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 ?
8001	12^99874-95	107783	Lelio R Paula	03/2017
8002	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
8003	2^358030-171	107778	Lelio R Paula	12/2011
8004	11^103488-4170	107772	Enzo Doria	12/2012
8005	2^357930-4547	107748	Yves Minet	03/2019
8006	2^357911-20089	107742	Enzo Doria	06/2013
8007	2^357885+12857	107735	Yves Minet	07/2010
8008	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
8009	7^127473+40	107728	Lelio R Paula	03/2017
8010	5*2^357850+9	107725	Lelio R Paula	09/2014
8011	2^357786-291191	107705	Enzo Doria	06/2015
8012	28907^5320+5320^28907	107705	Hans Havermann	10/2020
8013	18^85798-23	107700	Lelio R Paula	04/2017
8014	3*10^107697+61	107698	Robert Price	09/2020
8015	(14*10^107694-83)/3	107695	Robert Price	12/2018
8016	2^357688-1854269	107675	Enzo Doria	09/2015
8017	2^357671-112225	107670	Enzo Doria	06/2014
8018	34323^1370+1370^34323	107662	Hans Havermann	11/2020
8019	2^357618-21005	107654	Enzo Doria	06/2013
8020	2^357615-17505	107653	Enzo Doria	05/2013
8021	26350^12171+12171^26350	107649	Hans Havermann	11/2020
8023	(30^72871-1)/29	107638	Robert Price	12/2011
8022	Phi(72871,5#)	107638	Henri Lifchitz	12/2025
8024	25021^20026+20026^25021	107631	Hans Havermann	11/2020
8025	2^357521+1870217	107625	Enzo Doria	05/2016
8026	2^357477-1203	107612	Lelio R Paula	03/2017
8027	26008^13693+13693^26008	107583	Hans Havermann	10/2020
8028	25432^16991+16991^25432	107583	Hans Havermann	10/2020
8029	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
8030	5^153894-18	107568	Lelio R Paula	02/2017
8031	2^357324-69059	107566	Enzo Doria	11/2015
8032	467^40296+40296^467	107563	Norbert Schneider	03/2019
8033	29446^4495+4495^29446	107559	Hans Havermann	10/2020
8034	(8*10^107556-149)/3	107557	Robert Price	12/2021
8035	2^357283-869688105	107553	Lelio R Paula	01/2017
8036	2^357280-16805	107552	Enzo Doria	05/2013
8037	10^107547+481719	107548	Patrick De Geest	03/2017
8038	10^107547-47	107547	Lelio R Paula	02/2017
8039	(23*10^107540+37)/3	107541	Robert Price	02/2022
8040	17^87396-32	107537	Lelio R Paula	04/2017
8041	(746*10^107505+1)/9	107507	Robert Price	03/2020
8042	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
8043	2^357081+107	107493	Lelio R Paula	12/2011
8044	2^357058-3911	107486	Yves Minet	04/2017
8045	3^225274+64	107484	Lelio R Paula	03/2017
8046	5*10^107482-57	107483	Robert Price	03/2021
8047	18^85619-95	107476	Lelio R Paula	04/2017
8048	Phi(118283,10)/102584248160709208281690489429805181088536061161	107473	Anonymous	01/2026
8049	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
8050	3^225248-130	107471	Lelio R Paula	03/2017
8051	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
8052	27029^9448+9448^27029	107450	Hans Havermann	11/2020
8053	2^356935-18085	107449	Enzo Doria	05/2013
8054	55396^87+87^55396	107442	Hans Havermann	10/2020
8055	(14*10^107439-137)/3	107440	Robert Price	04/2021
8056	164^48505-48505^164	107432	Norman Luhn	09/2024
8057	10^107409+37	107410	Lelio R Paula	02/2017
8058	10^107409-329633	107409	Patrick De Geest	03/2017
8059	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
8060	2^356787-109027	107404	Enzo Doria	04/2014
8061	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
8062	3*10^107389+77	107390	Robert Price	09/2018
8063	(11*10^107385+61)/9	107386	Tyler Busby	01/2023
8064	5^153622-42	107378	Lelio R Paula	02/2017
8065	2^356699-97305	107378	Lelio R Paula	03/2017
8066	13129^26072-26072^13129	107371	Norbert Schneider	09/2022
8067	2^356654+85	107364	Lelio R Paula	11/2011
8068	2^356641-19921	107360	Enzo Doria	06/2013
8069	5*10^107355+11	107356	Robert Price	08/2019
8070	2^356623-465	107355	Lelio R Paula	03/2017
8071	19^83945-92	107345	Lelio R Paula	02/2017
8072	25491^16246+16246^25491	107337	Hans Havermann	11/2020
8073	10^107334+28149	107335	Patrick De Geest	03/2017
8074	10^107334-83	107334	Lelio R Paula	02/2017
8075	2^356518+885	107323	Lelio R Paula	03/2017
8076	(59*10^107322+391)/9	107323	Robert Price	03/2021
8077	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
8078	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
8079	2^356442-114713	107300	Enzo Doria	04/2015
8080	2^356425+72257	107295	Enzo Doria	04/2016
8081	2^356351-112237	107273	Enzo Doria	06/2014
8083	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
8082	2^356322+74539	107264	Enzo Doria	04/2016
8084	2^356274+1874479	107250	Enzo Doria	06/2016
8085	24606^22819+22819^24606	107241	Hans Havermann	10/2020
8086	(2^356243+3686)/2	107240	Stefano Morozzi	09/2020
8087	20^82422-93	107234	Lelio R Paula	02/2017
8088	2^356157-20365	107214	Enzo Doria	06/2013
8089	8*10^107209+99	107210	Robert Price	03/2021
8090	2^356129-18949	107206	Enzo Doria	05/2013
8091	(15^91163-1)/13873078234414574	107200	Paul Vanderveen	06/2025
8092	2^356100-109587	107197	Enzo Doria	04/2014
8093	165^48333+164	107178	Norbert Schneider	03/2026
8094	2*10^107173-37	107174	Robert Price	11/2021
8095	(2^355978+3262)/2	107160	Stefano Morozzi	02/2021
8096	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
8097	2^355968-64875	107158	Lelio R Paula	01/2017
8098	2^355952+1870321	107153	Enzo Doria	05/2016
8099	27069^9088+9088^27069	107152	Hans Havermann	11/2020
8100	2^355915-117	107142	Lelio R Paula	11/2011
8101	(16*10^107140+77)/3	107141	Robert Price	03/2019
8102	24628^22369+22369^24628	107124	Hans Havermann	11/2020
8103	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
8105	3^224495-8	107112	Lelio R Paula	12/2013
8104	Phi(227687,3)	107112	Henri Lifchitz	12/2025
8106	3*10^107096+23	107097	Robert Price	03/2022
8107	25077^18632+18632^25077	107086	Hans Havermann	10/2020
8108	7^126691-44	107067	Lelio R Paula	03/2017
8109	4^177830-8243	107065	Mike Oakes	02/2011
8110	(509*10^107057+13)/9	107059	Robert Price	05/2022
8111	2^355604+214051	107048	Enzo Doria	10/2023
8112	(2^355562+1702)/2	107035	Stefano Morozzi	09/2020
8113	10^107028+3593037	107029	Paul Bourdelais	10/2021
8114	10^107028-43301	107028	Alfred Reich	08/2024
8115	2^355524-21237	107024	Enzo Doria	06/2013
8117	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
8116	24843^20320+20320^24843	107022	Hans Havermann	10/2020
8118	2^355494-19901	107015	Enzo Doria	06/2013
8119	2^355454-869688105	107003	Lelio R Paula	01/2017
8120	4*10^106997+13	106998	Robert Price	02/2021
8121	(8*10^106985-629)/9	106985	Robert Price	01/2022
8122	2^355366+54615	106976	Lelio R Paula	01/2017
8123	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
8124	2^355275-19861	106949	Enzo Doria	06/2013
8125	27503^7738+7738^27503	106949	Hans Havermann	11/2020
8126	(85*10^106943+77)/9	106944	Robert Price	07/2022
8127	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
8128	4*10^106914-93	106915	Robert Price	07/2020
8129	(151^49069-1)/90910031243271150	106904	Paul Vanderveen	06/2025
8130	4*10^106892-3	106893	Robert Price	10/2015
8131	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
8132	2^355001+335931	106866	Enzo Doria	08/2024
8133	2^354946-3	106850	M. Frind & P. Underwood	08/2002
8134	(2^354945+3134)/2	106849	Stefano Morozzi	09/2020
8135	(46^64384+1)/(46^128+1)	106843	Martin Hopf	12/2023
8136	2^354873-18693	106828	Enzo Doria	05/2013
8137	(2^354831+3186)/2	106815	Stefano Morozzi	09/2020
8139	2^354828+4257	106814	Lelio R Paula	01/2017
8138	25216^17217+17217^25216	106814	Hans Havermann	10/2020
8140	(2^354799+1218)/2	106805	Stefano Morozzi	09/2020
8141	436^40459+40459^436	106791	Norbert Schneider	03/2019
8142	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
8143	(115*10^106772-7)/9	106774	Robert Price	02/2020
8144	2^354640-354640+1	106758	Robert Price	10/2014
8145	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
8146	2^354585+95	106741	Lelio R Paula	10/2011
8147	(206*10^106737+1)/9	106739	Robert Price	04/2022
8148	2^354553+189	106732	Lelio R Paula	10/2011
8150	(2^354546+1338)/2	106729	Stefano Morozzi	02/2021
8149	(8*10^106729-71)/9	106729	Serge Batalov	11/2022
8151	2^354514-109031	106720	Enzo Doria	04/2014
8152	2^354509-109465	106718	Enzo Doria	04/2014
8153	fibonacci(510628)+2	106715	Jon Grantham	08/2023
8154	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
8155	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
8156	15^90710+28	106684	Lelio R Paula	04/2017
8157	7^126237+34	106683	Lelio R Paula	03/2017
8158	2^354385-115315	106681	Enzo Doria	06/2015
8159	2^354327-19305	106664	Enzo Doria	06/2013
8160	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
8161	10^106636+97	106637	Lelio R Paula	02/2017
8162	10^106636-22923	106636	Patrick De Geest	03/2017
8163	2^354220-57	106631	Lelio R Paula	10/2011
8164	(68*10^106628-329)/9	106629	Robert Price	03/2021
8165	(29*10^106620-77)/3	106621	Robert Price	02/2020
8166	(746*10^106618+1)/9	106620	Robert Price	03/2020
8167	2*10^106613+29	106614	Robert Price	02/2021
8168	2^354157-17041	106612	Enzo Doria	05/2013
8169	12^98778+73	106600	Lelio R Paula	02/2017
8170	Phi(447629,-2)	106594	Henri Lifchitz	12/2025
8171	33333^1576+1576^33333	106585	Hans Havermann	11/2020
8172	2^354064+1870651	106584	Enzo Doria	05/2016
8173	24568^21779+21779^24568	106577	Hans Havermann	11/2020
8174	2^353992-57	106563	Lelio R Paula	10/2011
8175	9*10^106559+59	106560	Robert Price	01/2020
8176	7*10^106553+27	106554	Robert Price	11/2020
8177	28847^4938+4938^28847	106548	Hans Havermann	10/2020
8178	(20^81901-1)/42030774209	106546	Paul Vanderveen	06/2025
8180	NSW(139160)	106535	Robert Price	12/2018
8179	f(278321)	106535	Robert Price	07/2023
8181	(7*10^106516+113)/3	106517	Robert Price	02/2018
8182	2^353832-1853849	106515	Enzo Doria	09/2015
8185	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
8183	Phi(126037,7)	106513	Henri Lifchitz	12/2025
8184	Phi(252074,-7)	106513	Henri Lifchitz	02/2026
8186	2^353794-18453	106503	Enzo Doria	05/2013
8187	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
8188	2^353728+7695	106483	Lelio R Paula	01/2017
8189	26476^10509+10509^26476	106475	Hans Havermann	10/2020
8190	2^353672-303	106466	Yves Minet	02/2012
8191	6^136811+101	106460	Lelio R Paula	02/2017
8192	2^353641+1871981	106457	Enzo Doria	05/2016
8193	(8*10^106454-29)/3	106455	Robert Price	07/2018
8194	27845^6654+6654^27845	106454	Hans Havermann	11/2020
8195	10^106449-700001	106449	Robert Price	08/2021
8196	25316^16017+16017^25316	106444	Hans Havermann	11/2020
8197	2^353553+54615	106431	Lelio R Paula	01/2017
8198	2^353544-18897	106428	Enzo Doria	05/2013
8199	28894^4823+4823^28894	106426	Hans Havermann	11/2020
8200	(19*10^106422+29)/3	106423	Robert Price	12/2021
8201	(694*10^106418+53)/9	106420	Robert Price	02/2022
8202	6*10^106412-13	106413	Robert Price	07/2022
8203	25696^13829+13829^25696	106402	Hans Havermann	11/2020
8204	6^136729-133	106396	Lelio R Paula	02/2017
8205	2^353418+1605	106390	Lelio R Paula	01/2017
8206	2^353387+65	106381	Lelio R Paula	10/2011
8207	2^353372+74311	106376	Enzo Doria	04/2016
8208	2^353344-3693	106368	Yves Minet	03/2017
8209	(772*10^106365-7)/9	106367	Robert Price	06/2022
8210	(56*10^106351+619)/9	106352	Robert Price	05/2021
8212	2^353277-20089	106347	Enzo Doria	06/2013
8211	2^353275+72173	106347	Enzo Doria	04/2016
8213	2^353268-17705	106345	Enzo Doria	05/2013
8214	2^353267-19857	106344	Enzo Doria	06/2013
8215	(46*10^106343+143)/9	106344	Robert Price	01/2019
8217	(2^353189+3054)/2	106321	Stefano Morozzi	09/2020
8216	35087^1072+1072^35087	106321	Hans Havermann	10/2020
8218	(2^353184+1290)/2	106319	Stefano Morozzi	01/2021
8219	F(508799)/24738824977/1990778864897	106310	Serge Batalov	07/2024
8220	26985^8684+8684^26985	106287	Hans Havermann	10/2020
8221	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
8223	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
8222	(46*10^106277+107)/9	106278	Robert Price	06/2022
8224	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
8225	2^353025+72257	106272	Enzo Doria	04/2016
8228	2^352932-20345	106244	Enzo Doria	06/2013
8226	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
8227	25628^13983+13983^25628	106244	Hans Havermann	10/2020
8229	2^352883-187	106229	Lelio R Paula	10/2011
8230	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
8231	(55*10^106222+377)/9	106223	Robert Price	02/2019
8232	2^352814-131	106208	Lelio R Paula	10/2011
8233	2^352752+73951	106189	Enzo Doria	04/2016
8234	11876*25^75945+357	106171	Eric Chen	10/2023
8235	6^136434+5	106167	Lelio R Paula	11/2014
8236	25296^15737+15737^25296	106166	Hans Havermann	09/2020
8237	8*10^106157-13	106158	Robert Price	08/2019
8238	2^352641+225677	106156	Enzo Doria	08/2024
8239	7*5^151872-8	106155	Lelio R Paula	11/2014
8240	105^52520-2	106153	Lelio R Paula	10/2017
8241	(23*10^106152-29)/3	106153	Robert Price	03/2022
8242	2^352601-1604809	106144	Enzo Doria	05/2015
8243	12^98353-43	106141	Lelio R Paula	02/2017
8244	2^352585-18901	106139	Enzo Doria	05/2013
8245	26363^10614+10614^26363	106135	Hans Havermann	09/2020
8246	(2^352554-3)/193	106128	Lelio R Paula	12/2013
8247	2^352540+15015	106126	Lelio R Paula	01/2017
8248	25068^17119+17119^25068	106125	Hans Havermann	09/2020
8249	2^352524-3149	106121	Yves Minet	10/2014
8250	(7*10^106119-67)/3	106120	Robert Price	10/2021

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