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	2^354385-115315	106681	Enzo Doria	06/2015
4002	2^354327-19305	106664	Enzo Doria	06/2013
4003	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
4004	10^106636+97	106637	Lelio R Paula	02/2017
4005	10^106636-22923	106636	Patrick De Geest	03/2017
4006	2^354220-57	106631	Lelio R Paula	10/2011
4007	(29*10^106620-77)/3	106621	Robert Price	02/2020
4008	(746*10^106618+1)/9	106620	Robert Price	03/2020
4009	2^354157-17041	106612	Enzo Doria	05/2013
4010	12^98778+73	106600	Lelio R Paula	02/2017
4011	33333^1576+1576^33333	106585	Hans Havermann	11/2020
4012	2^354064+1870651	106584	Enzo Doria	05/2016
4013	24568^21779+21779^24568	106577	Hans Havermann	11/2020
4014	2^353992-57	106563	Lelio R Paula	10/2011
4015	9*10^106559+59	106560	Robert Price	01/2020
4016	7*10^106553+27	106554	Robert Price	11/2020
4017	28847^4938+4938^28847	106548	Hans Havermann	10/2020
4018	NSW(139160)	106535	Robert Price	12/2018
4019	(7*10^106516+113)/3	106517	Robert Price	02/2018
4020	2^353832-1853849	106515	Enzo Doria	09/2015
4021	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
4022	2^353794-18453	106503	Enzo Doria	05/2013
4023	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
4024	2^353728+7695	106483	Lelio R Paula	01/2017
4025	26476^10509+10509^26476	106475	Hans Havermann	10/2020
4026	2^353672-303	106466	Yves Minet	02/2012
4027	6^136811+101	106460	Lelio R Paula	02/2017
4028	2^353641+1871981	106457	Enzo Doria	05/2016
4029	(8*10^106454-29)/3	106455	Robert Price	07/2018
4030	27845^6654+6654^27845	106454	Hans Havermann	11/2020
4031	25316^16017+16017^25316	106444	Hans Havermann	11/2020
4032	2^353553+54615	106431	Lelio R Paula	01/2017
4033	2^353544-18897	106428	Enzo Doria	05/2013
4034	28894^4823+4823^28894	106426	Hans Havermann	11/2020
4035	25696^13829+13829^25696	106402	Hans Havermann	11/2020
4036	6^136729-133	106396	Lelio R Paula	02/2017
4037	2^353418+1605	106390	Lelio R Paula	01/2017
4038	2^353387+65	106381	Lelio R Paula	10/2011
4039	2^353372+74311	106376	Enzo Doria	04/2016
4040	2^353344-3693	106368	Yves Minet	03/2017
4042	2^353277-20089	106347	Enzo Doria	06/2013
4041	2^353275+72173	106347	Enzo Doria	04/2016
4043	2^353268-17705	106345	Enzo Doria	05/2013
4044	2^353267-19857	106344	Enzo Doria	06/2013
4045	(46*10^106343+143)/9	106344	Robert Price	01/2019
4047	(2^353189+3054)/2	106321	Stefano Morozzi	09/2020
4046	35087^1072+1072^35087	106321	Hans Havermann	10/2020
4048	(2^353184+1290)/2	106319	Stefano Morozzi	01/2021
4049	26985^8684+8684^26985	106287	Hans Havermann	10/2020
4050	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
4051	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
4052	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
4053	2^353025+72257	106272	Enzo Doria	04/2016
4056	2^352932-20345	106244	Enzo Doria	06/2013
4055	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
4054	25628^13983+13983^25628	106244	Hans Havermann	10/2020
4057	2^352883-187	106229	Lelio R Paula	10/2011
4058	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
4059	(55*10^106222+377)/9	106223	Robert Price	02/2019
4060	2^352814-131	106208	Lelio R Paula	10/2011
4061	2^352752+73951	106189	Enzo Doria	04/2016
4062	6^136434+5	106167	Lelio R Paula	11/2014
4063	25296^15737+15737^25296	106166	Hans Havermann	09/2020
4064	8*10^106157-13	106158	Robert Price	08/2019
4065	7*5^151872-8	106155	Lelio R Paula	11/2014
4066	105^52520-2	106153	Lelio R Paula	10/2017
4067	2^352601-1604809	106144	Enzo Doria	05/2015
4068	12^98353-43	106141	Lelio R Paula	02/2017
4069	2^352585-18901	106139	Enzo Doria	05/2013
4070	26363^10614+10614^26363	106135	Hans Havermann	09/2020
4071	(2^352554-3)/193	106128	Lelio R Paula	12/2013
4072	2^352540+15015	106126	Lelio R Paula	01/2017
4073	25068^17119+17119^25068	106125	Hans Havermann	09/2020
4074	2^352524-3149	106121	Yves Minet	10/2014
4075	2^352486-1858781	106109	Enzo Doria	04/2016
4076	2^352444+12705	106097	Lelio R Paula	01/2017
4077	28561^5182+5182^28561	106090	Hans Havermann	10/2020
4078	(182*10^106083+43)/9	106085	Robert Price	02/2020
4079	(266*10^106066+1)/3	106068	Robert Price	04/2020
4080	2^352228-18953	106032	Enzo Doria	05/2013
4081	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
4082	(2^352212+2250)/2	106027	Stefano Morozzi	01/2021
4083	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
4084	2^352107+1872533	105995	Enzo Doria	05/2016
4085	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
4086	2^352066-2591	105983	Yves Minet	07/2014
4087	2^352030+715	105972	Lelio R Paula	10/2011
4088	9*6^136176-5	105967	Lelio R Paula	11/2014
4089	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
4090	28582^5097+5097^28582	105963	Hans Havermann	09/2020
4091	155^48377+2	105962	Lelio R Paula	08/2013
4092	2^351865+1869707	105922	Enzo Doria	05/2016
4093	24974^17427+17427^24974	105921	Hans Havermann	09/2020
4094	25163^16194+16194^25163	105920	Hans Havermann	09/2020
4095	2^351831+23	105912	Lelio R Paula	10/2011
4096	9*2^351784-5	105899	Lelio R Paula	09/2014
4097	(2^351776+2766)/2	105895	Stefano Morozzi	01/2021
4098	(85*10^105881+203)/9	105882	Robert Price	09/2020
4099	2^351671-112387	105864	Enzo Doria	06/2014
4100	2^351669-109501	105863	Enzo Doria	04/2014
4101	2^351644+74731	105856	Enzo Doria	04/2016
4102	13^95025-42	105853	Lelio R Paula	12/2016
4103	2^351599+15015	105842	Lelio R Paula	01/2017
4104	19^82763+90	105834	Lelio R Paula	01/2017
4105	26050^11551+11551^26050	105832	Hans Havermann	09/2020
4106	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
4107	20^81329-51	105812	Lelio R Paula	01/2017
4108	(5*10^105811+211)/9	105811	Robert Price	02/2018
4109	2^351483+28425	105807	Lelio R Paula	01/2017
4110	25231^15610+15610^25231	105804	Hans Havermann	09/2020
4111	15^89960+86	105802	Lelio R Paula	02/2017
4112	2^351460-17289	105801	Enzo Doria	05/2013
4113	19^82735+22	105798	Lelio R Paula	01/2017
4114	2^351435-109077	105793	Enzo Doria	04/2014
4115	2^351393+1089	105780	Lelio R Paula	01/2017
4116	2^351364+72631	105772	Enzo Doria	04/2016
4117	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
4118	26818^8783+8783^26818	105761	Hans Havermann	09/2020
4121	2^351305+1872467	105754	Enzo Doria	05/2016
4120	3^221649+16	105754	Lelio R Paula	11/2016
4119	32511^1790+1790^32511	105754	Hans Havermann	09/2020
4122	8*3^221637-5	105749	Lelio R Paula	09/2014
4123	2^351279-2780449	105746	Enzo Doria	03/2016
4124	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
4125	15^89903-26	105735	Lelio R Paula	02/2017
4127	2^351213-73	105726	Lelio R Paula	10/2011
4126	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
4128	2^351192-4589	105720	Yves Minet	07/2011
4129	20^81250-33	105709	Lelio R Paula	12/2016
4130	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
4131	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
4132	2^351076-113159	105685	Enzo Doria	07/2014
4133	93^53688-2	105684	Lelio R Paula	09/2013
4134	2^351060-4559	105680	Yves Minet	07/2011
4135	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
4136	11^101473-750	105674	Enzo Doria	11/2012
4137	3*5^151181-8	105672	Lelio R Paula	11/2014
4138	15^89831-34	105650	Lelio R Paula	02/2017
4140	11^101448-360	105648	Enzo Doria	08/2012
4139	3*7^125011+4	105648	Lelio R Paula	11/2014
4141	2^350943-113269	105645	Enzo Doria	07/2014
4142	2*10^105636-91	105637	Robert Price	04/2020
4143	24231^22880+22880^24231	105634	Hans Havermann	09/2020
4144	35296^983+983^35296	105626	Hans Havermann	09/2020
4145	2^350868-19725	105622	Enzo Doria	06/2013
4146	2^350858-59291	105619	Enzo Doria	10/2015
4147	2^350851+135	105617	Lelio R Paula	10/2011
4148	2^350841-741	105614	Lelio R Paula	01/2017
4149	3*10^105582+77	105583	Robert Price	09/2018
4150	24915^17284+17284^24915	105581	Hans Havermann	09/2020
4151	(5*10^105576-53)/3	105577	Robert Price	09/2020
4152	8*10^105571+3	105572	Robert Price	08/2015
4153	2^350674-78557	105564	Jorge Menendez	03/2018
4154	2*5^151026-3	105563	Lelio R Paula	11/2014
4155	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
4156	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
4157	3^221211+236	105545	Lelio R Paula	11/2016
4158	(32*10^105530-77)/9	105531	Robert Price	06/2018
4159	10^105515+33	105516	Lelio R Paula	11/2016
4160	24644^19125+19125^24644	105516	Hans Havermann	10/2020
4161	10^105515-41033	105515	Patrick De Geest	12/2016
4162	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
4163	17^85732-72	105489	Lelio R Paula	01/2017
4164	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
4165	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
4166	25233^15118+15118^25233	105462	Hans Havermann	09/2020
4167	26261^10366+10366^26261	105454	Hans Havermann	09/2020
4168	2^350307-110329	105453	Enzo Doria	05/2014
4169	2^350253-20365	105437	Enzo Doria	06/2013
4170	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
4171	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
4172	2^350139-109009	105403	Enzo Doria	04/2014
4173	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
4174	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
4175	3*5^150763+4	105380	Lelio R Paula	11/2014
4176	12^97643+91	105375	Lelio R Paula	02/2017
4177	6*5^150744-7	105367	Lelio R Paula	11/2014
4178	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
4179	4*10^105364-39	105365	Robert Price	09/2020
4181	2^349996-112169	105360	Enzo Doria	06/2014
4180	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
4182	(418*10^105343+23)/9	105345	Robert Price	02/2020
4183	25490^13563+13563^25490	105334	Hans Havermann	10/2020
4184	11^101142-1080	105329	Enzo Doria	12/2012
4185	(68*10^105320-41)/9	105321	Robert Price	10/2013
4186	24800^17649+17649^24800	105319	Hans Havermann	09/2020
4187	3^220712-9934	105307	Enzo Doria	05/2014
4188	7*10^105296+9	105297	Robert Price	09/2015
4189	89*10^105284-7	105286	Robert Price	04/2020
4190	2^349739+1873373	105282	Enzo Doria	06/2016
4191	7^124574+24	105278	Lelio R Paula	11/2016
4192	2^349708-20957	105273	Enzo Doria	06/2013
4193	34115^1218+1218^34115	105267	Hans Havermann	09/2020
4194	2^349649-20469	105255	Enzo Doria	06/2013
4195	2^349607-20109	105243	Enzo Doria	06/2013
4196	(85*10^105242+473)/9	105243	Robert Price	01/2020
4197	2^349594-19085	105239	Enzo Doria	05/2013
4198	2^349530+1874479	105220	Enzo Doria	06/2016
4199	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
4200	(2^349452+3570)/2	105196	Stefano Morozzi	09/2020
4201	3^220464-112852	105189	Enzo Doria	07/2014
4202	2^349419-17349	105186	Enzo Doria	05/2013
4203	2^349400-2579	105180	Yves Minet	07/2014
4204	8*5^150471+3	105176	Lelio R Paula	11/2014
4205	655^37342+37342^655	105165	Norbert Schneider	08/2018
4206	13^94403+94	105160	Lelio R Paula	12/2016
4207	2^349301-112309	105151	Enzo Doria	06/2014
4208	30291^2960+2960^30291	105149	Hans Havermann	09/2020
4209	27350^6981+6981^27350	105132	Hans Havermann	09/2020
4211	9*2^349220+5	105127	Lelio R Paula	09/2014
4210	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
4212	7*3^220317+8	105119	Lelio R Paula	09/2014
4214	7^124386+88	105119	Lelio R Paula	11/2016
4213	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
4215	2^349171-19657	105111	Enzo Doria	06/2013
4216	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
4217	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
4218	(2^349111-5)/3	105093	Lelio R Paula	12/2013
4219	675^37142+37142^675	105087	Norbert Schneider	08/2018
4220	2^348981-2797573	105054	Enzo Doria	04/2016
4221	2^348869-6555	105021	Lelio R Paula	01/2017
4222	5^150217+78	104998	Lelio R Paula	11/2016
4223	(88*10^104989-1)/3	104991	Robert Price	04/2020
4224	(28*10^104972+149)/3	104973	Robert Price	12/2019
4225	24927^16262+16262^24927	104972	Hans Havermann	10/2020
4226	2^348703-113005	104971	Enzo Doria	06/2014
4228	2^348612-809	104943	Yves Minet	05/2013
4227	(73*10^104942-1)/9	104943	Robert Price	01/2015
4229	2^348583-350407	104934	Enzo Doria	06/2015
4230	2^348531-949	104919	Yves Minet	05/2012
4231	20^80636-59	104910	Lelio R Paula	12/2016
4232	8*10^104893-13	104894	Robert Price	08/2019
4234	2^348437+35	104890	Lelio R Paula	09/2011
4233	25208^14487+14487^25208	104890	Hans Havermann	09/2020
4235	2^348348+135	104864	Lelio R Paula	09/2011
4236	6*10^104852-31	104853	Robert Price	07/2020
4238	(2^348284+9)/25	104843	Lelio R Paula	12/2013
4237	75^55914-74	104843	Norbert Schneider	01/2015
4239	2^348268+255255	104840	Lelio R Paula	01/2017
4240	35540^891+891^35540	104839	Hans Havermann	09/2020
4241	5^149985-52	104836	Lelio R Paula	11/2016
4242	2^348224-20249	104826	Enzo Doria	06/2013
4243	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
4244	2^348212-20105	104823	Enzo Doria	06/2013
4245	24647^17898+17898^24647	104819	Hans Havermann	10/2020
4246	20^80562+19	104814	Lelio R Paula	12/2016
4247	2*10^104811-87	104812	Robert Price	04/2018
4248	2^348149-20053	104804	Enzo Doria	06/2013
4249	2^348095-171	104788	Lelio R Paula	09/2011
4250	25383^13412+13412^25383	104769	Hans Havermann	09/2020

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