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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See the Latest PRPs
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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 ?
4001	6^128661+97	100118	Lelio R Paula	10/2016
4002	19^78285+40	100108	Lelio R Paula	07/2016
4003	6^128640+5	100102	Lelio R Paula	11/2014
4004	(14*10^100075+61)/3	100076	Robert Price	12/2018
4005	28562^3189+3189^28562	100072	Hans Havermann	05/2018
4006	6^128565-127	100044	Lelio R Paula	08/2016
4007	2^332309-133	100035	Lelio R Paula	02/2011
4008	2^332307+731	100035	Lelio R Paula	07/2011
4009	2^332301+12927	100033	Lelio R Paula	04/2013
4010	23406^18781+18781^23406	100031	Hans Havermann	04/2018
4011	2^332277-4573	100026	Yves Minet	03/2019
4012	12^92684-13	100023	Lelio R Paula	07/2016
4013	78557*2^332193+55669	100005	Jorge Menendez	04/2019
4014	78557*2^332192+72689	100005	Jorge Menendez	04/2019
4015	10^100003+45799	100004	Stefano Morozzi	04/2019
4016	10^100003+155461	100004	Stefano Morozzi	04/2019
4017	10^100003+211389	100004	Stefano Morozzi	04/2019
4018	10^100003+381027	100004	Stefano Morozzi	04/2019
4019	10^100003+540703	100004	Stefano Morozzi	04/2019
4020	10^100003+823977	100004	Stefano Morozzi	04/2019
4032	10^100002+236023	100003	Stefano Morozzi	05/2018
4033	10^100002+433741	100003	Stefano Morozzi	05/2018
4021	2^332202+104659	100003	Stefano Morozzi	04/2019
4022	2^332202+857539	100003	Stefano Morozzi	04/2019
4023	2^332202+181773	100003	Stefano Morozzi	04/2019
4024	2^332202+687543	100003	Stefano Morozzi	04/2019
4025	2^332202+941595	100003	Stefano Morozzi	04/2019
4026	2^332202+445813	100003	Stefano Morozzi	04/2019
4027	2^332202+1599727	100003	Stefano Morozzi	04/2019
4028	2^332202+1389567	100003	Stefano Morozzi	04/2019
4029	2^332202+1206315	100003	Stefano Morozzi	04/2019
4030	2^332202+1958647	100003	Stefano Morozzi	04/2019
4031	10^100003-562857	100003	Patrick De Geest	07/2019
4034	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
4035	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
4036	10^100002-249519	100002	Patrick De Geest	07/2018
4037	10^100001+314199	100002	Patrick De Geest	07/2018
4106	25206!+p(4114)	100001	Henri Lifchitz	09/2005
4107	25206!-p(5447)	100001	Henri Lifchitz	10/2005
4108	25206!-p(12402)	100001	Henri Lifchitz	04/2006
4109	25206!-p(16290)	100001	Henri Lifchitz	09/2006
4110	25206!-p(19647)	100001	Henri Lifchitz	02/2007
4111	2^332194+11473	100001	Henri Lifchitz	03/2007
4101	10^100000+342909	100001	Milton L. Brown	12/2007
4102	10^100000+346579	100001	Robert Price	04/2012
4103	10^100000+829767	100001	Robert Price	05/2012
4104	10^100000+871899	100001	Robert Price	05/2012
4105	10^100000+1475997	100001	Robert Price	07/2012
4094	10^100000+1751769	100001	Robert Price	08/2012
4095	10^100000+2155489	100001	Robert Price	10/2012
4096	10^100000+2483527	100001	Robert Price	12/2012
4097	10^100000+2503087	100001	Robert Price	12/2012
4098	10^100000+2686179	100001	Robert Price	12/2012
4099	10^100000+2688933	100001	Robert Price	12/2012
4100	10^100000+3667159	100001	Robert Price	08/2013
4078	10^100000+3938473	100001	Robert Price	05/2015
4079	10^100000+3979761	100001	Robert Price	05/2015
4080	10^100000+4293973	100001	Robert Price	09/2015
4067	10^100000+4858267	100001	Robert Price	12/2015
4068	10^100000+5113299	100001	Robert Price	02/2016
4069	10^100000+5169411	100001	Robert Price	02/2016
4070	10^100000+5354043	100001	Robert Price	05/2016
4071	10^100000+5717979	100001	Robert Price	05/2016
4072	10^100000+6080631	100001	Robert Price	07/2016
4073	10^100000+6308469	100001	Robert Price	07/2016
4074	10^100000+6512023	100001	Robert Price	08/2016
4075	10^100000+6596557	100001	Robert Price	08/2016
4076	10^100000+7115409	100001	Robert Price	10/2016
4077	10^100000+7235803	100001	Robert Price	10/2016
4081	10^100000+7867333	100001	Robert Price	12/2016
4082	10^100000+8743093	100001	Robert Price	02/2017
4083	10^100000+8955391	100001	Robert Price	03/2017
4084	10^100000+9180019	100001	Robert Price	03/2017
4085	10^100000+9225987	100001	Robert Price	04/2017
4086	10^100000+9265587	100001	Robert Price	04/2017
4087	10^100000+9287049	100001	Robert Price	04/2017
4088	10^100000+9425053	100001	Robert Price	05/2017
4089	10^100000+9450769	100001	Robert Price	05/2017
4090	10^100000+9528747	100001	Robert Smith	05/2017
4091	10^100000+9548071	100001	Robert Price	06/2017
4092	10^100000+10064287	100001	Robert Price	08/2017
4093	10^100000+10229569	100001	Robert Price	10/2017
4038	10^100000+11187931	100001	Robert Price	03/2018
4039	10^100000+11264721	100001	Robert Price	04/2018
4040	10^100000+11477661	100001	Robert Price	05/2018
4041	10^100000+11644653	100001	Robert Price	07/2018
4042	10^100001-431439	100001	Patrick De Geest	07/2018
4043	10^100000+11769399	100001	Robert Price	08/2018
4044	10^100000+11848159	100001	Robert Price	08/2018
4045	10^100000+11863467	100001	Robert Price	08/2018
4064	10^100000+11992051	100001	Robert Price	09/2018
4065	2^332196-1-2*29696	100001	Matt Stath	11/2018
4066	10^100000+12363957	100001	Robert Price	11/2018
4046	2^332196+1+2*17152	100001	Matt Stath	12/2018
4047	10^100000+12778033	100001	Robert Price	02/2019
4048	10^100000+13581679	100001	Robert Price	05/2019
4049	10^100000+13613199	100001	Robert Price	05/2019
4050	10^100000+13752327	100001	Robert Price	05/2019
4051	10^100000+14139243	100001	Robert Price	06/2019
4052	10^100000+14151057	100001	Robert Price	06/2019
4053	10^100000+14218923	100001	Robert Price	06/2019
4054	10^100000+15136771	100001	Robert Price	09/2019
4055	10^100000+15219873	100001	Robert Price	10/2019
4056	10^100000+15274039	100001	Robert Price	10/2019
4057	10^100000+15394069	100001	Robert Price	10/2019
4058	10^100000+15547119	100001	Robert Price	10/2019
4059	10^100000+15932923	100001	Robert Price	11/2019
4060	10^100000+16345467	100001	Robert Price	12/2019
4061	10^100000+16672143	100001	Robert Price	01/2020
4062	10^100000+16731939	100001	Robert Price	02/2020
4063	10^100000+16907049	100001	Robert Price	03/2020
4112	10^99999+309403	100000	Daniel Heuer	01/2004
4113	10^100000-260199	100000	Patrick De Geest	01/2010
4114	10^99999-59511	99999	Patrick De Geest	07/2009
4115	10^99998+235437	99999	Patrick De Geest	02/2020
4116	10^99998-286587	99998	Patrick De Geest	02/2020
4117	10^99997+72297	99998	Patrick De Geest	02/2020
4118	10^99997-402627	99997	Patrick De Geest	02/2020
4119	10^99996+279853	99997	Patrick De Geest	02/2020
4120	10^99996-94961	99996	Patrick De Geest	02/2020
4121	10^99995+54633	99996	Patrick De Geest	02/2020
4122	10^99995-101429	99995	Patrick De Geest	02/2020
4123	10^99994+117271	99995	Patrick De Geest	02/2020
4124	10^99994-452289	99994	Patrick De Geest	02/2020
4125	10^99993+371311	99994	Patrick De Geest	02/2020
4126	10^99993-186491	99993	Patrick De Geest	02/2020
4127	10^99992+17431	99993	Patrick De Geest	02/2020
4128	10^99992-28607	99992	Patrick De Geest	02/2020
4129	10^99991+125391	99992	Patrick De Geest	02/2020
4130	10^99991-204573	99991	Patrick De Geest	02/2020
4131	10^99990+13899	99991	Patrick De Geest	02/2020
4132	10^99990-8111	99990	Patrick De Geest	02/2020
4133	2^332141-113073	99985	Enzo Doria	07/2014
4135	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
4134	23827^15702+15702^23827	99978	Hans Havermann	04/2018
4136	2^332085+1865897	99968	Enzo Doria	03/2016
4137	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
4138	2^332023+191	99949	Lelio R Paula	02/2011
4139	2^331938+71149	99924	Enzo Doria	04/2016
4140	2^331932-78795	99922	Lelio R Paula	09/2016
4141	2^331921+771	99919	Lelio R Paula	01/2013
4142	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
4143	2^331860-114989	99900	Enzo Doria	05/2015
4144	2^331746-11655	99866	Lelio R Paula	09/2016
4145	11^95891-28	99861	Lelio R Paula	08/2016
4146	(2^331694-5)/11	99849	Lelio R Paula	10/2013
4147	(3^209246+7)/64	99834	Lelio R Paula	09/2013
4148	25062^9617+9617^25062	99823	Hans Havermann	04/2018
4149	15^84866-52	99811	Lelio R Paula	08/2016
4150	13^89600+30	99810	Lelio R Paula	08/2016
4151	22950^22309+22309^22950	99798	Hans Havermann	03/2018
4152	5^142772-38	99794	Lelio R Paula	08/2016
4153	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
4154	2^331416-331416+1	99767	Robert Price	10/2014
4155	2^331256-57	99718	Lelio R Paula	12/2012
4156	28192^3443+3443^28192	99714	Hans Havermann	03/2018
4157	2^331185+737	99697	Lelio R Paula	01/2013
4158	(4*10^99693+149)/9	99693	Robert Price	03/2017
4159	2^331154+1880527	99688	Enzo Doria	10/2016
4161	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
4160	24354^12385+12385^24354	99679	Hans Havermann	03/2018
4162	2^331110+1870459	99675	Enzo Doria	05/2016
4163	5*2^331075+7	99665	Lelio R Paula	08/2014
4164	25776^7351+7351^25776	99659	Hans Havermann	02/2018
4165	(16*10^99656-31)/3	99657	Robert Price	03/2016
4166	2^330968+345	99632	Lelio R Paula	09/2016
4168	2*5^142528-7	99624	Lelio R Paula	11/2014
4167	2^330942+77329	99624	Enzo Doria	05/2016
4169	14^86914-99	99615	Lelio R Paula	08/2016
4170	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
4171	22971^21692+21692^22971	99610	Hans Havermann	03/2018
4172	2^330845+71687	99595	Enzo Doria	04/2016
4173	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
4174	24494^11613+11613^24494	99567	Hans Havermann	03/2018
4175	2^330735+8415	99562	Lelio R Paula	09/2016
4176	2^330720+74071	99557	Enzo Doria	04/2016
4177	31^66738-2	99531	Lelio R Paula	09/2013
4178	7*3^208567+4	99513	Lelio R Paula	08/2014
4179	(13*10^99508+47)/3	99509	Robert Price	01/2017
4180	2^330553+779	99507	Lelio R Paula	01/2013
4181	15^84606-94	99505	Lelio R Paula	08/2016
4182	6^127858+47	99493	Lelio R Paula	08/2016
4183	5^142337+48	99490	Lelio R Paula	08/2016
4184	7^117724-20	99489	Lelio R Paula	08/2016
4185	(29*10^99474-17)/3	99475	Erik Branger	09/2014
4186	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
4187	(68*10^99441+7)/3	99443	Robert Price	03/2016
4188	10^99434-123456789	99434	Robert Price	02/2020
4189	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
4190	23839^14802+14802^23839	99417	Hans Havermann	02/2018
4191	(2*10^99408+529)/9	99408	Robert Price	01/2017
4192	53^57646-2	99398	Lelio R Paula	09/2013
4193	2^330165+1870025	99390	Enzo Doria	05/2016
4194	2^330142-155	99383	Lelio R Paula	12/2012
4195	2^330088-115259	99367	Enzo Doria	06/2015
4196	24216^12671+12671^24216	99354	Hans Havermann	01/2018
4197	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
4198	(746*10^99303+1)/9	99305	Robert Price	02/2017
4199	3^208107+40	99293	Lelio R Paula	08/2016
4200	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
4201	8*3^208093+5	99287	Lelio R Paula	08/2014
4202	5^142043+56	99284	Lelio R Paula	08/2016
4203	22*10^99275+7	99277	Robert Price	04/2016
4204	2^329778+1876189	99274	Enzo Doria	07/2016
4205	(10^99239-13)/3	99239	Robert Price	02/2017
4206	3^207987+62	99236	Lelio R Paula	08/2016
4207	2^329638+49	99231	Lelio R Paula	12/2012
4208	7^117413-18	99226	Lelio R Paula	08/2016
4209	2^329586-458903	99216	Enzo Doria	04/2015
4210	2^329553+101	99206	Lelio R Paula	12/2012
4211	2^329551-112897	99205	Enzo Doria	06/2014
4212	(3^207925+7)/50	99204	Lelio R Paula	09/2013
4213	6^127458-17993	99182	Enzo Doria	03/2013
4214	27197^4428+4428^27197	99166	Hans Havermann	10/2017
4215	(46*10^99143-1)/9	99144	Robert Price	12/2014
4216	7*10^99133+69	99134	Robert Price	10/2017
4217	18^78968-3065	99127	Enzo Doria	03/2013
4218	25927^6654+6654^25927	99122	Hans Havermann	10/2017
4219	87915!4+16	99122	Robert Price	09/2019
4220	2^329259+189	99117	Lelio R Paula	12/2012
4221	8*10^99113+39	99114	Robert Price	01/2017
4222	6^127364+77	99109	Lelio R Paula	08/2016
4223	6^127285+13	99047	Lelio R Paula	08/2016
4224	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
4225	2^329007+73283	99041	Enzo Doria	04/2016
4226	5*3^207543-8	99024	Lelio R Paula	08/2014
4227	2^328885+149	99005	Lelio R Paula	12/2012
4228	23392^17075+17075^23392	99004	Hans Havermann	09/2017
4229	(2^328879-9)/119	99001	Lelio R Paula	10/2013
4230	5^141618+54	98987	Lelio R Paula	08/2016
4231	8*10^98982+51	98983	Robert Price	05/2017
4232	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
4233	2^328794-2797601	98977	Enzo Doria	04/2016
4234	6^127176+5	98963	Lelio R Paula	11/2014
4235	24262^11989+11989^24262	98960	Hans Havermann	09/2017
4236	2^328700-109709	98949	Enzo Doria	04/2014
4237	87771!4-128	98944	Robert Price	11/2019
4238	46711!2-2^46711	98916	Robert Price	09/2015
4239	9*7^117037+4	98909	Lelio R Paula	11/2014
4240	127^47012+126	98905	Norbert Schneider	01/2019
4241	(10^98890+149)/3	98890	Serge Batalov	12/2014
4242	22775^21978+21978^22775	98889	Hans Havermann	08/2017
4243	2^328497-216933	98888	Enzo Doria	05/2014
4244	2^328487+32769	98885	Lelio R Paula	08/2016
4245	3^207250-112358	98884	Enzo Doria	06/2014
4246	13^88754-90	98867	Lelio R Paula	08/2016
4247	2^328406+709	98861	Lelio R Paula	02/2013
4248	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
4249	7^116976+76	98857	Lelio R Paula	08/2016
4250	2^328335+1155	98839	Lelio R Paula	08/2016

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PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)