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	2^293416-1037	88328	Yves Minet	11/2012
4002	(2^293384-7)/3	88317	Lelio R Paula	01/2013
4003	(3^185092-5)/4	88311	Lelio R Paula	01/2013
4004	14^77039-57	88297	Lelio R Paula	11/2015
4005	5^126303+42	88283	Lelio R Paula	10/2015
4006	19^69025-18	88266	Theodore Burton	01/2006
4007	5*10^88261-3	88262	Dmitry Domanov	11/2010
4008	8^97731-7^(97731-1)	88260	Robert Price	04/2016
4009	5*10^88254+59	88255	Robert Price	09/2016
4010	4*3^184968-7	88253	Lelio R Paula	08/2014
4011	7^104426+88	88251	Lelio R Paula	10/2015
4012	2^293142+99	88245	Lelio R Paula	10/2012
4013	11^84736-2130	88244	Enzo Doria	12/2012
4014	2^293068-89	88223	Lelio R Paula	10/2012
4015	2^293014-109655	88207	Enzo Doria	04/2014
4016	8*7^104371-3	88205	Lelio R Paula	10/2014
4017	2^292995-2145	88201	Lelio R Paula	10/2013
4018	5*10^88182+77	88183	Robert Price	06/2016
4019	2^292929+43877	88181	Donovan Johnson	04/2005
4020	6^113321+131	88181	Lelio R Paula	12/2015
4021	2^292904-583949	88173	Paul Bourdelais	04/2013
4022	2^292894-111851	88170	Enzo Doria	05/2014
4023	2^292872-2797349	88164	Enzo Doria	03/2016
4024	2^292860-109685	88160	Enzo Doria	04/2014
4025	9*6^113288-5	88157	Lelio R Paula	10/2014
4026	(73*10^88105+17)/9	88106	Robert Price	10/2015
4027	11^84588+78	88090	Lelio R Paula	11/2015
4028	(265*10^88077+11)/3	88079	Robert Price	03/2017
4029	91^44959-90^44959	88077	Robert Price	07/2015
4030	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
4031	(10^88020+101)/3	88020	Robert Price	04/2016
4032	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
4033	p(18225)#/2+128	87929	Robert Price	04/2017
4034	4*6^112977+7	87914	Lelio R Paula	10/2014
4035	14^76677+69	87882	Lelio R Paula	11/2015
4036	(22*10^87863-1)/3	87864	Robert Price	12/2014
4037	2^291822-2797811	87848	Enzo Doria	04/2016
4038	2^291716-111389	87816	Enzo Doria	05/2014
4039	3^184039+1820	87809	Lelio R Paula	12/2015
4040	12^81356+41	87798	Lelio R Paula	11/2015
4041	6^112792-18983	87770	Enzo Doria	03/2013
4042	3*6^112787-5	87766	Lelio R Paula	10/2014
4043	7^103848+82	87762	Lelio R Paula	10/2015
4044	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
4045	(3^183915+5)/128	87748	Lelio R Paula	01/2013
4046	19^68619+24	87747	Lelio R Paula	12/2015
4048	2^291480+1185	87745	Lelio R Paula	10/2013
4047	2^291482+1867369	87745	Enzo Doria	03/2016
4049	2^291467-937	87741	Yves Minet	05/2013
4050	(25*10^87726+161)/3	87727	Robert Price	01/2017
4051	11^84239-2850	87726	Enzo Doria	12/2012
4052	10^87720+215541	87721	Patrick De Geest	01/2011
4053	10^87720-3	87720	Markus Tervooren	07/2010
4054	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
4055	93^44541-2	87679	Lelio R Paula	09/2013
4056	2^291261-109561	87679	Enzo Doria	04/2014
4057	(4*10^87669+149)/9	87669	Robert Price	03/2017
4058	2^291217+4257	87666	Lelio R Paula	10/2013
4059	2*12^81214-5^81214	87645	Mike Oakes	12/2010
4060	12^81188+85	87617	Lelio R Paula	11/2015
4061	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
4062	2^290958+127	87588	Lelio R Paula	09/2012
4063	2^290923-67	87577	Lelio R Paula	09/2012
4064	(13*10^87565+11)/3	87566	Robert Price	05/2015
4065	(2^290857-7)/55	87555	Lelio R Paula	01/2013
4066	2^290802+82875	87541	Lelio R Paula	10/2013
4067	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
4068	3^183441+236	87524	Lelio R Paula	12/2015
4069	2^290618-33	87485	Lelio R Paula	09/2012
4070	(184*10^87473-1)/3	87475	Robert Price	02/2017
4071	2^290534-115151	87460	Enzo Doria	06/2015
4072	2^290512-109757	87453	Enzo Doria	04/2014
4073	(32*10^87448-41)/9	87449	Robert Price	05/2015
4074	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
4075	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
4076	2^290426+82875	87427	Lelio R Paula	11/2013
4077	3*2^290415-7	87425	Lelio R Paula	08/2014
4079	10^87408+57	87409	Robert Price	03/2011
4078	2^290366+74779	87409	Enzo Doria	04/2016
4080	10^87408-123569	87408	Patrick De Geest	07/2013
4081	2^290265+58905	87379	Lelio R Paula	10/2013
4082	7^103391+16	87376	Lelio R Paula	10/2015
4083	8*7^103379+3	87367	Lelio R Paula	10/2014
4084	(2^290226+7)/71	87365	Lelio R Paula	01/2013
4085	13^78407-30	87341	Lelio R Paula	11/2015
4086	4*10^87337-99	87338	Robert Price	12/2016
4087	7*10^87319+39	87320	Robert Price	07/2016
4088	3*5^124921+2	87317	Lelio R Paula	10/2014
4089	3^182984+88	87306	Lelio R Paula	12/2015
4090	4*10^87287-99	87288	Robert Price	12/2016
4091	11^83813-1860	87283	Enzo Doria	12/2012
4092	734^30453+30453^734	87270	Norbert Schneider	04/2017
4093	12^80855+29	87258	Lelio R Paula	11/2015
4094	3*6^112119-5	87247	Lelio R Paula	10/2014
4095	12^80806+79	87205	Lelio R Paula	11/2015
4096	91382^9+9^91382	87201	Andrey Kulsha	11/2004
4097	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
4098	6^112054-47	87195	Lelio R Paula	12/2015
4099	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
4100	15^74131-68	87185	Lelio R Paula	11/2015
4101	2^289583-741	87174	Lelio R Paula	10/2013
4102	7^103146+12	87169	Lelio R Paula	10/2015
4103	5*2^289556-3	87166	Lelio R Paula	08/2014
4104	2^289543-112735	87162	Enzo Doria	06/2014
4105	8*3^182655-7	87150	Lelio R Paula	08/2014
4106	2*10^87144+81	87145	Robert Price	01/2017
4107	7^103106+2*3^103106	87135	Mike Oakes	08/2010
4108	8*3^182614+7	87130	Lelio R Paula	08/2014
4109	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
4110	3^182566+14	87107	Robert Price	09/2013
4111	(3^182385-5)/2	87020	Lelio R Paula	01/2013
4112	11^83534-8	86992	Lelio R Paula	11/2015
4113	4^144479-14267	86986	Mike Oakes	03/2011
4114	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
4115	(151*10^86963-1)/3	86965	Robert Price	04/2017
4116	15^73940-58	86961	Lelio R Paula	11/2015
4117	2^288761-113143	86926	Enzo Doria	07/2014
4118	2^288747+3083	86922	Yves Minet	03/2011
4119	30^58842+29	86917	Norbert Schneider	03/2017
4120	(10^86906-13)/3	86906	Robert Price	02/2017
4121	2^288692-110027	86905	Enzo Doria	04/2014
4122	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
4123	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
4124	3^182089-34	86879	Robert Price	11/2013
4125	2^288543-109801	86861	Enzo Doria	04/2014
4126	60^48847-59	86858	Norbert Schneider	10/2014
4127	2^288470-64875	86839	Lelio R Paula	10/2013
4128	10^86816+32997	86817	Patrick De Geest	07/2013
4129	10^86816-99	86816	Robert Price	05/2011
4130	41487!2+256	86786	Robert Price	01/2015
4131	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
4132	2^288243+76043	86770	Enzo Doria	04/2016
4133	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
4134	9*6^111495+5	86761	Lelio R Paula	10/2014
4135	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
4136	9*7^102654-2	86754	Lelio R Paula	10/2014
4137	2^288122-112841	86734	Enzo Doria	06/2014
4138	5^124062-68	86716	Lelio R Paula	10/2015
4139	(2^288007-3)/125	86697	Lelio R Paula	01/2013
4140	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
4141	7^102555+48	86670	Lelio R Paula	10/2015
4142	2^287809-111355	86640	Enzo Doria	05/2014
4143	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
4144	9*7^102504+8	86627	Lelio R Paula	10/2014
4145	3^181551+32	86622	Robert Price	11/2013
4146	2^287735-521347	86617	Paul Bourdelais	05/2013
4147	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
4148	2^287540-112967	86559	Enzo Doria	06/2014
4149	3^181407+20	86554	Robert Price	10/2013
4150	(13*10^86546+83)/3	86547	Robert Price	09/2016
4151	3^181378-2^(181378-1)	86540	Robert Price	01/2016
4152	83^45080-2	86513	Lelio R Paula	08/2013
4153	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
4154	25*29^59147+20936	86498	Curtis Bright	05/2015
4155	2^287298+1871359	86486	Enzo Doria	05/2016
4156	3*10^86478+89	86479	Robert Price	03/2017
4157	2^287272-79049	86478	Paul Bourdelais	02/2012
4158	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4159	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4160	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4161	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4162	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4163	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4164	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4165	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4166	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4167	(10^86453-1)/9	86453	Lew Baxter	10/2000
4168	87^44563-86^44563	86431	Robert Price	05/2015
4169	6^111057+61	86420	Lelio R Paula	12/2015
4170	2^287057-109909	86413	Enzo Doria	04/2014
4171	5^123608+22	86399	Lelio R Paula	10/2015
4172	(31*10^86364-121)/9	86365	Robert Price	06/2016
4173	2^286859+71663	86354	Enzo Doria	04/2016
4174	2^286740+29835	86318	Lelio R Paula	10/2013
4175	2*10^86310+9^86310	86311	Mike Oakes	05/2011
4176	11^82878-1860	86309	Enzo Doria	12/2012
4177	2^286547+16095	86260	Lelio R Paula	10/2013
4178	2^286455-110427	86232	Enzo Doria	05/2014
4179	(37*10^86230+53)/9	86231	Robert Price	05/2015
4180	8*3^180700+5	86217	Lelio R Paula	08/2014
4181	3^180697-40	86215	Lelio R Paula	12/2015
4182	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
4183	2^286165+77	86145	Lelio R Paula	08/2012
4184	9*2^286140+7	86138	Lelio R Paula	08/2014
4185	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
4186	10^86110+161113	86111	Patrick De Geest	07/2013
4187	10^86110-69	86110	Robert Price	05/2011
4188	2^286036-869688105	86106	Lelio R Paula	07/2016
4189	(77*10^86072+31)/9	86073	Robert Price	10/2015
4190	2^285923+345	86072	Lelio R Paula	09/2013
4191	13^77266-90	86070	Lelio R Paula	11/2015
4192	2^285910-458903	86068	Enzo Doria	04/2015
4193	2^285904-125	86066	Lelio R Paula	08/2012
4194	2^285836+65835	86046	Lelio R Paula	09/2013
4195	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
4196	(5*10^86011-107)/3	86012	Robert Price	01/2017
4197	6^110522+163	86003	Lelio R Paula	12/2015
4198	41^53323-40^53323	85999	Robert Price	07/2012
4199	2^285678-109617	85998	Enzo Doria	04/2014
4200	6^110506-16673	85991	Enzo Doria	02/2013
4202	2^285569-741	85965	Lelio R Paula	09/2013
4201	(32*10^85964+31)/9	85965	Robert Price	05/2015
4203	6*10^85910-7	85911	Dmitry Domanov	11/2010
4204	4*10^85881+63	85882	Robert Price	06/2016
4205	(10^85864+53)/9	85864	Robert Price	01/2015
4206	2^285230+345	85863	Lelio R Paula	09/2013
4207	2^285199+75683	85854	Enzo Doria	04/2016
4208	p(17832)#/2+512	85845	Robert Price	05/2017
4209	11^82426-1230	85838	Enzo Doria	11/2012
4210	2^285113-109881	85828	Enzo Doria	04/2014
4211	5^122746-92	85796	Lelio R Paula	10/2015
4212	2^285001-113461	85794	Enzo Doria	08/2014
4213	(11*10^85782-131)/3	85783	Robert Price	02/2017
4214	2^284913-110491	85768	Enzo Doria	05/2014
4215	6^110220+47	85768	Lelio R Paula	12/2015
4216	3*6^110202-5	85755	Lelio R Paula	10/2014
4217	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
4218	(3^179705+7)/250	85739	Lelio R Paula	12/2012
4219	2^284734-6555	85714	Lelio R Paula	09/2013
4220	(10^85712+53)/9	85712	Robert Price	01/2015
4221	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
4222	20^65855+83	85680	Lelio R Paula	01/2016
4223	6^110105+53	85679	Lelio R Paula	12/2015
4225	2^284567-7605	85664	Lelio R Paula	09/2013
4224	9*5^122555-2	85664	Lelio R Paula	10/2014
4226	5^122554-14	85662	Lelio R Paula	10/2015
4227	9*5^122543+4	85655	Lelio R Paula	10/2014
4228	3^179489-2^(179489-1)	85639	Robert Price	01/2016
4229	2^284429+177	85622	Lelio R Paula	08/2012
4230	2*3^179452+5	85621	Lelio R Paula	07/2014
4231	(19^66919+3^66919)/22	85572	Robert Price	07/2013
4232	66^47023-65	85561	Norbert Schneider	11/2014
4233	6^109943+13	85553	Lelio R Paula	12/2015
4234	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
4235	2^284133-3	85533	M. Frind & P. Underwood	07/2002
4236	2^284113+315	85527	Lelio R Paula	09/2013
4237	(16*10^85495-19)/3	85496	Robert Price	03/2016
4238	2^284004+177	85494	Lelio R Paula	08/2012
4239	(16*10^85473-91)/3	85474	Robert Price	06/2016
4240	3^179120+22	85462	Robert Price	12/2013
4241	2^283872-2792249	85454	Enzo Doria	03/2016
4242	(29*10^85438+259)/9	85439	Robert Price	04/2017
4243	2^283817+82875	85438	Lelio R Paula	09/2013
4244	(2^283815-5)/201	85435	Lelio R Paula	01/2013
4245	2^283796-125	85432	Lelio R Paula	08/2012
4246	(29*2^283784-1)/13	85428	Lelio R Paula	02/2014
4247	15^72592-28	85375	Lelio R Paula	11/2015
4248	2^283604-58695	85374	Lelio R Paula	09/2013
4249	(15*2^283583-1)/103051	85364	Lelio R Paula	02/2014
4250	15^72572+92	85352	Lelio R Paula	11/2015

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PRP Records

Probable Primes Top 10000

(173006 PRPs in the top)