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 (> 30000)	Who ?	When ?
4001	15^75619-88	88935	Lelio R Paula	11/2015
4002	2^295385-85	88920	Lelio R Paula	10/2012
4003	2^295385-16333	88920	Enzo Doria	04/2013
4004	2^295309+59	88897	Lelio R Paula	10/2012
4005	2^295288-109799	88891	Enzo Doria	04/2014
4006	2^295245+65	88878	Lelio R Paula	10/2012
4007	Padovan(727734)	88874	Eric W. Weisstein	04/2011
4008	18^70793-17	88865	Lelio R Paula	11/2015
4009	6^114196-17573	88862	Enzo Doria	02/2013
4010	302^35829+35829^302	88857	Norbert Schneider	12/2014
4011	3^186223+16	88851	Robert Price	10/2013
4012	3*2^295139+7	88847	Lelio R Paula	08/2014
4013	3^186212-113008	88846	Enzo Doria	07/2014
4014	87^45803-86	88836	Norbert Schneider	11/2015
4015	2^295094-110273	88833	Enzo Doria	05/2014
4016	2^295080+1869151	88828	Enzo Doria	05/2016
4017	2^295027-113407	88812	Enzo Doria	07/2014
4018	(2*10^88808-71)/3	88808	Robert Price	01/2017
4019	13^79722-80	88806	Lelio R Paula	11/2015
4020	3^186103+104	88794	Lelio R Paula	12/2015
4021	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
4022	2^294937-115003	88785	Enzo Doria	06/2015
4023	2^294868-109709	88765	Enzo Doria	04/2014
4024	2^294864-2985	88763	Yves Minet	09/2014
4025	2^294754+15015	88730	Lelio R Paula	10/2013
4026	(3^185951-7)/20	88720	Lelio R Paula	01/2013
4027	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
4028	(10^88680+11)/3	88680	Robert Price	11/2014
4029	2*7^104928-9	88675	Lelio R Paula	10/2014
4030	11^85150+12	88675	Lelio R Paula	11/2015
4031	8*6^113951+5	88673	Lelio R Paula	10/2014
4032	6^113940-18563	88663	Enzo Doria	03/2013
4033	38^56123-56123^38	88663	Norbert Schneider	02/2017
4034	2^294492-65	88651	Lelio R Paula	10/2012
4035	20^68120-53	88627	Lelio R Paula	01/2016
4036	2^294391-113257	88621	Enzo Doria	07/2014
4037	5^126784-15476	88619	Enzo Doria	02/2013
4038	2^294327+9	88602	Lelio R Paula	10/2012
4039	2^294320+18915	88600	Lelio R Paula	10/2013
4040	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
4041	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
4042	(2*10^88545+7)/9	88545	Erik Branger	03/2011
4043	2^294137-133	88545	Lelio R Paula	10/2012
4044	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
4045	4^147036+147036^4+1	88525	Robert Price	04/2014
4046	(14^77213-5^77213)/9	88496	Robert Price	04/2013
4047	2^293965+2793377	88493	Enzo Doria	03/2016
4048	11^84971-150	88489	Enzo Doria	08/2012
4049	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
4050	11^84958-2190	88475	Enzo Doria	12/2012
4051	2^293880-111347	88467	Enzo Doria	05/2014
4052	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
4053	10^88457+278733	88458	Patrick De Geest	07/2017
4054	10^88457-401	88457	Robert Price	06/2017
4055	11^84908-1680	88423	Enzo Doria	12/2012
4056	2^293679-112075	88407	Enzo Doria	06/2014
4057	6^113608-65	88405	Lelio R Paula	12/2015
4058	2^293624+82875	88390	Lelio R Paula	10/2013
4059	2^293612-112337	88387	Enzo Doria	06/2014
4060	758^30693+30693^758	88386	Norbert Schneider	05/2017
4061	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
4062	5*10^88377+77	88378	Robert Price	06/2016
4063	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
4064	2^293461-2785843	88341	Enzo Doria	03/2016
4065	2^293416-1037	88328	Yves Minet	11/2012
4066	(2^293384-7)/3	88317	Lelio R Paula	01/2013
4067	(3^185092-5)/4	88311	Lelio R Paula	01/2013
4068	14^77039-57	88297	Lelio R Paula	11/2015
4069	5^126303+42	88283	Lelio R Paula	10/2015
4070	19^69025-18	88266	Theodore Burton	01/2006
4071	5*10^88261-3	88262	Dmitry Domanov	11/2010
4072	8^97731-7^(97731-1)	88260	Robert Price	04/2016
4073	5*10^88254+59	88255	Robert Price	09/2016
4074	4*3^184968-7	88253	Lelio R Paula	08/2014
4075	7^104426+88	88251	Lelio R Paula	10/2015
4076	2^293142+99	88245	Lelio R Paula	10/2012
4077	11^84736-2130	88244	Enzo Doria	12/2012
4078	2^293068-89	88223	Lelio R Paula	10/2012
4079	2^293014-109655	88207	Enzo Doria	04/2014
4080	8*7^104371-3	88205	Lelio R Paula	10/2014
4081	2^292995-2145	88201	Lelio R Paula	10/2013
4082	5*10^88182+77	88183	Robert Price	06/2016
4083	2^292929+43877	88181	Donovan Johnson	04/2005
4084	6^113321+131	88181	Lelio R Paula	12/2015
4085	2^292904-583949	88173	Paul Bourdelais	04/2013
4086	2^292894-111851	88170	Enzo Doria	05/2014
4087	2^292872-2797349	88164	Enzo Doria	03/2016
4088	2^292860-109685	88160	Enzo Doria	04/2014
4089	9*6^113288-5	88157	Lelio R Paula	10/2014
4090	(73*10^88105+17)/9	88106	Robert Price	10/2015
4091	11^84588+78	88090	Lelio R Paula	11/2015
4092	(265*10^88077+11)/3	88079	Robert Price	03/2017
4093	91^44959-90^44959	88077	Robert Price	07/2015
4094	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
4095	(10^88020+101)/3	88020	Robert Price	04/2016
4096	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
4097	p(18225)#/2+128	87929	Robert Price	04/2017
4098	4*6^112977+7	87914	Lelio R Paula	10/2014
4099	14^76677+69	87882	Lelio R Paula	11/2015
4100	(22*10^87863-1)/3	87864	Robert Price	12/2014
4101	2^291822-2797811	87848	Enzo Doria	04/2016
4102	2^291716-111389	87816	Enzo Doria	05/2014
4103	(782*10^87809-71)/9	87811	Robert Price	06/2017
4104	3^184039+1820	87809	Lelio R Paula	12/2015
4105	12^81356+41	87798	Lelio R Paula	11/2015
4106	6^112792-18983	87770	Enzo Doria	03/2013
4107	3*6^112787-5	87766	Lelio R Paula	10/2014
4108	7^103848+82	87762	Lelio R Paula	10/2015
4109	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
4110	(3^183915+5)/128	87748	Lelio R Paula	01/2013
4111	19^68619+24	87747	Lelio R Paula	12/2015
4113	2^291480+1185	87745	Lelio R Paula	10/2013
4112	2^291482+1867369	87745	Enzo Doria	03/2016
4114	2^291467-937	87741	Yves Minet	05/2013
4115	(25*10^87726+161)/3	87727	Robert Price	01/2017
4116	11^84239-2850	87726	Enzo Doria	12/2012
4117	10^87720+215541	87721	Patrick De Geest	01/2011
4118	10^87720-3	87720	Markus Tervooren	07/2010
4119	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
4120	93^44541-2	87679	Lelio R Paula	09/2013
4121	2^291261-109561	87679	Enzo Doria	04/2014
4122	(4*10^87669+149)/9	87669	Robert Price	03/2017
4123	2^291217+4257	87666	Lelio R Paula	10/2013
4124	2*12^81214-5^81214	87645	Mike Oakes	12/2010
4125	12^81188+85	87617	Lelio R Paula	11/2015
4126	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
4127	2^290958+127	87588	Lelio R Paula	09/2012
4128	2^290923-67	87577	Lelio R Paula	09/2012
4129	3*10^87573-97	87574	Robert Price	08/2017
4130	(13*10^87565+11)/3	87566	Robert Price	05/2015
4131	(2^290857-7)/55	87555	Lelio R Paula	01/2013
4132	2^290802+82875	87541	Lelio R Paula	10/2013
4133	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
4134	3^183441+236	87524	Lelio R Paula	12/2015
4135	2^290618-33	87485	Lelio R Paula	09/2012
4136	(184*10^87473-1)/3	87475	Robert Price	02/2017
4137	2^290534-115151	87460	Enzo Doria	06/2015
4138	2^290512-109757	87453	Enzo Doria	04/2014
4139	(32*10^87448-41)/9	87449	Robert Price	05/2015
4140	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
4141	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
4142	2^290426+82875	87427	Lelio R Paula	11/2013
4143	3*2^290415-7	87425	Lelio R Paula	08/2014
4144	10^87408+57	87409	Robert Price	03/2011
4145	2^290366+74779	87409	Enzo Doria	04/2016
4146	10^87408-123569	87408	Patrick De Geest	07/2013
4147	2^290265+58905	87379	Lelio R Paula	10/2013
4148	7^103391+16	87376	Lelio R Paula	10/2015
4149	8*7^103379+3	87367	Lelio R Paula	10/2014
4150	(2^290226+7)/71	87365	Lelio R Paula	01/2013
4151	13^78407-30	87341	Lelio R Paula	11/2015
4152	4*10^87337-99	87338	Robert Price	12/2016
4153	7*10^87319+39	87320	Robert Price	07/2016
4154	3*5^124921+2	87317	Lelio R Paula	10/2014
4155	3^182984+88	87306	Lelio R Paula	12/2015
4156	4*10^87287-99	87288	Robert Price	12/2016
4157	11^83813-1860	87283	Enzo Doria	12/2012
4158	734^30453+30453^734	87270	Norbert Schneider	04/2017
4159	12^80855+29	87258	Lelio R Paula	11/2015
4160	3*6^112119-5	87247	Lelio R Paula	10/2014
4161	12^80806+79	87205	Lelio R Paula	11/2015
4162	91382^9+9^91382	87201	Andrey Kulsha	11/2004
4163	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
4164	6^112054-47	87195	Lelio R Paula	12/2015
4165	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
4166	15^74131-68	87185	Lelio R Paula	11/2015
4167	2^289583-741	87174	Lelio R Paula	10/2013
4168	7^103146+12	87169	Lelio R Paula	10/2015
4169	5*2^289556-3	87166	Lelio R Paula	08/2014
4170	2^289543-112735	87162	Enzo Doria	06/2014
4171	8*3^182655-7	87150	Lelio R Paula	08/2014
4172	2*10^87144+81	87145	Robert Price	01/2017
4173	7^103106+2*3^103106	87135	Mike Oakes	08/2010
4174	8*3^182614+7	87130	Lelio R Paula	08/2014
4175	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
4176	3^182566+14	87107	Robert Price	09/2013
4177	(3^182385-5)/2	87020	Lelio R Paula	01/2013
4178	11^83534-8	86992	Lelio R Paula	11/2015
4179	4^144479-14267	86986	Mike Oakes	03/2011
4180	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
4181	(151*10^86963-1)/3	86965	Robert Price	04/2017
4182	15^73940-58	86961	Lelio R Paula	11/2015
4183	2^288761-113143	86926	Enzo Doria	07/2014
4184	2^288747+3083	86922	Yves Minet	03/2011
4185	30^58842+29	86917	Norbert Schneider	03/2017
4186	(10^86906-13)/3	86906	Robert Price	02/2017
4187	2^288692-110027	86905	Enzo Doria	04/2014
4188	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
4189	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
4190	3^182089-34	86879	Robert Price	11/2013
4191	2^288543-109801	86861	Enzo Doria	04/2014
4192	60^48847-59	86858	Norbert Schneider	10/2014
4193	2^288470-64875	86839	Lelio R Paula	10/2013
4194	10^86816+32997	86817	Patrick De Geest	07/2013
4195	10^86816-99	86816	Robert Price	05/2011
4196	41487!2+256	86786	Robert Price	01/2015
4197	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
4198	2^288243+76043	86770	Enzo Doria	04/2016
4199	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
4200	9*6^111495+5	86761	Lelio R Paula	10/2014
4201	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
4202	9*7^102654-2	86754	Lelio R Paula	10/2014
4203	2^288122-112841	86734	Enzo Doria	06/2014
4204	5^124062-68	86716	Lelio R Paula	10/2015
4205	(2^288007-3)/125	86697	Lelio R Paula	01/2013
4206	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
4207	7^102555+48	86670	Lelio R Paula	10/2015
4208	77779!4+2	86660	Robert Price	08/2017
4209	2^287809-111355	86640	Enzo Doria	05/2014
4210	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
4211	9*7^102504+8	86627	Lelio R Paula	10/2014
4212	3^181551+32	86622	Robert Price	11/2013
4213	2^287735-521347	86617	Paul Bourdelais	05/2013
4214	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
4215	2^287540-112967	86559	Enzo Doria	06/2014
4216	3^181407+20	86554	Robert Price	10/2013
4217	(13*10^86546+83)/3	86547	Robert Price	09/2016
4218	3^181378-2^(181378-1)	86540	Robert Price	01/2016
4219	83^45080-2	86513	Lelio R Paula	08/2013
4220	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
4221	25*29^59147+20936	86498	Curtis Bright	05/2015
4222	2^287298+1871359	86486	Enzo Doria	05/2016
4223	3*10^86478+89	86479	Robert Price	03/2017
4224	2^287272-79049	86478	Paul Bourdelais	02/2012
4225	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4226	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4227	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4228	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4229	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4230	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4231	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4232	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4233	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4234	(10^86453-1)/9	86453	Lew Baxter	10/2000
4235	87^44563-86^44563	86431	Robert Price	05/2015
4236	6^111057+61	86420	Lelio R Paula	12/2015
4237	2^287057-109909	86413	Enzo Doria	04/2014
4238	5^123608+22	86399	Lelio R Paula	10/2015
4239	(31*10^86364-121)/9	86365	Robert Price	06/2016
4240	2^286859+71663	86354	Enzo Doria	04/2016
4241	2^286740+29835	86318	Lelio R Paula	10/2013
4242	2*10^86310+9^86310	86311	Mike Oakes	05/2011
4243	11^82878-1860	86309	Enzo Doria	12/2012
4244	2^286547+16095	86260	Lelio R Paula	10/2013
4245	2^286455-110427	86232	Enzo Doria	05/2014
4246	(37*10^86230+53)/9	86231	Robert Price	05/2015
4247	8*3^180700+5	86217	Lelio R Paula	08/2014
4248	3^180697-40	86215	Lelio R Paula	12/2015
4249	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
4250	2^286165+77	86145	Lelio R Paula	08/2012

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Probable Primes Top 10000

(180278 PRPs in the top)