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 ?
5001	10^88888+1292047	88889	Stefano Morozzi	07/2018
5002	10^88888+1456029	88889	Stefano Morozzi	07/2018
5003	10^88888-490287	88888	Patrick De Geest	09/2018
5004	2^295245+65	88878	Lelio R Paula	10/2012
5005	Padovan(727734)	88874	Eric W. Weisstein	04/2011
5006	18^70793-17	88865	Lelio R Paula	11/2015
5007	6^114196-17573	88862	Enzo Doria	02/2013
5008	302^35829+35829^302	88857	Norbert Schneider	12/2014
5009	3^186223+16	88851	Robert Price	10/2013
5010	3*2^295139+7	88847	Lelio R Paula	08/2014
5011	3^186212-113008	88846	Enzo Doria	07/2014
5012	87^45803-86	88836	Norbert Schneider	11/2015
5013	2^295094-110273	88833	Enzo Doria	05/2014
5014	2^295080+1869151	88828	Enzo Doria	05/2016
5015	2^295027-113407	88812	Enzo Doria	07/2014
5016	(2*10^88808-71)/3	88808	Robert Price	01/2017
5017	13^79722-80	88806	Lelio R Paula	11/2015
5018	3^186103+104	88794	Lelio R Paula	12/2015
5019	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
5020	2^294937-115003	88785	Enzo Doria	06/2015
5021	2^294868-109709	88765	Enzo Doria	04/2014
5022	2^294864-2985	88763	Yves Minet	09/2014
5023	(17*10^88761-41)/3	88762	Robert Price	09/2017
5024	2^294754+15015	88730	Lelio R Paula	10/2013
5025	(3^185951-7)/20	88720	Lelio R Paula	01/2013
5026	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
5027	(10^88680+11)/3	88680	Robert Price	11/2014
5028	2*7^104928-9	88675	Lelio R Paula	10/2014
5029	11^85150+12	88675	Lelio R Paula	11/2015
5030	8*6^113951+5	88673	Lelio R Paula	10/2014
5031	6^113940-18563	88663	Enzo Doria	03/2013
5032	38^56123-56123^38	88663	Norbert Schneider	02/2017
5033	2^294492-65	88651	Lelio R Paula	10/2012
5034	20^68120-53	88627	Lelio R Paula	01/2016
5035	122^42477-121	88623	Norbert Schneider	10/2018
5036	2^294391-113257	88621	Enzo Doria	07/2014
5037	5^126784-15476	88619	Enzo Doria	02/2013
5038	2^294327+9	88602	Lelio R Paula	10/2012
5039	2^294320+18915	88600	Lelio R Paula	10/2013
5040	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
5041	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
5043	(2*10^88545+7)/9	88545	Erik Branger	03/2011
5042	2^294137-133	88545	Lelio R Paula	10/2012
5044	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
5045	4^147036+147036^4+1	88525	Robert Price	04/2014
5046	(14^77213-5^77213)/9	88496	Robert Price	04/2013
5047	2^293965+2793377	88493	Enzo Doria	03/2016
5048	11^84971-150	88489	Enzo Doria	08/2012
5049	48^52626-47	88478	Norbert Schneider	08/2018
5050	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
5051	11^84958-2190	88475	Enzo Doria	12/2012
5052	2^293880-111347	88467	Enzo Doria	05/2014
5053	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
5054	10^88457+278733	88458	Patrick De Geest	07/2017
5055	10^88457-401	88457	Robert Price	06/2017
5056	11^84908-1680	88423	Enzo Doria	12/2012
5057	2^293679-112075	88407	Enzo Doria	06/2014
5058	6^113608-65	88405	Lelio R Paula	12/2015
5059	2^293624+82875	88390	Lelio R Paula	10/2013
5060	2^293612-112337	88387	Enzo Doria	06/2014
5061	758^30693+30693^758	88386	Norbert Schneider	05/2017
5062	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
5063	5*10^88377+77	88378	Robert Price	06/2016
5064	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
5065	2^293461-2785843	88341	Enzo Doria	03/2016
5066	2^293416-1037	88328	Yves Minet	11/2012
5067	(2^293384-7)/3	88317	Lelio R Paula	01/2013
5068	(3^185092-5)/4	88311	Lelio R Paula	01/2013
5069	(5*10^88303-173)/3	88304	Robert Price	11/2017
5070	14^77039-57	88297	Lelio R Paula	11/2015
5071	3*10^88293-59	88294	Robert Price	10/2017
5072	5^126303+42	88283	Lelio R Paula	10/2015
5074	19^69025-18	88266	Theodore Burton	01/2006
5073	140^41128+139	88266	Norbert Schneider	04/2019
5075	5*10^88261-3	88262	Dmitry Domanov	11/2010
5076	8^97731-7^(97731-1)	88260	Robert Price	04/2016
5077	5*10^88254+59	88255	Robert Price	09/2016
5078	4*3^184968-7	88253	Lelio R Paula	08/2014
5079	7^104426+88	88251	Lelio R Paula	10/2015
5080	2^293142+99	88245	Lelio R Paula	10/2012
5081	11^84736-2130	88244	Enzo Doria	12/2012
5082	(10^110315+1)/(10^22063+1)/5824812682167648578460281641	88225	Makoto Kamada	04/2019
5083	2^293068-89	88223	Lelio R Paula	10/2012
5084	2^293014-109655	88207	Enzo Doria	04/2014
5085	8*7^104371-3	88205	Lelio R Paula	10/2014
5086	2^292995-2145	88201	Lelio R Paula	10/2013
5087	5*10^88182+77	88183	Robert Price	06/2016
5089	2^292929+43877	88181	Donovan Johnson	04/2005
5088	6^113321+131	88181	Lelio R Paula	12/2015
5090	2^292904-583949	88173	Paul Bourdelais	04/2013
5091	2^292894-111851	88170	Enzo Doria	05/2014
5092	2^292872-2797349	88164	Enzo Doria	03/2016
5093	2^292860-109685	88160	Enzo Doria	04/2014
5094	9*6^113288-5	88157	Lelio R Paula	10/2014
5095	(2*10^88112-23)/3	88112	Robert Price	09/2017
5096	(73*10^88105+17)/9	88106	Robert Price	10/2015
5097	11^84588+78	88090	Lelio R Paula	11/2015
5098	(265*10^88077+11)/3	88079	Robert Price	03/2017
5099	91^44959-90^44959	88077	Robert Price	07/2015
5100	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
5101	(10^88020+101)/3	88020	Robert Price	04/2016
5102	52^51285-51	88006	Norbert Schneider	09/2018
5103	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
5104	(424*10^87930-1)/9	87932	Robert Price	11/2017
5105	p(18225)#/2+128	87929	Robert Price	04/2017
5106	4*6^112977+7	87914	Lelio R Paula	10/2014
5107	14^76677+69	87882	Lelio R Paula	11/2015
5108	(22*10^87863-1)/3	87864	Robert Price	12/2014
5109	2^291822-2797811	87848	Enzo Doria	04/2016
5110	2^291716-111389	87816	Enzo Doria	05/2014
5111	(782*10^87809-71)/9	87811	Robert Price	06/2017
5112	3^184039+1820	87809	Lelio R Paula	12/2015
5113	12^81356+41	87798	Lelio R Paula	11/2015
5114	6^112792-18983	87770	Enzo Doria	03/2013
5115	3*6^112787-5	87766	Lelio R Paula	10/2014
5116	7^103848+82	87762	Lelio R Paula	10/2015
5117	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
5118	(3^183915+5)/128	87748	Lelio R Paula	01/2013
5119	19^68619+24	87747	Lelio R Paula	12/2015
5121	2^291480+1185	87745	Lelio R Paula	10/2013
5120	2^291482+1867369	87745	Enzo Doria	03/2016
5122	2^291467-937	87741	Yves Minet	05/2013
5123	(25*10^87726+161)/3	87727	Robert Price	01/2017
5124	11^84239-2850	87726	Enzo Doria	12/2012
5125	10^87720+215541	87721	Patrick De Geest	01/2011
5126	10^87720-3	87720	Markus Tervooren	07/2010
5127	(5*10^87712-473)/9	87712	Robert Price	12/2017
5128	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
5129	93^44541-2	87679	Lelio R Paula	09/2013
5130	2^291261-109561	87679	Enzo Doria	04/2014
5131	(4*10^87669+149)/9	87669	Robert Price	03/2017
5132	2^291217+4257	87666	Lelio R Paula	10/2013
5133	2*12^81214-5^81214	87645	Mike Oakes	12/2010
5134	(5*10^87622-473)/9	87622	Robert Price	12/2017
5135	12^81188+85	87617	Lelio R Paula	11/2015
5136	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
5137	2^290958+127	87588	Lelio R Paula	09/2012
5138	2^290923-67	87577	Lelio R Paula	09/2012
5139	3*10^87573-97	87574	Robert Price	08/2017
5140	(13*10^87565+11)/3	87566	Robert Price	05/2015
5141	(2^290857-7)/55	87555	Lelio R Paula	01/2013
5142	2^290802+82875	87541	Lelio R Paula	10/2013
5143	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
5144	3^183441+236	87524	Lelio R Paula	12/2015
5145	2^290618-33	87485	Lelio R Paula	09/2012
5146	(184*10^87473-1)/3	87475	Robert Price	02/2017
5147	2^290534-115151	87460	Enzo Doria	06/2015
5148	2^290512-109757	87453	Enzo Doria	04/2014
5149	(32*10^87448-41)/9	87449	Robert Price	05/2015
5150	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
5151	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
5152	2^290426+82875	87427	Lelio R Paula	11/2013
5153	3*2^290415-7	87425	Lelio R Paula	08/2014
5154	10^87408+57	87409	Robert Price	03/2011
5155	2^290366+74779	87409	Enzo Doria	04/2016
5156	10^87408-123569	87408	Patrick De Geest	07/2013
5157	2^290265+58905	87379	Lelio R Paula	10/2013
5158	7^103391+16	87376	Lelio R Paula	10/2015
5159	(115*10^87368-7)/9	87370	Robert Price	11/2017
5160	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
5161	8*7^103379+3	87367	Lelio R Paula	10/2014
5162	(2^290226+7)/71	87365	Lelio R Paula	01/2013
5163	13^78407-30	87341	Lelio R Paula	11/2015
5164	4*10^87337-99	87338	Robert Price	12/2016
5165	7*10^87319+39	87320	Robert Price	07/2016
5166	3*5^124921+2	87317	Lelio R Paula	10/2014
5167	3^182984+88	87306	Lelio R Paula	12/2015
5168	(10^87323-1)/(9*33909262597306826117)	87303	Alfred Reich	02/2019
5169	4*10^87287-99	87288	Robert Price	12/2016
5170	11^83813-1860	87283	Enzo Doria	12/2012
5171	734^30453+30453^734	87270	Norbert Schneider	04/2017
5172	12^80855+29	87258	Lelio R Paula	11/2015
5173	3*6^112119-5	87247	Lelio R Paula	10/2014
5174	12^80806+79	87205	Lelio R Paula	11/2015
5175	91382^9+9^91382	87201	Andrey Kulsha	11/2004
5176	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
5177	6^112054-47	87195	Lelio R Paula	12/2015
5178	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
5179	15^74131-68	87185	Lelio R Paula	11/2015
5180	2^289583-741	87174	Lelio R Paula	10/2013
5181	7^103146+12	87169	Lelio R Paula	10/2015
5182	5*2^289556-3	87166	Lelio R Paula	08/2014
5183	2^289543-112735	87162	Enzo Doria	06/2014
5184	8*3^182655-7	87150	Lelio R Paula	08/2014
5185	2*10^87144+81	87145	Robert Price	01/2017
5186	7^103106+2*3^103106	87135	Mike Oakes	08/2010
5187	8*3^182614+7	87130	Lelio R Paula	08/2014
5188	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
5189	3^182566+14	87107	Robert Price	09/2013
5190	(3^182385-5)/2	87020	Lelio R Paula	01/2013
5191	11^83534-8	86992	Lelio R Paula	11/2015
5192	4^144479-14267	86986	Mike Oakes	03/2011
5193	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
5194	(151*10^86963-1)/3	86965	Robert Price	04/2017
5195	15^73940-58	86961	Lelio R Paula	11/2015
5196	2^288761-113143	86926	Enzo Doria	07/2014
5197	2^288747+3083	86922	Yves Minet	03/2011
5198	30^58842+29	86917	Norbert Schneider	03/2017
5199	(10^86906-13)/3	86906	Robert Price	02/2017
5200	2^288692-110027	86905	Enzo Doria	04/2014
5201	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
5202	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
5203	3^182089-34	86879	Robert Price	11/2013
5204	2^288543-109801	86861	Enzo Doria	04/2014
5205	60^48847-59	86858	Norbert Schneider	10/2014
5206	2^288470-64875	86839	Lelio R Paula	10/2013
5207	10^86816+32997	86817	Patrick De Geest	07/2013
5208	10^86816-99	86816	Robert Price	05/2011
5209	(89*10^86802-539)/9	86803	Robert Price	11/2017
5210	41487!2+256	86786	Robert Price	01/2015
5211	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
5212	2^288243+76043	86770	Enzo Doria	04/2016
5213	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
5214	9*6^111495+5	86761	Lelio R Paula	10/2014
5215	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
5216	9*7^102654-2	86754	Lelio R Paula	10/2014
5217	2^288122-112841	86734	Enzo Doria	06/2014
5218	5^124062-68	86716	Lelio R Paula	10/2015
5219	(2^288007-3)/125	86697	Lelio R Paula	01/2013
5220	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
5221	7^102555+48	86670	Lelio R Paula	10/2015
5222	2^287902-4961	86668	Yves Minet	05/2019
5223	77779!4+2	86660	Robert Price	08/2017
5224	2^287809-111355	86640	Enzo Doria	05/2014
5225	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
5226	9*7^102504+8	86627	Lelio R Paula	10/2014
5227	3^181551+32	86622	Robert Price	11/2013
5228	2^287735-521347	86617	Paul Bourdelais	05/2013
5229	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
5230	2^287540-112967	86559	Enzo Doria	06/2014
5231	3^181407+20	86554	Robert Price	10/2013
5232	(13*10^86546+83)/3	86547	Robert Price	09/2016
5233	2^287482-4715	86541	Yves Minet	05/2019
5234	3^181378-2^(181378-1)	86540	Robert Price	01/2016
5235	83^45080-2	86513	Lelio R Paula	08/2013
5236	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
5237	25*29^59147+20936	86498	Curtis Bright	05/2015
5238	2^287298+1871359	86486	Enzo Doria	05/2016
5239	118^41740-117	86481	Norbert Schneider	08/2018
5240	3*10^86478+89	86479	Robert Price	03/2017
5241	2^287272-79049	86478	Paul Bourdelais	02/2012
5242	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5243	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5244	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5245	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5246	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5247	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5248	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5249	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5250	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016

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PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)