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 ?
4001	2^331416-331416+1	99767	Robert Price	10/2014
4002	2^331256-57	99718	Lelio R Paula	12/2012
4003	28192^3443+3443^28192	99714	Hans Havermann	03/2018
4004	2^331185+737	99697	Lelio R Paula	01/2013
4005	(4*10^99693+149)/9	99693	Robert Price	03/2017
4006	2^331154+1880527	99688	Enzo Doria	10/2016
4008	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
4007	24354^12385+12385^24354	99679	Hans Havermann	03/2018
4009	2^331110+1870459	99675	Enzo Doria	05/2016
4010	5*2^331075+7	99665	Lelio R Paula	08/2014
4011	25776^7351+7351^25776	99659	Hans Havermann	02/2018
4012	(16*10^99656-31)/3	99657	Robert Price	03/2016
4013	2^330968+345	99632	Lelio R Paula	09/2016
4015	2*5^142528-7	99624	Lelio R Paula	11/2014
4014	2^330942+77329	99624	Enzo Doria	05/2016
4016	14^86914-99	99615	Lelio R Paula	08/2016
4017	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
4018	22971^21692+21692^22971	99610	Hans Havermann	03/2018
4019	2^330845+71687	99595	Enzo Doria	04/2016
4020	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
4021	24494^11613+11613^24494	99567	Hans Havermann	03/2018
4022	2^330735+8415	99562	Lelio R Paula	09/2016
4023	2^330720+74071	99557	Enzo Doria	04/2016
4024	31^66738-2	99531	Lelio R Paula	09/2013
4025	7*3^208567+4	99513	Lelio R Paula	08/2014
4026	(13*10^99508+47)/3	99509	Robert Price	01/2017
4027	2^330553+779	99507	Lelio R Paula	01/2013
4028	15^84606-94	99505	Lelio R Paula	08/2016
4029	6^127858+47	99493	Lelio R Paula	08/2016
4030	5^142337+48	99490	Lelio R Paula	08/2016
4031	7^117724-20	99489	Lelio R Paula	08/2016
4032	(29*10^99474-17)/3	99475	Erik Branger	09/2014
4033	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
4034	(68*10^99441+7)/3	99443	Robert Price	03/2016
4035	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
4036	23839^14802+14802^23839	99417	Hans Havermann	02/2018
4037	(2*10^99408+529)/9	99408	Robert Price	01/2017
4038	53^57646-2	99398	Lelio R Paula	09/2013
4039	2^330165+1870025	99390	Enzo Doria	05/2016
4040	2^330142-155	99383	Lelio R Paula	12/2012
4041	2^330088-115259	99367	Enzo Doria	06/2015
4043	24216^12671+12671^24216	99354	Hans Havermann	01/2018
4042	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
4044	(746*10^99303+1)/9	99305	Robert Price	02/2017
4045	3^208107+40	99293	Lelio R Paula	08/2016
4046	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
4047	8*3^208093+5	99287	Lelio R Paula	08/2014
4048	5^142043+56	99284	Lelio R Paula	08/2016
4049	22*10^99275+7	99277	Robert Price	04/2016
4050	2^329778+1876189	99274	Enzo Doria	07/2016
4051	(10^99239-13)/3	99239	Robert Price	02/2017
4052	3^207987+62	99236	Lelio R Paula	08/2016
4053	2^329638+49	99231	Lelio R Paula	12/2012
4054	7^117413-18	99226	Lelio R Paula	08/2016
4055	2^329586-458903	99216	Enzo Doria	04/2015
4056	2^329553+101	99206	Lelio R Paula	12/2012
4057	2^329551-112897	99205	Enzo Doria	06/2014
4058	(3^207925+7)/50	99204	Lelio R Paula	09/2013
4059	6^127458-17993	99182	Enzo Doria	03/2013
4060	27197^4428+4428^27197	99166	Hans Havermann	10/2017
4061	(46*10^99143-1)/9	99144	Robert Price	12/2014
4062	7*10^99133+69	99134	Robert Price	10/2017
4063	18^78968-3065	99127	Enzo Doria	03/2013
4064	25927^6654+6654^25927	99122	Hans Havermann	10/2017
4065	87915!4+16	99122	Robert Price	09/2019
4066	2^329259+189	99117	Lelio R Paula	12/2012
4067	8*10^99113+39	99114	Robert Price	01/2017
4068	6^127364+77	99109	Lelio R Paula	08/2016
4069	6^127285+13	99047	Lelio R Paula	08/2016
4070	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
4071	2^329007+73283	99041	Enzo Doria	04/2016
4072	5*3^207543-8	99024	Lelio R Paula	08/2014
4073	2^328885+149	99005	Lelio R Paula	12/2012
4074	23392^17075+17075^23392	99004	Hans Havermann	09/2017
4075	(2^328879-9)/119	99001	Lelio R Paula	10/2013
4076	5^141618+54	98987	Lelio R Paula	08/2016
4077	8*10^98982+51	98983	Robert Price	05/2017
4078	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
4079	2^328794-2797601	98977	Enzo Doria	04/2016
4080	6^127176+5	98963	Lelio R Paula	11/2014
4081	24262^11989+11989^24262	98960	Hans Havermann	09/2017
4082	2^328700-109709	98949	Enzo Doria	04/2014
4083	87771!4-128	98944	Robert Price	11/2019
4084	46711!2-2^46711	98916	Robert Price	09/2015
4085	9*7^117037+4	98909	Lelio R Paula	11/2014
4086	127^47012+126	98905	Norbert Schneider	01/2019
4087	(10^98890+149)/3	98890	Serge Batalov	12/2014
4088	22775^21978+21978^22775	98889	Hans Havermann	08/2017
4089	2^328497-216933	98888	Enzo Doria	05/2014
4090	2^328487+32769	98885	Lelio R Paula	08/2016
4091	3^207250-112358	98884	Enzo Doria	06/2014
4092	13^88754-90	98867	Lelio R Paula	08/2016
4093	2^328406+709	98861	Lelio R Paula	02/2013
4094	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
4095	7^116976+76	98857	Lelio R Paula	08/2016
4096	2^328335+1155	98839	Lelio R Paula	08/2016
4098	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
4097	287^40210+40210^287	98832	Norbert Schneider	11/2014
4099	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
4100	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
4101	65^54491+48	98788	Lelio R Paula	04/2016
4102	3^207042+98	98785	Lelio R Paula	08/2016
4103	3^206977-112756	98754	Enzo Doria	07/2014
4104	7^116846-50	98747	Lelio R Paula	08/2016
4105	2^327967-28635	98728	Lelio R Paula	08/2016
4106	707^34642+34642^707	98710	Norbert Schneider	12/2017
4107	6^126850-47	98709	Lelio R Paula	08/2016
4108	8*6^126830-7	98694	Lelio R Paula	11/2014
4109	11^94770-270	98693	Enzo Doria	08/2012
4110	2^327832+43	98688	Lelio R Paula	12/2012
4111	2^327795+761	98677	Lelio R Paula	02/2013
4112	10^98669+147411	98670	Patrick De Geest	11/2016
4114	10^98669-9^(98669-1)	98669	Robert Price	05/2016
4113	10^98669-105249	98669	Patrick De Geest	11/2016
4115	2^327671-109801	98639	Enzo Doria	04/2014
4116	24398^11037+11037^24398	98638	Hans Havermann	10/2019
4117	5^141090-14	98618	Lelio R Paula	08/2016
4118	20^75799+47	98617	Lelio R Paula	08/2016
4119	2^327515-1017	98592	Lelio R Paula	08/2016
4120	6^126692+97681	98586	Mike Oakes	04/2011
4121	2^327467-741	98578	Lelio R Paula	08/2016
4122	(2^327329+9)/19	98535	Lelio R Paula	10/2013
4123	7^116577-66	98519	Lelio R Paula	08/2016
4124	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
4125	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
4126	2^327162-66945	98486	Lelio R Paula	08/2016
4127	4*10^98472-3	98473	Erik Branger	11/2013
4128	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
4129	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
4130	13^88363+94	98432	Lelio R Paula	08/2016
4131	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
4132	6^126481+41	98422	Lelio R Paula	08/2016
4133	78*10^98413-7	98415	Robert Price	05/2017
4134	7^116416+46	98383	Lelio R Paula	08/2016
4135	7^116407-24	98376	Lelio R Paula	07/2016
4136	439^37228+37228^439	98374	Norbert Schneider	08/2018
4138	2^326782-1860671	98372	Enzo Doria	03/2016
4137	17^79948+58	98372	Lelio R Paula	08/2016
4139	3^206143-98	98356	Lelio R Paula	08/2016
4140	8*5^140705+7	98350	Lelio R Paula	11/2014
4141	2^326585+11	98312	Lelio R Paula	12/2012
4142	2^326582-459161	98311	Enzo Doria	05/2015
4143	(2^326548+9)/5	98301	Lelio R Paula	10/2013
4144	2^326538+71659	98298	Enzo Doria	04/2016
4145	15^83575-58	98292	Lelio R Paula	08/2016
4146	10^98288+3	98289	Robert Price	03/2011
4147	10^98288-117017	98288	Patrick De Geest	11/2011
4148	(44*10^98284-719)/9	98285	Robert Price	12/2017
4149	2^326421-2797573	98263	Enzo Doria	04/2016
4150	2^326401+16095	98257	Lelio R Paula	07/2016
4151	7^116240-116240^7	98235	Norbert Schneider	05/2017
4152	17^79826-78	98222	Lelio R Paula	08/2016
4153	2^326268-809	98217	Yves Minet	04/2011
4154	22659^21590+21590^22659	98210	Hans Havermann	10/2019
4155	(418*10^98199+23)/9	98201	Robert Price	08/2017
4156	12*10^98198-7	98200	Robert Price	11/2017
4157	15^83496-76	98199	Lelio R Paula	08/2016
4158	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
4159	9*5^140471-4	98186	Lelio R Paula	11/2014
4160	2^326069-2383	98157	Yves Minet	10/2013
4161	2^325973+1185	98128	Lelio R Paula	07/2016
4162	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
4163	2^325945-1847269	98120	Enzo Doria	07/2015
4164	8*10^98111-67	98112	Robert Price	10/2017
4165	2^325866+15	98096	Lelio R Paula	12/2012
4166	2^325765+1974305	98066	Enzo Doria	06/2016
4167	2^325733-58695	98056	Lelio R Paula	07/2016
4168	2^325717-3645	98051	Lelio R Paula	07/2016
4169	23968^12293+12293^23968	98021	Hans Havermann	11/2019
4170	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
4171	(7*10^98007-13)/3	98008	Robert Price	06/2016
4172	2^325512-459959	97989	Enzo Doria	05/2015
4173	(3^205354-8)/17	97978	Lelio R Paula	09/2013
4174	2^325433+76817	97966	Enzo Doria	05/2016
4175	5*10^97963+81	97964	Robert Price	08/2017
4176	2^325390-109061	97953	Enzo Doria	04/2014
4177	13^87921+24	97940	Lelio R Paula	08/2016
4178	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
4179	2^325215+12909	97900	Lelio R Paula	07/2016
4180	7*10^97874-69	97875	Robert Price	01/2017
4182	(17^79537+5^79537)/22	97865	Robert Price	06/2013
4181	15^83212+22	97865	Lelio R Paula	08/2016
4183	2^325087-109057	97861	Enzo Doria	04/2014
4184	2^325074+1870657	97858	Enzo Doria	05/2016
4186	2^325066-2111	97855	Yves Minet	08/2013
4185	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
4187	18^77944-89	97841	Lelio R Paula	07/2016
4188	119^47136+118	97833	Norbert Schneider	09/2018
4189	6^125720-17663	97830	Enzo Doria	02/2013
4190	2^324972-2069	97827	Yves Minet	05/2013
4191	2^324958-4691	97823	Yves Minet	05/2019
4192	2^324944-2788319	97818	Enzo Doria	03/2016
4193	22845^19112+19112^22845	97807	Hans Havermann	10/2019
4195	4*10^97799-9	97800	Erik Branger	11/2013
4194	2^324882+577294575	97800	Lelio R Paula	09/2016
4196	2^324863-1867921	97794	Enzo Doria	04/2016
4197	6^125662-18473	97785	Enzo Doria	03/2013
4198	12^90604+11	97779	Lelio R Paula	07/2016
4199	5^139830+24	97737	Lelio R Paula	04/2016
4200	2^324612+1155	97718	Lelio R Paula	07/2016
4201	19^76404-44	97702	Lelio R Paula	07/2016
4202	2^324505-2983	97686	Yves Minet	04/2011
4203	(144^45259+1)/145	97684	Paul Bourdelais	08/2019
4204	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
4205	6^125488-17843	97649	Enzo Doria	02/2013
4206	7^115515-2	97622	Lelio R Paula	09/2013
4207	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
4208	6^125418-5	97595	Lelio R Paula	11/2014
4209	2^324076+1155	97557	Lelio R Paula	07/2016
4210	(2^324074+9)/13	97555	Lelio R Paula	10/2013
4211	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
4212	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
4213	2^323946+73939	97518	Enzo Doria	04/2016
4214	2^323937+1866947	97515	Enzo Doria	03/2016
4215	6^125290-18533	97495	Enzo Doria	03/2013
4216	2^323845+101	97488	Lelio R Paula	12/2012
4217	18^77662+65	97487	Lelio R Paula	07/2016
4218	2^323772+76771	97466	Enzo Doria	05/2016
4219	2^323765-112213	97463	Enzo Doria	06/2014
4220	2^323720-6555	97450	Lelio R Paula	07/2016
4221	2^323694-1860401	97442	Enzo Doria	03/2016
4222	20^74886+3	97429	Lelio R Paula	06/2016
4224	3*10^97399+73	97400	Robert Price	04/2016
4223	7^115252-50	97400	Lelio R Paula	07/2016
4225	224737#+393581	97389	Nicolas PALAU	12/2016
4226	(26*10^97353+31)/3	97354	Robert Price	07/2016
4227	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
4228	(38*10^97329+187)/9	97330	Robert Price	11/2017
4229	86455!4+8	97319	Robert Price	09/2019
4230	p(19982)#/2-1024	97293	Robert Price	09/2017
4231	6^125021-85	97286	Lelio R Paula	08/2016
4232	2^323164-47355	97283	Lelio R Paula	07/2016
4233	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
4234	2^323054-6555	97249	Lelio R Paula	07/2016
4235	9*10^97247-29	97248	Robert Price	05/2017
4236	(31*10^97242+41)/9	97243	Robert Price	04/2015
4237	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
4238	12^90098-41	97233	Lelio R Paula	07/2016
4239	2^322928-216929	97212	Enzo Doria	05/2014
4240	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
4241	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
4242	2^322725+75761	97150	Enzo Doria	04/2016
4243	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
4244	(41*10^97085+373)/9	97086	Robert Price	04/2017
4245	2^322413+77	97056	Lelio R Paula	12/2012
4246	2^322406+177	97054	Lelio R Paula	12/2012
4247	(14*10^97044+31)/9	97045	Robert Price	02/2015
4248	2^322302+255255	97023	Lelio R Paula	07/2016
4249	2^322196-113093	96991	Enzo Doria	07/2014
4250	2^322000-1861469	96932	Enzo Doria	03/2016

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Probable Primes Top 10000

(255244 PRPs in the top)