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	10^90453-3969	90453	Patrick De Geest	11/2018
4752	10^90440+1359	90441	Patrick De Geest	11/2018
4753	(3^189545-8)/5	90436	Lelio R Paula	01/2013
4754	(7*2^300406-1)/3	90432	Lelio R Paula	02/2014
4755	10^90430+3339	90431	Patrick De Geest	11/2018
4756	10^90414-1547	90414	Patrick De Geest	11/2018
4757	10^90404-6429	90404	Patrick De Geest	11/2018
4758	10^90401+2077	90402	Patrick De Geest	11/2018
4759	4*5^129332+3	90400	Lelio R Paula	10/2014
4760	10^90397-323	90397	Patrick De Geest	11/2018
4761	2^300249-16245	90384	Enzo Doria	04/2013
4762	(7*10^90371-313)/9	90371	Robert Price	11/2016
4763	10^90363-3557	90363	Patrick De Geest	11/2018
4765	2*6^116118+7	90358	Lelio R Paula	10/2014
4764	10^90358-4979	90358	Patrick De Geest	11/2018
4766	10^90356-7197	90356	Patrick De Geest	11/2018
4767	10^90353-1089	90353	Patrick De Geest	11/2018
4768	(24737*2^300101+1)/25	90343	Lelio R Paula	06/2014
4769	4*10^90334-21	90335	Robert Price	04/2016
4770	10^90322-9551	90322	Patrick De Geest	11/2018
4771	10^90316+9991	90317	Patrick De Geest	11/2018
4773	2^300019-110335	90315	Enzo Doria	05/2014
4772	10^90315-8561	90315	Patrick De Geest	11/2018
4774	FAB2(300001,5032)	90310	Robert Price	05/2019
4775	FAB2(300001,29405)	90310	Robert Price	05/2019
4776	2^299949-1005	90294	Lelio R Paula	11/2013
4777	10^90279-1551	90279	Patrick De Geest	09/2018
4778	2^299868-109613	90270	Enzo Doria	04/2014
4779	10^90259-9443	90259	Patrick De Geest	09/2018
4780	10^90252-8103	90252	Patrick De Geest	09/2018
4781	5*2^299799-3	90250	Lelio R Paula	08/2014
4782	13^81008-2	90239	Lelio R Paula	09/2013
4783	64^49957-63^49957	90232	Robert Price	07/2013
4784	10^90227+56281	90228	Patrick De Geest	06/2016
4787	2^299725+315	90227	Lelio R Paula	11/2013
4785	10^90227-1000000001	90227	Robert Price	05/2016
4786	10^90227-68763	90227	Patrick De Geest	06/2016
4788	5^129082+48	90225	Lelio R Paula	03/2016
4789	2^299699+195	90219	Lelio R Paula	10/2012
4790	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
4791	10^90209+8971	90210	Patrick De Geest	09/2018
4792	10^90208-2247	90208	Patrick De Geest	09/2018
4793	116^43693-115	90203	Norbert Schneider	08/2018
4794	10^90202+3553	90203	Patrick De Geest	09/2018
4795	3^189053+280	90202	Lelio R Paula	04/2016
4796	2^299639-187	90201	Lelio R Paula	10/2012
4797	10^90199-2891	90199	Patrick De Geest	09/2018
4798	2^299631+183	90198	Lelio R Paula	10/2012
4799	10^90196-9683	90196	Patrick De Geest	09/2018
4800	10^90193-9809	90193	Patrick De Geest	09/2018
4801	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
4802	2^299567+113	90179	Lelio R Paula	10/2012
4803	2^299550+189	90174	Lelio R Paula	10/2012
4804	10^90170-6749	90170	Patrick De Geest	09/2018
4805	(2^299535+3)/29	90168	Lelio R Paula	01/2013
4806	10^90160-5613	90160	Patrick De Geest	09/2018
4807	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
4808	3^188938+8680	90147	Lelio R Paula	04/2016
4809	10^90146-2027	90146	Patrick De Geest	09/2018
4811	6^115840-55	90142	Lelio R Paula	05/2016
4810	(5*10^90142-473)/9	90142	Robert Price	12/2017
4812	8*7^106659+5	90139	Lelio R Paula	10/2014
4813	2^299406-16653	90131	Enzo Doria	05/2013
4815	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
4814	10^90128-8387	90128	Patrick De Geest	09/2018
4816	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
4817	6^115819-53	90125	Lelio R Paula	05/2016
4818	10^90123+6313	90124	Patrick De Geest	09/2018
4819	6^115816-16853	90123	Enzo Doria	02/2013
4820	6^115813-23	90121	Lelio R Paula	05/2016
4821	(22*10^90110+161)/3	90111	Robert Price	02/2017
4822	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
4823	10^90105-767	90105	Patrick De Geest	09/2018
4824	10^90104-7703	90104	Patrick De Geest	09/2018
4825	10^90103+9159	90104	Patrick De Geest	09/2018
4826	10^90101-3207	90101	Patrick De Geest	09/2018
4827	(29*10^90096-17)/3	90097	Erik Branger	09/2014
4828	10^90089-3573	90089	Patrick De Geest	09/2018
4829	2^299247+1870529	90083	Enzo Doria	05/2016
4830	10^90079+1609	90080	Patrick De Geest	09/2018
4831	2^299229-2797783	90077	Enzo Doria	04/2016
4832	2^299220-16317	90075	Enzo Doria	04/2013
4833	11^86491-1350	90072	Enzo Doria	12/2012
4834	10^90071-1233	90071	Patrick De Geest	09/2018
4835	10^90069-7841	90069	Patrick De Geest	09/2018
4836	(31*10^90064-1)/3	90066	Robert Price	03/2017
4837	10^90060-839	90060	Patrick De Geest	09/2018
4838	10^90052+2361	90053	Patrick De Geest	09/2018
4839	10^90047+619	90048	Patrick De Geest	09/2018
4840	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
4841	2^299112+73951	90042	Enzo Doria	04/2016
4842	8^99702+7^(99702-1)	90040	Robert Price	02/2016
4843	10^90038-9687	90038	Patrick De Geest	09/2018
4844	5*10^90033+3	90034	Dmitry Domanov	11/2010
4845	10^90030-1461	90030	Patrick De Geest	09/2018
4846	243^37738+37738^243	90029	Norbert Schneider	01/2015
4847	10^90025-8703	90025	Patrick De Geest	09/2018
4848	2^299048-113297	90023	Enzo Doria	07/2014
4849	10^90015+849	90016	Patrick De Geest	09/2018
4850	10^90010+6811	90011	Patrick De Geest	09/2018
4851	10^90010-183597	90010	Patrick De Geest	11/2018
4852	10^90009+58321	90010	Patrick De Geest	11/2018
4853	10^90008+847	90009	Patrick De Geest	09/2018
4854	10^90009-356013	90009	Patrick De Geest	11/2018
4856	3^188648+92	90008	Lelio R Paula	12/2015
4855	10^90008-706049	90008	Patrick De Geest	11/2018
4857	5*2^298991+7	90006	Lelio R Paula	08/2014
4858	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
4859	10^90000+8869	90001	Patrick De Geest	12/2009
4861	10^89999+82939	90000	Dirk Augustin	04/2007
4860	10^90000-140343	90000	Patrick De Geest	12/2009
4862	10^89999-194891	89999	Patrick De Geest	11/2009
4863	19^70365-78	89980	Lelio R Paula	12/2015
4864	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
4865	2^298852-64875	89964	Lelio R Paula	11/2013
4866	18^71659+37	89952	Lelio R Paula	12/2015
4867	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
4868	17^73067+20	89906	Lelio R Paula	11/2015
4869	2^298637-99	89899	Lelio R Paula	10/2012
4870	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
4871	9*10^89858+19	89859	Robert Price	05/2016
4872	2^298501+1870067	89858	Enzo Doria	05/2016
4873	11^86280-98	89852	Lelio R Paula	11/2015
4874	2^298473-110059	89850	Enzo Doria	04/2014
4875	19^70263-32	89850	Lelio R Paula	12/2015
4876	(299*10^89836-17)/3	89838	Robert Price	01/2017
4877	3^188286+14	89836	Robert Price	09/2013
4878	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
4879	2^298367+58905	89818	Lelio R Paula	11/2013
4880	2^298319-109657	89803	Enzo Doria	04/2014
4881	8*10^89800+81	89801	Robert Price	05/2017
4882	18^71505-91	89759	Lelio R Paula	12/2015
4883	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
4884	2^298079-109531	89731	Enzo Doria	04/2014
4885	117^43380+116	89718	Norbert Schneider	08/2018
4886	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
4887	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
4888	2^298003-66945	89708	Lelio R Paula	11/2013
4889	(23*10^89705-83)/3	89706	Robert Price	09/2017
4890	17^72900-54	89700	Lelio R Paula	11/2015
4891	3*2^297956+5	89695	Lelio R Paula	08/2014
4892	20^68938-11	89691	Lelio R Paula	01/2016
4893	89*10^89687-7	89689	Robert Price	03/2017
4894	2^297923+77783	89684	Enzo Doria	05/2016
4895	11^86107-24576000	89672	Enzo Doria	02/2013
4896	2^297878-111911	89671	Enzo Doria	05/2014
4897	7^106084+40	89652	Lelio R Paula	10/2015
4898	(86*10^89640-311)/9	89641	Robert Price	10/2017
4899	3*10^89608-59	89609	Robert Price	10/2017
4900	3^187780-11038	89594	Enzo Doria	05/2014
4901	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
4902	5^128141-36	89567	Lelio R Paula	10/2015
4903	4*7^105951+9	89540	Lelio R Paula	10/2014
4904	(7*10^89539-439)/9	89539	Robert Price	09/2017
4905	2^297397+177257	89526	Enzo Doria	05/2016
4906	2^297346-16241	89511	Enzo Doria	04/2013
4907	(5*10^89510+79)/3	89511	Robert Price	11/2017
4909	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
4908	2^297328-869688105	89505	Lelio R Paula	07/2016
4910	2^297325-459043	89504	Enzo Doria	05/2015
4911	2^297310-112391	89500	Enzo Doria	06/2014
4912	2^297296-112157	89496	Enzo Doria	06/2014
4913	57^50966-2	89490	Lelio R Paula	08/2013
4914	(266*10^89482+1)/3	89484	Robert Price	02/2016
4915	(14*10^89480-101)/3	89481	Robert Price	04/2017
4916	2^297122+99	89443	Lelio R Paula	10/2012
4917	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
4918	(25*10^89413+161)/3	89414	Robert Price	01/2017
4919	2^296990+1870699	89403	Enzo Doria	05/2016
4920	2^296972-1017	89398	Lelio R Paula	11/2013
4921	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
4922	(85*10^89375-31)/9	89376	Robert Price	11/2015
4923	9*2^296870+7	89368	Lelio R Paula	08/2014
4924	100^44683-99^44683	89366	Robert Price	07/2013
4925	2^296810+76519	89349	Enzo Doria	05/2016
4926	8^98928+7^(98928+1)	89341	Robert Price	06/2016
4927	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
4928	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
4930	2^296736-432149	89327	Paul Bourdelais	05/2013
4929	2^296737-112519	89327	Enzo Doria	06/2014
4931	2^296718-3645	89322	Lelio R Paula	11/2013
4932	2^296681-16221	89310	Enzo Doria	04/2013
4933	2^296669-16513	89307	Enzo Doria	04/2013
4934	2^296619-16357	89292	Enzo Doria	04/2013
4935	2^296614-110051	89290	Enzo Doria	04/2014
4936	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
4937	(2*10^89279+457)/9	89279	Robert Price	01/2017
4938	15^75907-28	89274	Lelio R Paula	11/2015
4939	2^296547-37	89270	Yves Minet	01/2012
4940	2^296485+191	89251	Lelio R Paula	10/2012
4941	2^296467-75	89246	Lelio R Paula	10/2012
4942	2^296416-109535	89231	Enzo Doria	04/2014
4943	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
4944	66^49037-65	89225	Norbert Schneider	11/2014
4945	2^296377-16245	89219	Enzo Doria	04/2013
4946	2^296372-64875	89217	Lelio R Paula	11/2013
4947	5*6^114648-7	89215	Lelio R Paula	10/2014
4948	3*10^89206+13	89207	Robert Price	08/2017
4949	7*3^186960-4	89204	Lelio R Paula	08/2014
4950	2^296290-112133	89193	Enzo Doria	06/2014
4951	6^114620-17003	89192	Enzo Doria	02/2013
4952	(4*10^89189+41)/9	89189	Robert Price	11/2014
4953	2^296261-161181	89184	Enzo Doria	04/2013
4954	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
4955	3^186903-10	89176	Robert Price	09/2013
4958	7*10^89169-3	89170	Dmitry Domanov	11/2010
4957	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
4956	(43*10^89169+47)/9	89170	Robert Price	12/2017
4959	(10^89160+29)/3	89160	Serge Batalov	12/2014
4960	(28*10^89141-97)/3	89142	Robert Price	07/2016
4961	2^296116-734639	89140	Paul Bourdelais	04/2013
4962	6^114544-133	89133	Lelio R Paula	12/2015
4963	2^296076-113297	89128	Enzo Doria	07/2014
4964	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
4965	5*10^89118+81	89119	Robert Price	08/2017
4966	2^296037-1411	89117	Yves Minet	01/2013
4967	2^296020-2604809	89111	Enzo Doria	05/2015
4968	2^296016+81	89110	Henri Lifchitz	02/2007
4969	2^296010-11	89108	Lelio R Paula	10/2012
4970	2^295998-111911	89105	Enzo Doria	05/2014
4971	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
4972	2^295939-16621	89087	Enzo Doria	04/2013
4973	2^295934-109691	89086	Enzo Doria	04/2014
4974	(185*10^89063+7)/3	89065	Robert Price	02/2017
4975	2^295831+143	89055	Lelio R Paula	10/2012
4976	31^59713-30	89054	Theodore Burton	02/2007
4977	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
4979	123^42608+2	89047	Lelio R Paula	05/2013
4978	6^114433-114433^6	89047	Norbert Schneider	04/2017
4980	2^295800-459659	89045	Enzo Doria	05/2015
4981	(52*10^89037-1)/3	89039	Robert Price	02/2017
4982	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
4983	11^85470-5850	89008	Enzo Doria	02/2013
4984	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
4985	(p(18424)#-4)/2	88985	Robert Price	09/2017
4986	2^295564-189	88974	Lelio R Paula	10/2012
4987	2^295557+73097	88972	Enzo Doria	04/2016
4988	11^85433-5760	88970	Enzo Doria	01/2013
4989	6*10^88938-91	88939	Robert Price	11/2017
4990	15^75619-88	88935	Lelio R Paula	11/2015
4991	2^295385-85	88920	Lelio R Paula	10/2012
4992	2^295385-16333	88920	Enzo Doria	04/2013
4993	2^295309+59	88897	Lelio R Paula	10/2012
4994	2^295288-109799	88891	Enzo Doria	04/2014
4995	10^88888+170373	88889	Stefano Morozzi	07/2018
4996	10^88888+271399	88889	Stefano Morozzi	07/2018
4997	10^88888+375397	88889	Stefano Morozzi	07/2018
4998	10^88888+548823	88889	Stefano Morozzi	07/2018
4999	10^88888+820861	88889	Stefano Morozzi	07/2018
5000	10^88888+1206349	88889	Stefano Morozzi	07/2018

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Probable Primes Top 10000

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