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 ?
7751	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
7752	26583^11702+11702^26583	108147	Hans Havermann	11/2020
7753	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
7754	6^138956-59	108129	Lelio R Paula	02/2017
7755	2^359184+30285	108126	Lelio R Paula	04/2017
7756	13^97059+10	108119	Lelio R Paula	03/2017
7757	2^359137-81	108112	Lelio R Paula	12/2011
7759	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
7758	2^359110-11655	108103	Lelio R Paula	04/2017
7760	2^359069-933075	108091	Paul Bourdelais	06/2021
7761	26227^13222+13222^26227	108090	Hans Havermann	10/2020
7762	8*6^138875+5	108067	Lelio R Paula	11/2014
7763	2^358987-216919	108066	Enzo Doria	05/2014
7764	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
7765	39^67918-67918^39	108062	Norbert Schneider	02/2017
7766	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
7767	25282^18767+18767^25282	108040	Hans Havermann	11/2020
7768	(918^36457-1)/917	108014	Tom Wu	08/2025
7769	2^358785-16933	108006	Enzo Doria	05/2013
7770	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
7771	6^138770-77	107985	Lelio R Paula	02/2017
7772	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
7773	10^107976+19	107977	Lelio R Paula	02/2017
7774	10^107976-202103	107976	Patrick De Geest	03/2017
7775	2^358684+75781	107975	Enzo Doria	04/2016
7776	24928^21411+21411^24928	107955	Hans Havermann	10/2020
7777	99^54094+2	107952	Lelio R Paula	06/2013
7778	(2^358583-9)/391	107942	Lelio R Paula	12/2013
7779	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
7780	2^358538+55	107931	Lelio R Paula	12/2011
7781	2^358517-109009	107925	Enzo Doria	03/2014
7782	26395^12258+12258^26395	107914	Hans Havermann	10/2020
7783	3^226159+104	107906	Lelio R Paula	03/2017
7784	7*10^107870+39	107871	Robert Price	01/2023
7785	2^358310-11655	107863	Lelio R Paula	03/2017
7786	(68*10^107852-329)/9	107853	Robert Price	03/2021
7787	2^358275-112987	107852	Enzo Doria	07/2014
7788	3^226038+4	107848	Tyler NeSmith	01/2021
7789	2^358233-20005	107839	Enzo Doria	06/2013
7790	2^358194+175	107828	Lelio R Paula	12/2011
7791	107^53125-106	107812	Norbert Schneider	12/2016
7792	(25*10^107804+161)/3	107805	Robert Price	09/2019
7793	3^225922-2	107793	Lelio R Paula	10/2013
7794	12^99874-95	107783	Lelio R Paula	03/2017
7795	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
7796	2^358030-171	107778	Lelio R Paula	12/2011
7797	11^103488-4170	107772	Enzo Doria	12/2012
7798	2^357930-4547	107748	Yves Minet	03/2019
7799	2^357911-20089	107742	Enzo Doria	06/2013
7800	2^357885+12857	107735	Yves Minet	07/2010
7801	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
7802	7^127473+40	107728	Lelio R Paula	03/2017
7803	5*2^357850+9	107725	Lelio R Paula	09/2014
7804	2^357786-291191	107705	Enzo Doria	06/2015
7805	28907^5320+5320^28907	107705	Hans Havermann	10/2020
7806	18^85798-23	107700	Lelio R Paula	04/2017
7807	3*10^107697+61	107698	Robert Price	09/2020
7808	(14*10^107694-83)/3	107695	Robert Price	12/2018
7809	2^357688-1854269	107675	Enzo Doria	09/2015
7810	2^357671-112225	107670	Enzo Doria	06/2014
7811	34323^1370+1370^34323	107662	Hans Havermann	11/2020
7812	2^357618-21005	107654	Enzo Doria	06/2013
7813	2^357615-17505	107653	Enzo Doria	05/2013
7814	26350^12171+12171^26350	107649	Hans Havermann	11/2020
7816	(30^72871-1)/29	107638	Robert Price	12/2011
7815	Phi(72871,5#)	107638	Henri Lifchitz	12/2025
7817	25021^20026+20026^25021	107631	Hans Havermann	11/2020
7818	2^357521+1870217	107625	Enzo Doria	05/2016
7819	2^357477-1203	107612	Lelio R Paula	03/2017
7820	26008^13693+13693^26008	107583	Hans Havermann	10/2020
7821	25432^16991+16991^25432	107583	Hans Havermann	10/2020
7822	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
7823	5^153894-18	107568	Lelio R Paula	02/2017
7824	2^357324-69059	107566	Enzo Doria	11/2015
7825	467^40296+40296^467	107563	Norbert Schneider	03/2019
7826	29446^4495+4495^29446	107559	Hans Havermann	10/2020
7827	(8*10^107556-149)/3	107557	Robert Price	12/2021
7828	2^357283-869688105	107553	Lelio R Paula	01/2017
7829	2^357280-16805	107552	Enzo Doria	05/2013
7830	10^107547+481719	107548	Patrick De Geest	03/2017
7831	10^107547-47	107547	Lelio R Paula	02/2017
7832	(23*10^107540+37)/3	107541	Robert Price	02/2022
7833	17^87396-32	107537	Lelio R Paula	04/2017
7834	(746*10^107505+1)/9	107507	Robert Price	03/2020
7835	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
7836	2^357081+107	107493	Lelio R Paula	12/2011
7837	2^357058-3911	107486	Yves Minet	04/2017
7838	3^225274+64	107484	Lelio R Paula	03/2017
7839	5*10^107482-57	107483	Robert Price	03/2021
7840	18^85619-95	107476	Lelio R Paula	04/2017
7841	Phi(118283,10)/102584248160709208281690489429805181088536061161	107473	Anonymous	01/2026
7842	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
7843	3^225248-130	107471	Lelio R Paula	03/2017
7844	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
7845	27029^9448+9448^27029	107450	Hans Havermann	11/2020
7846	2^356935-18085	107449	Enzo Doria	05/2013
7847	55396^87+87^55396	107442	Hans Havermann	10/2020
7848	(14*10^107439-137)/3	107440	Robert Price	04/2021
7849	164^48505-48505^164	107432	Norman Luhn	09/2024
7850	10^107409+37	107410	Lelio R Paula	02/2017
7851	10^107409-329633	107409	Patrick De Geest	03/2017
7852	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
7853	2^356787-109027	107404	Enzo Doria	04/2014
7854	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
7855	3*10^107389+77	107390	Robert Price	09/2018
7856	(11*10^107385+61)/9	107386	Tyler Busby	01/2023
7857	5^153622-42	107378	Lelio R Paula	02/2017
7858	2^356699-97305	107378	Lelio R Paula	03/2017
7859	13129^26072-26072^13129	107371	Norbert Schneider	09/2022
7860	2^356654+85	107364	Lelio R Paula	11/2011
7861	2^356641-19921	107360	Enzo Doria	06/2013
7862	5*10^107355+11	107356	Robert Price	08/2019
7863	2^356623-465	107355	Lelio R Paula	03/2017
7864	19^83945-92	107345	Lelio R Paula	02/2017
7865	25491^16246+16246^25491	107337	Hans Havermann	11/2020
7866	10^107334+28149	107335	Patrick De Geest	03/2017
7867	10^107334-83	107334	Lelio R Paula	02/2017
7868	2^356518+885	107323	Lelio R Paula	03/2017
7869	(59*10^107322+391)/9	107323	Robert Price	03/2021
7870	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
7871	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
7872	2^356442-114713	107300	Enzo Doria	04/2015
7873	2^356425+72257	107295	Enzo Doria	04/2016
7874	2^356351-112237	107273	Enzo Doria	06/2014
7876	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
7875	2^356322+74539	107264	Enzo Doria	04/2016
7877	2^356274+1874479	107250	Enzo Doria	06/2016
7878	24606^22819+22819^24606	107241	Hans Havermann	10/2020
7879	(2^356243+3686)/2	107240	Stefano Morozzi	09/2020
7880	20^82422-93	107234	Lelio R Paula	02/2017
7881	2^356157-20365	107214	Enzo Doria	06/2013
7882	8*10^107209+99	107210	Robert Price	03/2021
7883	2^356129-18949	107206	Enzo Doria	05/2013
7884	(15^91163-1)/13873078234414574	107200	Paul Vanderveen	06/2025
7885	2^356100-109587	107197	Enzo Doria	04/2014
7886	165^48333+164	107178	Norbert Schneider	03/2026
7887	2*10^107173-37	107174	Robert Price	11/2021
7888	(2^355978+3262)/2	107160	Stefano Morozzi	02/2021
7889	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
7890	2^355968-64875	107158	Lelio R Paula	01/2017
7891	2^355952+1870321	107153	Enzo Doria	05/2016
7892	27069^9088+9088^27069	107152	Hans Havermann	11/2020
7893	2^355915-117	107142	Lelio R Paula	11/2011
7894	(16*10^107140+77)/3	107141	Robert Price	03/2019
7895	24628^22369+22369^24628	107124	Hans Havermann	11/2020
7896	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
7898	3^224495-8	107112	Lelio R Paula	12/2013
7897	Phi(227687,3)	107112	Henri Lifchitz	12/2025
7899	3*10^107096+23	107097	Robert Price	03/2022
7900	25077^18632+18632^25077	107086	Hans Havermann	10/2020
7901	7^126691-44	107067	Lelio R Paula	03/2017
7902	4^177830-8243	107065	Mike Oakes	02/2011
7903	(509*10^107057+13)/9	107059	Robert Price	05/2022
7904	2^355604+214051	107048	Enzo Doria	10/2023
7905	(2^355562+1702)/2	107035	Stefano Morozzi	09/2020
7906	10^107028+3593037	107029	Paul Bourdelais	10/2021
7907	10^107028-43301	107028	Alfred Reich	08/2024
7908	2^355524-21237	107024	Enzo Doria	06/2013
7910	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
7909	24843^20320+20320^24843	107022	Hans Havermann	10/2020
7911	2^355494-19901	107015	Enzo Doria	06/2013
7912	2^355454-869688105	107003	Lelio R Paula	01/2017
7913	4*10^106997+13	106998	Robert Price	02/2021
7914	(8*10^106985-629)/9	106985	Robert Price	01/2022
7915	2^355366+54615	106976	Lelio R Paula	01/2017
7916	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
7917	2^355275-19861	106949	Enzo Doria	06/2013
7918	27503^7738+7738^27503	106949	Hans Havermann	11/2020
7919	(85*10^106943+77)/9	106944	Robert Price	07/2022
7920	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
7921	4*10^106914-93	106915	Robert Price	07/2020
7922	(151^49069-1)/90910031243271150	106904	Paul Vanderveen	06/2025
7923	4*10^106892-3	106893	Robert Price	10/2015
7924	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
7925	2^355001+335931	106866	Enzo Doria	08/2024
7926	2^354946-3	106850	M. Frind & P. Underwood	08/2002
7927	(2^354945+3134)/2	106849	Stefano Morozzi	09/2020
7928	(46^64384+1)/(46^128+1)	106843	Martin Hopf	12/2023
7929	2^354873-18693	106828	Enzo Doria	05/2013
7930	(2^354831+3186)/2	106815	Stefano Morozzi	09/2020
7932	2^354828+4257	106814	Lelio R Paula	01/2017
7931	25216^17217+17217^25216	106814	Hans Havermann	10/2020
7933	(2^354799+1218)/2	106805	Stefano Morozzi	09/2020
7934	436^40459+40459^436	106791	Norbert Schneider	03/2019
7935	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
7936	(115*10^106772-7)/9	106774	Robert Price	02/2020
7937	2^354640-354640+1	106758	Robert Price	10/2014
7938	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
7939	2^354585+95	106741	Lelio R Paula	10/2011
7940	(206*10^106737+1)/9	106739	Robert Price	04/2022
7941	2^354553+189	106732	Lelio R Paula	10/2011
7943	(2^354546+1338)/2	106729	Stefano Morozzi	02/2021
7942	(8*10^106729-71)/9	106729	Serge Batalov	11/2022
7944	2^354514-109031	106720	Enzo Doria	04/2014
7945	2^354509-109465	106718	Enzo Doria	04/2014
7946	fibonacci(510628)+2	106715	Jon Grantham	08/2023
7947	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
7948	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
7949	15^90710+28	106684	Lelio R Paula	04/2017
7950	7^126237+34	106683	Lelio R Paula	03/2017
7951	2^354385-115315	106681	Enzo Doria	06/2015
7952	2^354327-19305	106664	Enzo Doria	06/2013
7953	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
7954	10^106636+97	106637	Lelio R Paula	02/2017
7955	10^106636-22923	106636	Patrick De Geest	03/2017
7956	2^354220-57	106631	Lelio R Paula	10/2011
7957	(68*10^106628-329)/9	106629	Robert Price	03/2021
7958	(29*10^106620-77)/3	106621	Robert Price	02/2020
7959	(746*10^106618+1)/9	106620	Robert Price	03/2020
7960	2*10^106613+29	106614	Robert Price	02/2021
7961	2^354157-17041	106612	Enzo Doria	05/2013
7962	12^98778+73	106600	Lelio R Paula	02/2017
7963	Phi(447629,-2)	106594	Henri Lifchitz	12/2025
7964	33333^1576+1576^33333	106585	Hans Havermann	11/2020
7965	2^354064+1870651	106584	Enzo Doria	05/2016
7966	24568^21779+21779^24568	106577	Hans Havermann	11/2020
7967	2^353992-57	106563	Lelio R Paula	10/2011
7968	9*10^106559+59	106560	Robert Price	01/2020
7969	7*10^106553+27	106554	Robert Price	11/2020
7970	28847^4938+4938^28847	106548	Hans Havermann	10/2020
7971	(20^81901-1)/42030774209	106546	Paul Vanderveen	06/2025
7973	NSW(139160)	106535	Robert Price	12/2018
7972	f(278321)	106535	Robert Price	07/2023
7974	(7*10^106516+113)/3	106517	Robert Price	02/2018
7975	2^353832-1853849	106515	Enzo Doria	09/2015
7978	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
7976	Phi(126037,7)	106513	Henri Lifchitz	12/2025
7977	Phi(252074,-7)	106513	Henri Lifchitz	02/2026
7979	2^353794-18453	106503	Enzo Doria	05/2013
7980	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
7981	2^353728+7695	106483	Lelio R Paula	01/2017
7982	26476^10509+10509^26476	106475	Hans Havermann	10/2020
7983	2^353672-303	106466	Yves Minet	02/2012
7984	6^136811+101	106460	Lelio R Paula	02/2017
7985	2^353641+1871981	106457	Enzo Doria	05/2016
7986	(8*10^106454-29)/3	106455	Robert Price	07/2018
7987	27845^6654+6654^27845	106454	Hans Havermann	11/2020
7988	10^106449-700001	106449	Robert Price	08/2021
7989	25316^16017+16017^25316	106444	Hans Havermann	11/2020
7990	2^353553+54615	106431	Lelio R Paula	01/2017
7991	2^353544-18897	106428	Enzo Doria	05/2013
7992	28894^4823+4823^28894	106426	Hans Havermann	11/2020
7993	(19*10^106422+29)/3	106423	Robert Price	12/2021
7994	(694*10^106418+53)/9	106420	Robert Price	02/2022
7995	6*10^106412-13	106413	Robert Price	07/2022
7996	25696^13829+13829^25696	106402	Hans Havermann	11/2020
7997	6^136729-133	106396	Lelio R Paula	02/2017
7998	2^353418+1605	106390	Lelio R Paula	01/2017
7999	2^353387+65	106381	Lelio R Paula	10/2011
8000	2^353372+74311	106376	Enzo Doria	04/2016

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