97779	Lelio R Paula	07/2016
4976	5^139830+24	97737	Lelio R Paula	04/2016
4977	(2^324672+1198)/2	97736	Stefano Morozzi	09/2020
4978	2^324612+1155	97718	Lelio R Paula	07/2016
4979	(2^324597+3542)/2	97714	Stefano Morozzi	09/2020
4980	19^76404-44	97702	Lelio R Paula	07/2016
4981	2^324505-2983	97686	Yves Minet	04/2011
4982	(144^45259+1)/145	97684	Paul Bourdelais	08/2019
4983	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
4984	6^125488-17843	97649	Enzo Doria	02/2013
4985	(2^324350+3198)/2	97639	Stefano Morozzi	09/2020
4986	7^115515-2	97622	Lelio R Paula	09/2013
4987	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
4988	6^125418-5	97595	Lelio R Paula	11/2014
4989	(2^324193+3522)/2	97592	Stefano Morozzi	09/2020
4990	(2^324172+666)/2	97586	Stefano Morozzi	09/2020
4991	2^324076+1155	97557	Lelio R Paula	07/2016
4992	(2^324074+9)/13	97555	Lelio R Paula	10/2013
4993	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
4994	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
4995	2^323946+73939	97518	Enzo Doria	04/2016
4996	2^323937+1866947	97515	Enzo Doria	03/2016
4998	6^125290-18533	97495	Enzo Doria	03/2013
4997	(2^323870+1650)/2	97495	Stefano Morozzi	09/2020
4999	2^323845+101	97488	Lelio R Paula	12/2012
5000	18^77662+65	97487	Lelio R Paula	07/2016

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Probable Primes Top 10000

(271067 PRPs in the top)