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	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
4002	33490^19859+19859^33490	143939	Hans Havermann	01/2021
4003	(853*10^143931-7)/9	143933	Robert Price	07/2021
4004	2^478088+27	143919	Robert Price	11/2015
4005	(8*10^143898-137)/3	143899	Robert Price	03/2022
4006	7*10^143857-93	143858	Robert Price	08/2020
4007	3*10^143844+61	143845	Robert Price	09/2020
4008	41358^3005+3005^41358	143837	Hans Havermann	01/2021
4009	2^477475-22071	143735	Enzo Doria	07/2013
4010	2^477417-22123	143717	Enzo Doria	07/2013
4011	2^477359-3577	143700	Yves Minet	03/2017
4012	39435^4402+4402^39435	143688	Hans Havermann	01/2021
4013	(14*10^143662-71)/3	143663	Robert Price	12/2018
4014	6^184614+5	143658	Paul Bourdelais	01/2021
4015	46371^1252+1252^46371	143640	Hans Havermann	12/2020
4016	34975^12748+12748^34975	143588	Hans Havermann	01/2021
4017	2^476936-396765	143573	Enzo Doria	07/2013
4018	2^476888-2791229	143558	Enzo Doria	01/2016
4019	2^476868-1859939	143552	Enzo Doria	11/2015
4020	40807^3294+3294^40807	143548	Hans Havermann	12/2020
4021	755^49878+49878^755	143547	Norbert Schneider	04/2019
4022	(19^112247-4^112247)/15	143536	Robert Price	03/2021
4023	35561^10872+10872^35561	143536	Hans Havermann	06/2021
4024	37637^6492+6492^37637	143487	Hans Havermann	05/2021
4025	61567^214+214^61567	143477	Hans Havermann	05/2021
4026	25933^32504-32504^25933	143468	Frank Doornink	03/2024
4027	2^476558-113627	143459	Enzo Doria	08/2014
4028	2^476478-45	143435	Lelio R Paula	11/2017
4029	36380^8757+8757^36380	143423	Hans Havermann	06/2021
4030	32510^25707+25707^32510	143371	Hans Havermann	05/2021
4031	8*10^143361+17	143362	Robert Price	07/2021
4032	(2^475854+9)/73	143245	Lelio R Paula	08/2015
4033	2^475813-113239	143234	Enzo Doria	07/2014
4034	(19*10^143212+137)/3	143213	Robert Price	03/2022
4035	32218^27849+27849^32218	143203	Hans Havermann	04/2021
4036	580*33^94296+19	143193	Eric Chen	12/2023
4037	2^475624-114059	143178	Enzo Doria	11/2014
4038	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
4039	2^475480-2786129	143134	Enzo Doria	10/2015
4040	33912^16621+16621^33912	143131	Hans Havermann	05/2021
4041	(19*10^143129-43)/3	143130	Robert Price	05/2019
4042	31830^31373+31373^31830	143126	Hans Havermann	05/2021
4043	6*10^143105-53	143106	Robert Price	05/2021
4044	(14*10^143097+73)/3	143098	Robert Price	12/2018
4045	2^475299-111937	143080	Enzo Doria	05/2014
4046	35488^10753+10753^35488	143071	Hans Havermann	04/2021
4047	29695^31986-31986^29695	143064	Frank Doornink	06/2024
4048	2^475160-2797859	143038	Enzo Doria	04/2016
4049	(2^475069+3)/395	143008	Lelio R Paula	08/2015
4050	2^475027-461437	142998	Enzo Doria	07/2015
4051	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
4052	(8*10^142932+43)/3	142933	Robert Price	06/2018
4053	35055^11942+11942^35055	142922	Hans Havermann	05/2021
4054	37650^6239+6239^37650	142887	Hans Havermann	05/2021
4055	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
4056	31205^31784-31784^31205	142845	Frank Doornink	01/2024
4057	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
4058	2^474417-59923	142814	Enzo Doria	10/2015
4059	4*10^142810-21	142811	Robert Price	09/2018
4060	32287^26494+26494^32287	142811	Hans Havermann	06/2021
4061	37162^6965+6965^37162	142811	Hans Havermann	06/2021
4062	(34*10^142805-601)/9	142806	Robert Price	07/2022
4063	37456^6493+6493^37456	142799	Hans Havermann	05/2021
4064	35141^11572+11572^35141	142793	Hans Havermann	05/2021
4065	32231^26908+26908^32231	142780	Hans Havermann	05/2021
4066	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
4067	2^474053+2897	142705	Lelio R Paula	08/2012
4068	(10^142699+359)/9	142699	Serge Batalov	12/2014
4069	26073^32312-32312^26073	142696	Frank Doornink	03/2024
4070	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
4071	2^473740-1856639	142610	Enzo Doria	09/2015
4072	(25*10^142573-403)/9	142574	Robert Price	12/2020
4073	2^473617-114223	142573	Enzo Doria	12/2014
4074	36115^8856+8856^36115	142555	Hans Havermann	05/2021
4075	fibonacci(682007)+4	142531	Jon Grantham	08/2023
4076	2^473257+1873217	142465	Enzo Doria	06/2016
4077	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
4078	32750^22371+22371^32750	142453	Hans Havermann	06/2021
4079	(61*10^142446-1)/3	142448	Robert Price	01/2020
4080	(14*10^142440+61)/3	142441	Robert Price	12/2018
4081	(10^142425+359)/9	142425	Serge Batalov	12/2014
4082	2^473101+773027	142418	Enzo Doria	05/2016
4083	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
4084	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
4085	36915^7162+7162^36915	142309	Hans Havermann	05/2021
4086	2^472634-109511	142278	Enzo Doria	04/2014
4087	31870^28997+28997^31870	142216	Hans Havermann	06/2021
4088	(48^84589+1)/49	142213	Robert Price	01/2014
4089	7*10^142189+87	142190	Robert Price	07/2019
4090	2^472258+7	142164	Lelio R Paula	08/2015
4091	40135^3484+3484^40135	142162	Hans Havermann	05/2021
4092	9*33^93598+26	142131	Eric Chen	12/2023
4093	(23*10^142105+91)/3	142106	Robert Price	08/2019
4094	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
4095	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
4096	(16*10^142058+197)/3	142059	Robert Price	04/2019
4097	9*10^142037+91	142038	Robert Price	10/2020
4098	(4*10^142034+17)/3	142035	Tyler Busby	01/2023
4099	2^471792+1880881	142024	Enzo Doria	11/2016
4100	(509*10^142018+31)/9	142020	Robert Price	08/2022
4101	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
4102	(4*10^141926-79)/3	141927	Robert Price	02/2018
4103	2^471464-111546435	141925	Paul Bourdelais	10/2021
4104	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
4105	(14*10^141853+37)/3	141854	Robert Price	12/2018
4106	(41*10^141836-59)/9	141837	Robert Price	10/2018
4107	4*5^202913-9	141831	Lelio R Paula	04/2015
4108	2*7^167812-3	141818	Lelio R Paula	12/2014
4109	2^471043+35	141799	Robert Price	11/2015
4110	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
4111	43636^1773+1773^43636	141761	Hans Havermann	05/2021
4112	(2*10^141751-17)/3	141751	Serge Batalov	11/2022
4113	(53*10^141722-611)/9	141723	Robert Price	02/2022
4114	(11*10^141718-131)/3	141719	Robert Price	09/2018
4115	(61*10^141716+47)/9	141717	Robert Price	07/2022
4116	26057^32088-32088^26057	141699	Frank Doornink	03/2024
4117	2^470692+76771	141693	Enzo Doria	05/2016
4118	50160^667+667^50160	141659	Hans Havermann	05/2021
4119	31522^31181+31181^31522	141657	Hans Havermann	05/2021
4120	29487^31690-31690^29487	141643	Frank Doornink	06/2024
4121	33076^19135+19135^33076	141626	Hans Havermann	04/2021
4122	28237^31818-31818^28237	141617	Frank Doornink	06/2024
4123	(91*10^141610+71)/9	141612	Robert Price	01/2022
4124	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
4125	(5*10^141594-23)/9	141594	Serge Batalov	11/2022
4126	31932^27155+27155^31932	141582	Hans Havermann	05/2021
4127	36449^7660+7660^36449	141577	Hans Havermann	05/2021
4128	2^470305-459373	141576	Enzo Doria	05/2015
4129	32195^24936+24936^32195	141556	Hans Havermann	05/2021
4130	2^470183+72623	141540	Enzo Doria	04/2016
4131	2^470173-16465	141537	Enzo Doria	04/2013
4132	37297^6234+6234^37297	141534	Hans Havermann	05/2021
4133	(509*10^141479+13)/9	141481	Robert Price	05/2022
4134	44*10^141476+9	141478	Robert Price	10/2020
4135	2^469974-1841	141477	Enzo Doria	05/2014
4136	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
4137	312*33^93158+23	141465	Eric Chen	12/2023
4138	2*10^141448+63	141449	Robert Price	05/2018
4139	2^469824+43	141432	Lelio R Paula	09/2017
4140	2*10^141407-27	141408	Robert Price	05/2018
4141	(214*10^141385-1)/3	141387	Robert Price	01/2021
4142	2^469630-59711	141373	Enzo Doria	10/2015
4143	35277^10172+10172^35277	141370	Hans Havermann	04/2021
4144	33397^17100+17100^33397	141370	Hans Havermann	04/2021
4145	(25*10^141366-331)/9	141367	Robert Price	08/2018
4146	36986^6639+6639^36986	141365	Hans Havermann	06/2021
4147	34572^12271+12271^34572	141361	Hans Havermann	06/2021
4148	37179^6338+6338^37179	141353	Hans Havermann	05/2021
4149	(2^469564-3)/611	141351	Lelio R Paula	08/2015
4150	197^61601+2	141342	Lelio R Paula	08/2017
4151	33420^16951+16951^33420	141340	Hans Havermann	05/2021
4152	31623^29458+29458^31623	141330	Hans Havermann	05/2021
4153	48112^865+865^48112	141306	Hans Havermann	05/2021
4154	2^469372-112949	141296	Enzo Doria	07/2014
4155	5*10^141294-63	141295	Robert Price	04/2021
4156	3^296115+4	141283	Tyler NeSmith	01/2021
4157	(64*10^141256+161)/9	141257	Robert Price	08/2022
4158	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
4159	143^65536+106^65536	141253	Serge Batalov	03/2018
4160	(11*10^141243-23)/3	141244	Robert Price	09/2021
4162	2^469198+782569	141243	Enzo Doria	10/2016
4161	38129^5062+5062^38129	141243	Hans Havermann	05/2021
4163	2^469076-2786939	141206	Enzo Doria	11/2015
4164	38630^4521+4521^38630	141202	Hans Havermann	05/2021
4165	31755^27836+27836^31755	141139	Hans Havermann	05/2021
4166	35554^9325+9325^35554	141137	Hans Havermann	05/2021
4167	2^468804+1874941	141125	Enzo Doria	06/2016
4168	2^468787+81353	141119	Enzo Doria	08/2016
4169	30204^31493-31493^30204	141091	Frank Doornink	06/2024
4170	2^468595-350407	141062	Enzo Doria	06/2015
4171	2^468564+87855	141052	Lelio R Paula	01/2016
4172	2^468551-21987	141048	Enzo Doria	07/2013
4173	2^468523-7	141040	Lelio R Paula	08/2015
4174	(25*10^141019-13)/3	141020	Robert Price	09/2019
4175	2^468405+87855	141004	Lelio R Paula	01/2016
4176	39338^3831+3831^39338	140961	Hans Havermann	05/2021
4177	31458^30239+30239^31458	140950	Hans Havermann	05/2021
4178	8*10^140932+29	140933	Robert Price	11/2021
4179	33166^17691+17691^33166	140881	Hans Havermann	06/2021
4180	2^467978-113051	140876	Enzo Doria	07/2014
4181	2^467780-344429	140816	Enzo Doria	07/2015
4182	9*10^140802-89	140803	Robert Price	04/2020
4183	2^467605-1855603	140764	Enzo Doria	09/2015
4184	(9^147503-5^147503)/4	140754	Jon Grantham	07/2023
4185	5*10^140744-7	140745	Robert Price	09/2015
4186	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
4187	2^467401-1850023	140702	Enzo Doria	08/2015
4188	(14*10^140693+13)/9	140694	Tyler Busby	02/2023
4189	(266*10^140681-17)/3	140683	Robert Price	07/2020
4190	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
4191	32138^23781+23781^32138	140644	Hans Havermann	05/2021
4192	31654^27735+27735^31654	140640	Hans Havermann	05/2021
4193	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
4194	2^467166-1854941	140631	Enzo Doria	09/2015
4195	(203*10^140615-11)/3	140617	Robert Price	12/2020
4196	(85*10^140609+473)/9	140610	Robert Price	01/2020
4197	39231^3836+3836^39231	140600	Hans Havermann	06/2021
4198	5*3^294676+2^294676	140597	Jon Grantham	08/2023
4199	2^466866-1840571	140541	Enzo Doria	06/2015
4200	2^466829-459523	140530	Enzo Doria	05/2015
4201	2^466692-113213	140489	Enzo Doria	07/2014
4202	23*10^140464-3	140466	Robert Price	10/2021
4203	(2*10^140461-17)/3	140461	Serge Batalov	11/2022
4204	29^96047-30	140459	Anonymous	09/2024
4205	31335^30364+30364^31335	140455	Hans Havermann	05/2021
4206	28511^31524-31524^28511	140440	Frank Doornink	06/2024
4207	32795^19126+19126^32795	140416	Hans Havermann	05/2021
4208	(44*10^140410-503)/9	140411	Robert Price	12/2018
4209	28332^31535-31535^28332	140403	Frank Doornink	06/2024
4210	153^64265-2	140400	Lelio R Paula	11/2017
4211	30323^31322-31322^30323	140379	Frank Doornink	06/2024
4212	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
4213	(29*10^140337-17)/3	140338	Robert Price	09/2019
4214	2^466181-112735	140335	Enzo Doria	07/2014
4215	(16*10^140290-37)/3	140291	Robert Price	05/2021
4216	(5*10^140281-119)/3	140282	Robert Price	03/2018
4217	34568^11415+11415^34568	140259	Hans Havermann	05/2021
4218	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
4219	33632^14781+14781^33632	140236	Hans Havermann	05/2021
4220	31803^25670+25670^31803	140233	Hans Havermann	05/2021
4221	2^465803-114817	140221	Enzo Doria	05/2015
4222	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
4223	2^465503-112735	140131	Enzo Doria	07/2014
4224	(16*10^140091+167)/3	140092	Robert Price	06/2019
4225	(8*10^140087-137)/3	140088	Robert Price	03/2022
4226	6^179964+179964^6-1	140040	Robert Price	04/2014
4227	(89*10^140008-179)/9	140009	Robert Price	12/2019
4228	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
4229	2^465072-344789	140001	Enzo Doria	07/2015
4230	34742^10683+10683^34742	139965	Hans Havermann	05/2021
4231	5*10^139945+81	139946	Robert Price	03/2019
4232	32648^19335+19335^32648	139941	Hans Havermann	05/2021
4233	2^464864-17	139939	Lelio R Paula	09/2017
4234	8*10^139920+51	139921	Robert Price	08/2019
4235	(85*10^139913-1)/3	139915	Robert Price	02/2020
4236	31203^30436+30436^31203	139896	Hans Havermann	04/2021
4237	2^464642+22189	139872	Enzo Doria	09/2023
4238	26138^31663-31663^26138	139865	Frank Doornink	03/2024
4239	(16^116139+619)/5	139845	Anonymous	08/2022
4240	(2^464556+619)/5	139845	Eric Chen	10/2023
4241	4*10^139839-27	139840	Robert Price	08/2021
4242	33582^14573+14573^33582	139821	Hans Havermann	05/2021
4243	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
4245	2*10^139800-21	139801	Robert Price	09/2020
4244	32628^19261+19261^32628	139801	Hans Havermann	04/2021
4246	(13*10^139782+191)/3	139783	Robert Price	11/2018
4247	(64*10^139776+791)/9	139777	Robert Price	01/2022
4248	(695*10^139772+7)/9	139774	Robert Price	12/2021
4249	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
4250	(74*10^139723+133)/9	139724	Robert Price	06/2019

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Probable Primes Top 10000

(300835 PRPs in the top)