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	2^294391-113257	88621	Enzo Doria	07/2014
4002	5^126784-15476	88619	Enzo Doria	02/2013
4003	2^294327+9	88602	Lelio R Paula	10/2012
4004	2^294320+18915	88600	Lelio R Paula	10/2013
4005	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
4006	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
4008	(2*10^88545+7)/9	88545	Erik Branger	03/2011
4007	2^294137-133	88545	Lelio R Paula	10/2012
4009	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
4010	4^147036+147036^4+1	88525	Robert Price	04/2014
4011	(14^77213-5^77213)/9	88496	Robert Price	04/2013
4012	2^293965+2793377	88493	Enzo Doria	03/2016
4013	11^84971-150	88489	Enzo Doria	08/2012
4014	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
4015	11^84958-2190	88475	Enzo Doria	12/2012
4016	2^293880-111347	88467	Enzo Doria	05/2014
4017	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
4018	10^88457-401	88457	Robert Price	06/2017
4019	11^84908-1680	88423	Enzo Doria	12/2012
4020	2^293679-112075	88407	Enzo Doria	06/2014
4021	6^113608-65	88405	Lelio R Paula	12/2015
4022	2^293624+82875	88390	Lelio R Paula	10/2013
4023	2^293612-112337	88387	Enzo Doria	06/2014
4024	758^30693+30693^758	88386	Norbert Schneider	05/2017
4025	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
4026	5*10^88377+77	88378	Robert Price	06/2016
4027	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
4028	2^293461-2785843	88341	Enzo Doria	03/2016
4029	2^293416-1037	88328	Yves Minet	11/2012
4030	(2^293384-7)/3	88317	Lelio R Paula	01/2013
4031	(3^185092-5)/4	88311	Lelio R Paula	01/2013
4032	14^77039-57	88297	Lelio R Paula	11/2015
4033	5^126303+42	88283	Lelio R Paula	10/2015
4034	19^69025-18	88266	Theodore Burton	01/2006
4035	5*10^88261-3	88262	Dmitry Domanov	11/2010
4036	8^97731-7^(97731-1)	88260	Robert Price	04/2016
4037	5*10^88254+59	88255	Robert Price	09/2016
4038	4*3^184968-7	88253	Lelio R Paula	08/2014
4039	7^104426+88	88251	Lelio R Paula	10/2015
4040	2^293142+99	88245	Lelio R Paula	10/2012
4041	11^84736-2130	88244	Enzo Doria	12/2012
4042	2^293068-89	88223	Lelio R Paula	10/2012
4043	2^293014-109655	88207	Enzo Doria	04/2014
4044	8*7^104371-3	88205	Lelio R Paula	10/2014
4045	2^292995-2145	88201	Lelio R Paula	10/2013
4046	5*10^88182+77	88183	Robert Price	06/2016
4048	2^292929+43877	88181	Donovan Johnson	04/2005
4047	6^113321+131	88181	Lelio R Paula	12/2015
4049	2^292904-583949	88173	Paul Bourdelais	04/2013
4050	2^292894-111851	88170	Enzo Doria	05/2014
4051	2^292872-2797349	88164	Enzo Doria	03/2016
4052	2^292860-109685	88160	Enzo Doria	04/2014
4053	9*6^113288-5	88157	Lelio R Paula	10/2014
4054	(73*10^88105+17)/9	88106	Robert Price	10/2015
4055	11^84588+78	88090	Lelio R Paula	11/2015
4056	(265*10^88077+11)/3	88079	Robert Price	03/2017
4057	91^44959-90^44959	88077	Robert Price	07/2015
4058	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
4059	(10^88020+101)/3	88020	Robert Price	04/2016
4060	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
4061	p(18225)#/2+128	87929	Robert Price	04/2017
4062	4*6^112977+7	87914	Lelio R Paula	10/2014
4063	14^76677+69	87882	Lelio R Paula	11/2015
4064	(22*10^87863-1)/3	87864	Robert Price	12/2014
4065	2^291822-2797811	87848	Enzo Doria	04/2016
4066	2^291716-111389	87816	Enzo Doria	05/2014
4067	(782*10^87809-71)/9	87811	Robert Price	06/2017
4068	3^184039+1820	87809	Lelio R Paula	12/2015
4069	12^81356+41	87798	Lelio R Paula	11/2015
4070	6^112792-18983	87770	Enzo Doria	03/2013
4071	3*6^112787-5	87766	Lelio R Paula	10/2014
4072	7^103848+82	87762	Lelio R Paula	10/2015
4073	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
4074	(3^183915+5)/128	87748	Lelio R Paula	01/2013
4075	19^68619+24	87747	Lelio R Paula	12/2015
4077	2^291480+1185	87745	Lelio R Paula	10/2013
4076	2^291482+1867369	87745	Enzo Doria	03/2016
4078	2^291467-937	87741	Yves Minet	05/2013
4079	(25*10^87726+161)/3	87727	Robert Price	01/2017
4080	11^84239-2850	87726	Enzo Doria	12/2012
4081	10^87720+215541	87721	Patrick De Geest	01/2011
4082	10^87720-3	87720	Markus Tervooren	07/2010
4083	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
4085	93^44541-2	87679	Lelio R Paula	09/2013
4084	2^291261-109561	87679	Enzo Doria	04/2014
4086	(4*10^87669+149)/9	87669	Robert Price	03/2017
4087	2^291217+4257	87666	Lelio R Paula	10/2013
4088	2*12^81214-5^81214	87645	Mike Oakes	12/2010
4089	12^81188+85	87617	Lelio R Paula	11/2015
4090	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
4091	2^290958+127	87588	Lelio R Paula	09/2012
4092	2^290923-67	87577	Lelio R Paula	09/2012
4093	(13*10^87565+11)/3	87566	Robert Price	05/2015
4094	(2^290857-7)/55	87555	Lelio R Paula	01/2013
4095	2^290802+82875	87541	Lelio R Paula	10/2013
4096	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
4097	3^183441+236	87524	Lelio R Paula	12/2015
4098	2^290618-33	87485	Lelio R Paula	09/2012
4099	(184*10^87473-1)/3	87475	Robert Price	02/2017
4100	2^290534-115151	87460	Enzo Doria	06/2015
4101	2^290512-109757	87453	Enzo Doria	04/2014
4102	(32*10^87448-41)/9	87449	Robert Price	05/2015
4103	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
4104	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
4105	2^290426+82875	87427	Lelio R Paula	11/2013
4106	3*2^290415-7	87425	Lelio R Paula	08/2014
4108	10^87408+57	87409	Robert Price	03/2011
4107	2^290366+74779	87409	Enzo Doria	04/2016
4109	10^87408-123569	87408	Patrick De Geest	07/2013
4110	2^290265+58905	87379	Lelio R Paula	10/2013
4111	7^103391+16	87376	Lelio R Paula	10/2015
4112	8*7^103379+3	87367	Lelio R Paula	10/2014
4113	(2^290226+7)/71	87365	Lelio R Paula	01/2013
4114	13^78407-30	87341	Lelio R Paula	11/2015
4115	4*10^87337-99	87338	Robert Price	12/2016
4116	7*10^87319+39	87320	Robert Price	07/2016
4117	3*5^124921+2	87317	Lelio R Paula	10/2014
4118	3^182984+88	87306	Lelio R Paula	12/2015
4119	4*10^87287-99	87288	Robert Price	12/2016
4120	11^83813-1860	87283	Enzo Doria	12/2012
4121	734^30453+30453^734	87270	Norbert Schneider	04/2017
4122	12^80855+29	87258	Lelio R Paula	11/2015
4123	3*6^112119-5	87247	Lelio R Paula	10/2014
4124	12^80806+79	87205	Lelio R Paula	11/2015
4125	91382^9+9^91382	87201	Andrey Kulsha	11/2004
4126	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
4127	6^112054-47	87195	Lelio R Paula	12/2015
4128	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
4129	15^74131-68	87185	Lelio R Paula	11/2015
4130	2^289583-741	87174	Lelio R Paula	10/2013
4131	7^103146+12	87169	Lelio R Paula	10/2015
4132	5*2^289556-3	87166	Lelio R Paula	08/2014
4133	2^289543-112735	87162	Enzo Doria	06/2014
4134	8*3^182655-7	87150	Lelio R Paula	08/2014
4135	2*10^87144+81	87145	Robert Price	01/2017
4136	7^103106+2*3^103106	87135	Mike Oakes	08/2010
4137	8*3^182614+7	87130	Lelio R Paula	08/2014
4138	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
4139	3^182566+14	87107	Robert Price	09/2013
4140	(3^182385-5)/2	87020	Lelio R Paula	01/2013
4141	11^83534-8	86992	Lelio R Paula	11/2015
4142	4^144479-14267	86986	Mike Oakes	03/2011
4143	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
4144	(151*10^86963-1)/3	86965	Robert Price	04/2017
4145	15^73940-58	86961	Lelio R Paula	11/2015
4146	2^288761-113143	86926	Enzo Doria	07/2014
4147	2^288747+3083	86922	Yves Minet	03/2011
4148	30^58842+29	86917	Norbert Schneider	03/2017
4149	(10^86906-13)/3	86906	Robert Price	02/2017
4150	2^288692-110027	86905	Enzo Doria	04/2014
4151	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
4152	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
4153	3^182089-34	86879	Robert Price	11/2013
4154	2^288543-109801	86861	Enzo Doria	04/2014
4155	60^48847-59	86858	Norbert Schneider	10/2014
4156	2^288470-64875	86839	Lelio R Paula	10/2013
4157	10^86816+32997	86817	Patrick De Geest	07/2013
4158	10^86816-99	86816	Robert Price	05/2011
4159	41487!2+256	86786	Robert Price	01/2015
4160	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
4161	2^288243+76043	86770	Enzo Doria	04/2016
4162	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
4163	9*6^111495+5	86761	Lelio R Paula	10/2014
4164	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
4165	9*7^102654-2	86754	Lelio R Paula	10/2014
4166	2^288122-112841	86734	Enzo Doria	06/2014
4167	5^124062-68	86716	Lelio R Paula	10/2015
4168	(2^288007-3)/125	86697	Lelio R Paula	01/2013
4169	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
4170	7^102555+48	86670	Lelio R Paula	10/2015
4171	2^287809-111355	86640	Enzo Doria	05/2014
4172	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
4173	9*7^102504+8	86627	Lelio R Paula	10/2014
4174	3^181551+32	86622	Robert Price	11/2013
4175	2^287735-521347	86617	Paul Bourdelais	05/2013
4176	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
4177	2^287540-112967	86559	Enzo Doria	06/2014
4178	3^181407+20	86554	Robert Price	10/2013
4179	(13*10^86546+83)/3	86547	Robert Price	09/2016
4180	3^181378-2^(181378-1)	86540	Robert Price	01/2016
4181	83^45080-2	86513	Lelio R Paula	08/2013
4182	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
4183	25*29^59147+20936	86498	Curtis Bright	05/2015
4184	2^287298+1871359	86486	Enzo Doria	05/2016
4185	3*10^86478+89	86479	Robert Price	03/2017
4186	2^287272-79049	86478	Paul Bourdelais	02/2012
4187	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4188	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4189	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4190	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4191	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4192	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4193	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4194	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4195	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4196	(10^86453-1)/9	86453	Lew Baxter	10/2000
4197	87^44563-86^44563	86431	Robert Price	05/2015
4198	6^111057+61	86420	Lelio R Paula	12/2015
4199	2^287057-109909	86413	Enzo Doria	04/2014
4200	5^123608+22	86399	Lelio R Paula	10/2015
4201	(31*10^86364-121)/9	86365	Robert Price	06/2016
4202	2^286859+71663	86354	Enzo Doria	04/2016
4203	2^286740+29835	86318	Lelio R Paula	10/2013
4204	2*10^86310+9^86310	86311	Mike Oakes	05/2011
4205	11^82878-1860	86309	Enzo Doria	12/2012
4206	2^286547+16095	86260	Lelio R Paula	10/2013
4207	2^286455-110427	86232	Enzo Doria	05/2014
4208	(37*10^86230+53)/9	86231	Robert Price	05/2015
4209	8*3^180700+5	86217	Lelio R Paula	08/2014
4210	3^180697-40	86215	Lelio R Paula	12/2015
4211	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
4212	2^286165+77	86145	Lelio R Paula	08/2012
4213	9*2^286140+7	86138	Lelio R Paula	08/2014
4214	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
4215	10^86110+161113	86111	Patrick De Geest	07/2013
4216	10^86110-69	86110	Robert Price	05/2011
4217	2^286036-869688105	86106	Lelio R Paula	07/2016
4218	(77*10^86072+31)/9	86073	Robert Price	10/2015
4219	2^285923+345	86072	Lelio R Paula	09/2013
4220	13^77266-90	86070	Lelio R Paula	11/2015
4221	2^285910-458903	86068	Enzo Doria	04/2015
4222	2^285904-125	86066	Lelio R Paula	08/2012
4223	2^285836+65835	86046	Lelio R Paula	09/2013
4224	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
4225	(5*10^86011-107)/3	86012	Robert Price	01/2017
4226	6^110522+163	86003	Lelio R Paula	12/2015
4227	41^53323-40^53323	85999	Robert Price	07/2012
4228	2^285678-109617	85998	Enzo Doria	04/2014
4229	6^110506-16673	85991	Enzo Doria	02/2013
4231	2^285569-741	85965	Lelio R Paula	09/2013
4230	(32*10^85964+31)/9	85965	Robert Price	05/2015
4232	6*10^85910-7	85911	Dmitry Domanov	11/2010
4233	4*10^85881+63	85882	Robert Price	06/2016
4234	(10^85864+53)/9	85864	Robert Price	01/2015
4235	2^285230+345	85863	Lelio R Paula	09/2013
4236	2^285199+75683	85854	Enzo Doria	04/2016
4237	p(17832)#/2+512	85845	Robert Price	05/2017
4238	11^82426-1230	85838	Enzo Doria	11/2012
4239	2^285113-109881	85828	Enzo Doria	04/2014
4240	5^122746-92	85796	Lelio R Paula	10/2015
4241	2^285001-113461	85794	Enzo Doria	08/2014
4242	(11*10^85782-131)/3	85783	Robert Price	02/2017
4243	2^284913-110491	85768	Enzo Doria	05/2014
4244	6^110220+47	85768	Lelio R Paula	12/2015
4245	3*6^110202-5	85755	Lelio R Paula	10/2014
4246	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
4247	(3^179705+7)/250	85739	Lelio R Paula	12/2012
4248	2^284734-6555	85714	Lelio R Paula	09/2013
4249	(10^85712+53)/9	85712	Robert Price	01/2015
4250	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015

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PRP Records

Probable Primes Top 10000

(174961 PRPs in the top)