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 ?
5001	19^83945-92	107345	Lelio R Paula	02/2017
5002	25491^16246+16246^25491	107337	Hans Havermann	11/2020
5003	10^107334+28149	107335	Patrick De Geest	03/2017
5004	10^107334-83	107334	Lelio R Paula	02/2017
5005	2^356518+885	107323	Lelio R Paula	03/2017
5006	(59*10^107322+391)/9	107323	Robert Price	03/2021
5007	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
5008	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
5009	2^356442-114713	107300	Enzo Doria	04/2015
5010	2^356425+72257	107295	Enzo Doria	04/2016
5011	2^356351-112237	107273	Enzo Doria	06/2014
5013	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
5012	2^356322+74539	107264	Enzo Doria	04/2016
5014	2^356274+1874479	107250	Enzo Doria	06/2016
5015	24606^22819+22819^24606	107241	Hans Havermann	10/2020
5016	(2^356243+3686)/2	107240	Stefano Morozzi	09/2020
5017	20^82422-93	107234	Lelio R Paula	02/2017
5018	2^356157-20365	107214	Enzo Doria	06/2013
5019	8*10^107209+99	107210	Robert Price	03/2021
5020	2^356129-18949	107206	Enzo Doria	05/2013
5021	2^356100-109587	107197	Enzo Doria	04/2014
5022	2*10^107173-37	107174	Robert Price	11/2021
5023	(2^355978+3262)/2	107160	Stefano Morozzi	02/2021
5024	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
5025	2^355968-64875	107158	Lelio R Paula	01/2017
5026	2^355952+1870321	107153	Enzo Doria	05/2016
5027	27069^9088+9088^27069	107152	Hans Havermann	11/2020
5028	2^355915-117	107142	Lelio R Paula	11/2011
5029	(16*10^107140+77)/3	107141	Robert Price	03/2019
5030	24628^22369+22369^24628	107124	Hans Havermann	11/2020
5031	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
5032	3^224495-8	107112	Lelio R Paula	12/2013
5033	25077^18632+18632^25077	107086	Hans Havermann	10/2020
5034	7^126691-44	107067	Lelio R Paula	03/2017
5035	4^177830-8243	107065	Mike Oakes	02/2011
5036	(2^355562+1702)/2	107035	Stefano Morozzi	09/2020
5037	10^107028+3593037	107029	Paul Bourdelais	10/2021
5038	2^355524-21237	107024	Enzo Doria	06/2013
5040	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
5039	24843^20320+20320^24843	107022	Hans Havermann	10/2020
5041	2^355494-19901	107015	Enzo Doria	06/2013
5042	2^355454-869688105	107003	Lelio R Paula	01/2017
5043	4*10^106997+13	106998	Robert Price	02/2021
5044	2^355366+54615	106976	Lelio R Paula	01/2017
5045	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
5046	2^355275-19861	106949	Enzo Doria	06/2013
5047	27503^7738+7738^27503	106949	Hans Havermann	11/2020
5048	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
5049	4*10^106914-93	106915	Robert Price	07/2020
5050	4*10^106892-3	106893	Robert Price	10/2015
5051	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
5052	2^354946-3	106850	M. Frind & P. Underwood	08/2002
5053	(2^354945+3134)/2	106849	Stefano Morozzi	09/2020
5054	2^354873-18693	106828	Enzo Doria	05/2013
5055	(2^354831+3186)/2	106815	Stefano Morozzi	09/2020
5057	2^354828+4257	106814	Lelio R Paula	01/2017
5056	25216^17217+17217^25216	106814	Hans Havermann	10/2020
5058	(2^354799+1218)/2	106805	Stefano Morozzi	09/2020
5059	436^40459+40459^436	106791	Norbert Schneider	03/2019
5060	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
5061	(115*10^106772-7)/9	106774	Robert Price	02/2020
5062	2^354640-354640+1	106758	Robert Price	10/2014
5063	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
5064	2^354585+95	106741	Lelio R Paula	10/2011
5065	2^354553+189	106732	Lelio R Paula	10/2011
5066	(2^354546+1338)/2	106729	Stefano Morozzi	02/2021
5067	2^354514-109031	106720	Enzo Doria	04/2014
5068	2^354509-109465	106718	Enzo Doria	04/2014
5069	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
5070	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
5071	15^90710+28	106684	Lelio R Paula	04/2017
5072	7^126237+34	106683	Lelio R Paula	03/2017
5073	2^354385-115315	106681	Enzo Doria	06/2015
5074	2^354327-19305	106664	Enzo Doria	06/2013
5075	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
5076	10^106636+97	106637	Lelio R Paula	02/2017
5077	10^106636-22923	106636	Patrick De Geest	03/2017
5078	2^354220-57	106631	Lelio R Paula	10/2011
5079	(68*10^106628-329)/9	106629	Robert Price	03/2021
5080	(29*10^106620-77)/3	106621	Robert Price	02/2020
5081	(746*10^106618+1)/9	106620	Robert Price	03/2020
5082	2*10^106613+29	106614	Robert Price	02/2021
5083	2^354157-17041	106612	Enzo Doria	05/2013
5084	12^98778+73	106600	Lelio R Paula	02/2017
5085	33333^1576+1576^33333	106585	Hans Havermann	11/2020
5086	2^354064+1870651	106584	Enzo Doria	05/2016
5087	24568^21779+21779^24568	106577	Hans Havermann	11/2020
5088	2^353992-57	106563	Lelio R Paula	10/2011
5089	9*10^106559+59	106560	Robert Price	01/2020
5090	7*10^106553+27	106554	Robert Price	11/2020
5091	28847^4938+4938^28847	106548	Hans Havermann	10/2020
5092	NSW(139160)	106535	Robert Price	12/2018
5093	(7*10^106516+113)/3	106517	Robert Price	02/2018
5094	2^353832-1853849	106515	Enzo Doria	09/2015
5095	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
5096	2^353794-18453	106503	Enzo Doria	05/2013
5097	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
5098	2^353728+7695	106483	Lelio R Paula	01/2017
5099	26476^10509+10509^26476	106475	Hans Havermann	10/2020
5100	2^353672-303	106466	Yves Minet	02/2012
5101	6^136811+101	106460	Lelio R Paula	02/2017
5102	2^353641+1871981	106457	Enzo Doria	05/2016
5103	(8*10^106454-29)/3	106455	Robert Price	07/2018
5104	27845^6654+6654^27845	106454	Hans Havermann	11/2020
5105	10^106449-700001	106449	Robert Price	08/2021
5106	25316^16017+16017^25316	106444	Hans Havermann	11/2020
5107	2^353553+54615	106431	Lelio R Paula	01/2017
5108	2^353544-18897	106428	Enzo Doria	05/2013
5109	28894^4823+4823^28894	106426	Hans Havermann	11/2020
5110	(19*10^106422+29)/3	106423	Robert Price	12/2021
5111	25696^13829+13829^25696	106402	Hans Havermann	11/2020
5112	6^136729-133	106396	Lelio R Paula	02/2017
5113	2^353418+1605	106390	Lelio R Paula	01/2017
5114	2^353387+65	106381	Lelio R Paula	10/2011
5115	2^353372+74311	106376	Enzo Doria	04/2016
5116	2^353344-3693	106368	Yves Minet	03/2017
5117	(56*10^106351+619)/9	106352	Robert Price	05/2021
5119	2^353277-20089	106347	Enzo Doria	06/2013
5118	2^353275+72173	106347	Enzo Doria	04/2016
5120	2^353268-17705	106345	Enzo Doria	05/2013
5121	2^353267-19857	106344	Enzo Doria	06/2013
5122	(46*10^106343+143)/9	106344	Robert Price	01/2019
5124	(2^353189+3054)/2	106321	Stefano Morozzi	09/2020
5123	35087^1072+1072^35087	106321	Hans Havermann	10/2020
5125	(2^353184+1290)/2	106319	Stefano Morozzi	01/2021
5126	26985^8684+8684^26985	106287	Hans Havermann	10/2020
5127	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
5128	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
5129	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
5130	2^353025+72257	106272	Enzo Doria	04/2016
5133	2^352932-20345	106244	Enzo Doria	06/2013
5131	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
5132	25628^13983+13983^25628	106244	Hans Havermann	10/2020
5134	2^352883-187	106229	Lelio R Paula	10/2011
5135	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
5136	(55*10^106222+377)/9	106223	Robert Price	02/2019
5137	2^352814-131	106208	Lelio R Paula	10/2011
5138	2^352752+73951	106189	Enzo Doria	04/2016
5139	6^136434+5	106167	Lelio R Paula	11/2014
5140	25296^15737+15737^25296	106166	Hans Havermann	09/2020
5141	8*10^106157-13	106158	Robert Price	08/2019
5142	7*5^151872-8	106155	Lelio R Paula	11/2014
5143	105^52520-2	106153	Lelio R Paula	10/2017
5144	2^352601-1604809	106144	Enzo Doria	05/2015
5145	12^98353-43	106141	Lelio R Paula	02/2017
5146	2^352585-18901	106139	Enzo Doria	05/2013
5147	26363^10614+10614^26363	106135	Hans Havermann	09/2020
5148	(2^352554-3)/193	106128	Lelio R Paula	12/2013
5149	2^352540+15015	106126	Lelio R Paula	01/2017
5150	25068^17119+17119^25068	106125	Hans Havermann	09/2020
5151	2^352524-3149	106121	Yves Minet	10/2014
5152	(7*10^106119-67)/3	106120	Robert Price	10/2021
5153	2^352486-1858781	106109	Enzo Doria	04/2016
5154	2^352444+12705	106097	Lelio R Paula	01/2017
5155	28561^5182+5182^28561	106090	Hans Havermann	10/2020
5156	(182*10^106083+43)/9	106085	Robert Price	02/2020
5157	(266*10^106066+1)/3	106068	Robert Price	04/2020
5158	2^352228-18953	106032	Enzo Doria	05/2013
5159	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
5160	(2^352212+2250)/2	106027	Stefano Morozzi	01/2021
5161	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
5162	2^352107+1872533	105995	Enzo Doria	05/2016
5163	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
5164	2^352066-2591	105983	Yves Minet	07/2014
5165	2^352030+715	105972	Lelio R Paula	10/2011
5166	9*6^136176-5	105967	Lelio R Paula	11/2014
5167	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
5168	28582^5097+5097^28582	105963	Hans Havermann	09/2020
5169	155^48377+2	105962	Lelio R Paula	08/2013
5170	(23*10^105944-119)/3	105945	Robert Price	07/2021
5171	2^351865+1869707	105922	Enzo Doria	05/2016
5172	24974^17427+17427^24974	105921	Hans Havermann	09/2020
5173	25163^16194+16194^25163	105920	Hans Havermann	09/2020
5174	2^351831+23	105912	Lelio R Paula	10/2011
5175	(2^351818+3798)/2	105908	Stefano Morozzi	02/2021
5176	9*2^351784-5	105899	Lelio R Paula	09/2014
5177	(2^351776+2766)/2	105895	Stefano Morozzi	01/2021
5178	(85*10^105881+203)/9	105882	Robert Price	09/2020
5179	2^351671-112387	105864	Enzo Doria	06/2014
5180	2^351669-109501	105863	Enzo Doria	04/2014
5181	2^351644+74731	105856	Enzo Doria	04/2016
5182	13^95025-42	105853	Lelio R Paula	12/2016
5183	2^351599+15015	105842	Lelio R Paula	01/2017
5184	19^82763+90	105834	Lelio R Paula	01/2017
5185	(205*10^105831-1)/3	105833	Robert Price	11/2021
5186	26050^11551+11551^26050	105832	Hans Havermann	09/2020
5187	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
5188	20^81329-51	105812	Lelio R Paula	01/2017
5189	(5*10^105811+211)/9	105811	Robert Price	02/2018
5190	2^351483+28425	105807	Lelio R Paula	01/2017
5191	25231^15610+15610^25231	105804	Hans Havermann	09/2020
5192	15^89960+86	105802	Lelio R Paula	02/2017
5193	2^351460-17289	105801	Enzo Doria	05/2013
5194	19^82735+22	105798	Lelio R Paula	01/2017
5195	2^351435-109077	105793	Enzo Doria	04/2014
5196	2^351393+1089	105780	Lelio R Paula	01/2017
5197	2^351364+72631	105772	Enzo Doria	04/2016
5198	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
5199	26818^8783+8783^26818	105761	Hans Havermann	09/2020
5202	2^351305+1872467	105754	Enzo Doria	05/2016
5201	3^221649+16	105754	Lelio R Paula	11/2016
5200	32511^1790+1790^32511	105754	Hans Havermann	09/2020
5203	8*3^221637-5	105749	Lelio R Paula	09/2014
5204	2^351279-2780449	105746	Enzo Doria	03/2016
5205	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
5206	15^89903-26	105735	Lelio R Paula	02/2017
5208	2^351213-73	105726	Lelio R Paula	10/2011
5207	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
5209	2^351192-4589	105720	Yves Minet	07/2011
5210	20^81250-33	105709	Lelio R Paula	12/2016
5211	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
5212	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
5213	2^351076-113159	105685	Enzo Doria	07/2014
5214	93^53688-2	105684	Lelio R Paula	09/2013
5215	2^351060-4559	105680	Yves Minet	07/2011
5216	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
5217	11^101473-750	105674	Enzo Doria	11/2012
5218	3*5^151181-8	105672	Lelio R Paula	11/2014
5219	15^89831-34	105650	Lelio R Paula	02/2017
5221	11^101448-360	105648	Enzo Doria	08/2012
5220	3*7^125011+4	105648	Lelio R Paula	11/2014
5222	2^350943-113269	105645	Enzo Doria	07/2014
5223	2*10^105636-91	105637	Robert Price	04/2020
5224	24231^22880+22880^24231	105634	Hans Havermann	09/2020
5225	35296^983+983^35296	105626	Hans Havermann	09/2020
5226	2^350868-19725	105622	Enzo Doria	06/2013
5227	2^350858-59291	105619	Enzo Doria	10/2015
5228	2^350851+135	105617	Lelio R Paula	10/2011
5229	2^350841-741	105614	Lelio R Paula	01/2017
5230	3*10^105582+77	105583	Robert Price	09/2018
5231	24915^17284+17284^24915	105581	Hans Havermann	09/2020
5232	(5*10^105576-53)/3	105577	Robert Price	09/2020
5233	8*10^105571+3	105572	Robert Price	08/2015
5234	2^350674-78557	105564	Jorge Menendez	03/2018
5235	2*5^151026-3	105563	Lelio R Paula	11/2014
5236	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
5237	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
5238	3^221211+236	105545	Lelio R Paula	11/2016
5239	(32*10^105530-77)/9	105531	Robert Price	06/2018
5240	10^105515+33	105516	Lelio R Paula	11/2016
5241	24644^19125+19125^24644	105516	Hans Havermann	10/2020
5242	10^105515-41033	105515	Patrick De Geest	12/2016
5243	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
5244	17^85732-72	105489	Lelio R Paula	01/2017
5245	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
5246	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
5247	25233^15118+15118^25233	105462	Hans Havermann	09/2020
5248	26261^10366+10366^26261	105454	Hans Havermann	09/2020
5249	2^350307-110329	105453	Enzo Doria	05/2014
5250	2^350253-20365	105437	Enzo Doria	06/2013

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