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	2^346527-111817	104316	Enzo Doria	05/2014
4752	92105!4+8	104312	Robert Price	09/2019
4753	6^134013+163	104283	Lelio R Paula	11/2016
4754	(2^346318+862)/2	104252	Stefano Morozzi	02/2021
4755	18^83049-89	104250	Lelio R Paula	01/2017
4756	(2^346311+606)/2	104250	Stefano Morozzi	09/2020
4757	(166*10^104230+11)/3	104232	Robert Price	03/2021
4758	2^346213+484049	104221	Enzo Doria	04/2017
4759	18^83021-91	104214	Lelio R Paula	01/2017
4761	10^104212+128779	104213	Patrick De Geest	05/2016
4762	10^104212+237447	104213	Patrick De Geest	05/2016
4763	10^104212+242139	104213	Patrick De Geest	05/2016
4764	10^104212+269199	104213	Patrick De Geest	05/2016
4760	24254^19803+19803^24254	104213	Hans Havermann	09/2020
4765	(10^104212-71)/1	104212	Serge Batalov	12/2014
4766	23678^23821-23821^23678	104202	Norbert Schneider	01/2020
4767	2^346078+7695	104180	Lelio R Paula	12/2016
4768	2^346055-19537	104173	Enzo Doria	05/2013
4769	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
4770	2^346037-20125	104168	Enzo Doria	06/2013
4771	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
4772	6^133854-17993	104159	Enzo Doria	03/2013
4773	2^345990+1874239	104154	Enzo Doria	06/2016
4774	2^345988-20373	104153	Enzo Doria	06/2013
4775	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
4776	(26*10^104132-503)/9	104133	Robert Price	07/2018
4777	3*5^148968+8	104125	Lelio R Paula	11/2014
4778	(7*10^104113+53)/3	104114	Robert Price	05/2018
4779	p(21253)#/2+8	104113	Robert Price	01/2017
4780	33582^1259+1259^33582	104106	Hans Havermann	09/2020
4781	32958^1441+1441^32958	104104	Hans Havermann	09/2020
4782	29127^3748+3748^29127	104095	Hans Havermann	09/2020
4783	322^41507+41507^322	104094	Norbert Schneider	12/2014
4784	6^133768-17423	104092	Enzo Doria	03/2013
4785	2^345786-19557	104092	Enzo Doria	05/2013
4787	171^46606-2	104072	Lelio R Paula	10/2017
4786	(29*10^104071+91)/3	104072	Robert Price	04/2020
4788	2^345704-149	104068	Lelio R Paula	09/2011
4789	25821^10712+10712^25821	104056	Hans Havermann	09/2020
4790	(2^345662+2038)/2	104055	Stefano Morozzi	09/2020
4791	6^133704-17273	104042	Enzo Doria	02/2013
4792	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
4793	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
4794	2^345547+11	104021	Lelio R Paula	09/2011
4795	(19*10^104014-49)/3	104015	Robert Price	05/2019
4796	(2^345519+1794)/2	104012	Stefano Morozzi	01/2021
4797	2^345504+723	104008	Lelio R Paula	09/2011
4798	2^345498-20037	104006	Enzo Doria	06/2013
4800	18^82854-37	104005	Lelio R Paula	01/2017
4799	(2^345497+2070)/2	104005	Stefano Morozzi	09/2020
4801	2^345486-109065	104002	Enzo Doria	04/2014
4802	2^345487-1851507	104002	Enzo Doria	08/2015
4804	2^345476+777	103999	Lelio R Paula	09/2011
4803	(2^345477+1554)/2	103999	Stefano Morozzi	09/2020
4805	4*10^103981-83	103982	Robert Price	10/2018
4806	(2^345327+3206)/2	103954	Stefano Morozzi	09/2020
4807	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
4808	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
4809	(19*10^103907+77)/3	103908	Robert Price	05/2019
4810	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
4811	2^345106-112181	103888	Enzo Doria	06/2014
4812	(2^345105+1326)/2	103887	Stefano Morozzi	02/2021
4813	2^345079+99	103880	Lelio R Paula	09/2011
4814	(2^345034+1198)/2	103866	Stefano Morozzi	09/2020
4815	11^99736-1500	103865	Enzo Doria	12/2012
4816	(2^345010+2082)/2	103859	Stefano Morozzi	09/2020
4817	23263^23784-23784^23263	103857	Norbert Schneider	01/2020
4818	23927^21814+21814^23927	103813	Hans Havermann	09/2020
4819	2^344842-20157	103808	Enzo Doria	06/2013
4820	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
4821	2^344802-20765	103796	Enzo Doria	06/2013
4822	2^344794-3821	103794	Yves Minet	05/2011
4823	2^344782-109103	103790	Enzo Doria	04/2014
4824	3^217521-112292	103784	Enzo Doria	06/2014
4825	2^344759-3505	103783	Lelio R Paula	11/2016
4826	2^344735-147	103776	Lelio R Paula	09/2011
4827	L(496533)-p(496533)	103770	Robert Price	02/2018
4828	2*10^103749-69	103750	Robert Price	03/2018
4829	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
4830	2^344607-108891	103738	Enzo Doria	03/2014
4831	(2^344608+3798)/2	103738	Stefano Morozzi	02/2021
4832	(148*10^103718-1)/3	103720	Robert Price	03/2020
4833	2^344541-19561	103718	Enzo Doria	05/2013
4834	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
4835	(2^344503+1758)/2	103706	Stefano Morozzi	09/2020
4836	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
4837	2^344444-455	103688	Yves Minet	03/2012
4838	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
4839	(2^344367+2738)/2	103665	Stefano Morozzi	01/2021
4841	2^344317-109933	103650	Enzo Doria	04/2014
4840	26055^9508+9508^26055	103650	Hans Havermann	09/2020
4842	2^344309-1852033	103648	Enzo Doria	08/2015
4843	25729^10672+10672^25729	103643	Hans Havermann	09/2020
4844	(2^344289+1166)/2	103642	Stefano Morozzi	09/2020
4845	3*10^103637+61	103638	Robert Price	09/2020
4846	(2^344246+1614)/2	103629	Stefano Morozzi	09/2020
4847	2^344213-21253	103619	Enzo Doria	06/2013
4848	2^344196-465	103614	Lelio R Paula	11/2016
4849	2^344187-20001	103611	Enzo Doria	06/2013
4850	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
4851	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
4852	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
4853	2^344085-20365	103580	Enzo Doria	06/2013
4854	5^148169+54	103566	Lelio R Paula	11/2016
4855	2^344017-108795	103560	Enzo Doria	03/2014
4856	(2^343974+2670)/2	103547	Stefano Morozzi	09/2020
4857	2^343971-5077	103546	Lelio R Paula	09/2011
4858	(7*10^103531+71)/3	103532	Robert Price	05/2018
4859	2^343899+141	103524	Lelio R Paula	08/2011
4860	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
4861	6^133029-67	103517	Lelio R Paula	11/2016
4862	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
4863	66*10^103507+7	103509	Robert Price	07/2020
4864	26297^8614+8614^26297	103485	Hans Havermann	09/2020
4865	(2^343764+2658)/2	103483	Stefano Morozzi	09/2020
4866	26499^8036+8036^26499	103480	Hans Havermann	09/2020
4867	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
4868	5^148014-24	103458	Lelio R Paula	11/2016
4869	28316^4503+4503^28316	103453	Hans Havermann	09/2020
4870	(22*10^103450+53)/3	103451	Robert Price	07/2019
4871	2^343604+9931	103436	Yves Minet	01/2011
4872	2^343601-21189	103435	Enzo Doria	06/2013
4873	2^343508-115229	103407	Enzo Doria	06/2015
4874	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
4875	3^216685-113056	103386	Enzo Doria	07/2014
4876	24829^14580+14580^24829	103382	Hans Havermann	08/2020
4877	91355!4+1024	103381	Robert Price	09/2019
4878	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
4879	11^99262-20	103371	Lelio R Paula	12/2016
4880	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
4881	(2^343363+3570)/2	103363	Stefano Morozzi	09/2020
4883	2^343356-2791889	103361	Enzo Doria	03/2016
4882	(25*10^103360-241)/9	103361	Robert Price	05/2018
4884	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
4885	24826^14511+14511^24826	103319	Hans Havermann	09/2020
4886	2^343182-171	103309	Lelio R Paula	08/2011
4887	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
4888	2^343079-1835611	103278	Enzo Doria	05/2015
4889	2^343063-1147	103273	Yves Minet	06/2013
4890	24741^14930+14930^24741	103271	Hans Havermann	09/2020
4891	(16*10^103255-73)/3	103256	Robert Price	07/2020
4892	9*6^132689+7	103254	Lelio R Paula	11/2014
4893	2^342979-18085	103247	Enzo Doria	05/2013
4894	(16*10^103244-31)/3	103245	Robert Price	03/2019
4895	2^342966-16995	103244	Lelio R Paula	11/2016
4896	23797^21774+21774^23797	103230	Hans Havermann	09/2020
4897	25388^11637+11637^25388	103224	Hans Havermann	09/2020
4898	(2^342876+2086)/2	103216	Stefano Morozzi	09/2020
4899	(16*10^103214-31)/3	103215	Robert Price	03/2019
4901	(37*10^103211+611)/9	103212	Robert Price	11/2018
4900	(238*10^103210-1)/3	103212	Robert Price	04/2020
4902	5^147650+16	103203	Lelio R Paula	11/2016
4903	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
4904	2^342817+2707067	103199	Enzo Doria	03/2016
4905	43^63177-42	103198	Theodore Burton	02/2007
4906	2^342805-21025	103195	Enzo Doria	06/2013
4907	24129^18890+18890^24129	103182	Hans Havermann	09/2020
4908	2^342714+12285	103168	Lelio R Paula	11/2016
4909	18^82178-4481	103156	Enzo Doria	03/2013
4910	2^342665-17349	103153	Enzo Doria	05/2013
4911	30408^2467+2467^30408	103150	Hans Havermann	09/2020
4912	(2^342615+3090)/2	103138	Stefano Morozzi	09/2020
4913	2^342612+175	103137	Lelio R Paula	08/2011
4914	5*2^342585-3	103130	Lelio R Paula	09/2014
4915	(16*10^103127+77)/3	103128	Robert Price	03/2019
4916	(2^342527+3774)/2	103111	Stefano Morozzi	02/2021
4917	2^342503-19209	103104	Enzo Doria	05/2013
4918	(2^342484+2586)/2	103098	Stefano Morozzi	09/2020
4919	2^342476+51	103096	Lelio R Paula	08/2011
4920	2^342460-18885	103091	Enzo Doria	05/2013
4921	(2^342442+862)/2	103086	Stefano Morozzi	02/2021
4922	(194*10^103074-17)/3	103076	Robert Price	09/2020
4923	7^121968+82	103075	Lelio R Paula	10/2016
4924	2^342392-108863	103071	Enzo Doria	03/2014
4925	(2^342389+806)/2	103070	Stefano Morozzi	01/2021
4926	3^216014+28	103065	Lelio R Paula	11/2016
4927	2^342353-108879	103059	Enzo Doria	03/2014
4928	10^103055+276081	103056	Patrick De Geest	12/2016
4929	10^103055-53	103055	Lelio R Paula	11/2016
4930	(58*10^103046+419)/9	103047	Robert Price	05/2019
4931	7^121933+4	103046	Lelio R Paula	11/2014
4932	(2^342235+3618)/2	103023	Stefano Morozzi	09/2020
4933	19^80560-68	103017	Lelio R Paula	10/2016
4934	2^342209+76607	103016	Enzo Doria	05/2016
4936	328^40945+40945^328	103013	Norbert Schneider	12/2014
4935	12^95454-91	103013	Lelio R Paula	10/2016
4937	25833^9716+9716^25833	103009	Hans Havermann	01/2019
4938	65^56809-64^56809	102990	Robert Price	08/2013
4939	5^147338-6	102985	Lelio R Paula	11/2014
4940	2^342084-112739	102978	Enzo Doria	06/2014
4941	9*6^132330+7	102974	Lelio R Paula	11/2014
4942	2^342034-16737	102963	Enzo Doria	05/2013
4943	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
4944	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
4945	2^341991-17421	102950	Enzo Doria	05/2013
4946	2^341969-112225	102943	Enzo Doria	06/2014
4947	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
4948	2^341859+1869413	102910	Enzo Doria	05/2016
4949	10^102909+61	102910	Lelio R Paula	11/2016
4950	10^102909-67049	102909	Patrick De Geest	12/2016
4951	23814^20935+20935^23814	102898	Hans Havermann	02/2019
4952	28345^4264+4264^28345	102888	Hans Havermann	02/2019
4953	25665^10204+10204^25665	102886	Hans Havermann	02/2019
4954	26288^8181+8181^26288	102860	Hans Havermann	02/2019
4955	2^341659+1836773	102850	Enzo Doria	03/2016
4956	2^341608-110639	102835	Enzo Doria	05/2014
4957	10^102824+49	102825	Lelio R Paula	11/2016
4958	10^102824-168011	102824	Patrick De Geest	12/2016
4959	11^98708-8	102794	Lelio R Paula	10/2016
4960	2^341466+4429	102792	Lelio R Paula	09/2011
4961	2^341460-107	102790	Lelio R Paula	08/2011
4962	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
4963	2^341355+21	102759	Lelio R Paula	08/2011
4964	2^341246+40755	102726	Lelio R Paula	11/2016
4965	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
4966	7^121547+78	102720	Lelio R Paula	10/2016
4967	2^341223-461197	102719	Enzo Doria	06/2015
4968	27838^4893+4893^27838	102711	Hans Havermann	03/2019
4970	2^341190-20577	102709	Enzo Doria	06/2013
4969	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
4971	6^131976-65	102698	Lelio R Paula	10/2016
4972	2^341134+2533	102692	Henri Lifchitz	09/2005
4973	13^92184-54	102688	Lelio R Paula	10/2016
4974	2^341116-20873	102687	Enzo Doria	06/2013
4975	2^341094-19953	102680	Enzo Doria	06/2013
4976	23761^20950+20950^23761	102676	Hans Havermann	03/2019
4977	2^341053+129	102668	Lelio R Paula	08/2011
4979	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
4978	7^121471+94	102655	Lelio R Paula	10/2016
4981	2^341004-173	102653	Lelio R Paula	08/2011
4980	20^78901+3	102653	Lelio R Paula	10/2016
4982	(2^341001+1674)/2	102652	Stefano Morozzi	09/2020
4983	5^146853-52	102646	Lelio R Paula	10/2016
4984	2^340969-216931	102642	Enzo Doria	05/2014
4985	122^49196+121	102641	Norbert Schneider	10/2018
4986	2^340952+1870021	102637	Enzo Doria	05/2016
4987	5*2^340940-3	102634	Lelio R Paula	08/2014
4988	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
4989	25876^9239+9239^25876	102615	Hans Havermann	02/2019
4990	(4*10^102612+83)/3	102613	Robert Price	02/2018
4991	75^54717+74	102598	Norbert Schneider	01/2015
4992	(17*10^102597+13)/3	102598	Robert Price	01/2019
4993	2^340806-20393	102593	Enzo Doria	06/2013
4994	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
4995	6^131821+77	102577	Lelio R Paula	10/2016
4996	(203*10^102561-11)/3	102563	Robert Price	12/2020
4997	2^340688-29	102558	Henri Lifchitz	05/2005
4998	2^340685-109101	102557	Enzo Doria	04/2014
4999	65^56567-64	102552	Norbert Schneider	11/2014
5000	26230^8121+8121^26230	102550	Hans Havermann	03/2019

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