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 ?
6751	2^361563-109501	108842	Enzo Doria	04/2014
6752	12^100852+83	108838	Lelio R Paula	03/2017
6753	2^361497+767	108822	Lelio R Paula	01/2012
6754	L(520691)/78103651/1057002731/42794551909	108791	Serge Batalov	07/2024
6755	28019^7630+7630^28019	108785	Hans Havermann	10/2020
6756	24723^24758-24758^24723	108765	Norbert Schneider	11/2020
6757	2^361280-112349	108757	Enzo Doria	06/2014
6758	2^361271-5955	108754	Lelio R Paula	04/2017
6759	12^100757+19	108736	Lelio R Paula	03/2017
6760	25368^19333+19333^25368	108735	Hans Havermann	11/2020
6761	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
6762	2^361153-111546435	108718	Paul Bourdelais	10/2021
6763	14^94849-61	108710	Lelio R Paula	05/2017
6764	27267^9700+9700^27267	108708	Hans Havermann	11/2020
6765	(19^85009-5^85009)/14	108705	Robert Price	07/2013
6766	24832^23853+23853^24832	108704	Hans Havermann	11/2020
6767	27502^8963+8963^27502	108701	Hans Havermann	11/2020
6768	(130^51419-1)/129	108695	Anonymous	06/2024
6769	25807^16278+16278^25807	108689	Hans Havermann	11/2020
6770	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
6771	2^360973+1299	108664	Lelio R Paula	04/2017
6772	24^78728+23	108662	Anonymous	09/2024
6773	2^360959-109101	108660	Enzo Doria	04/2014
6774	6*5^155454+7	108659	Lelio R Paula	11/2014
6775	10^108656+79	108657	Lelio R Paula	02/2017
6776	10^108656-50001	108656	Patrick De Geest	03/2017
6777	2^360918-35	108648	Lelio R Paula	01/2012
6778	4*10^108646-47	108647	Robert Price	10/2021
6779	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
6780	3*10^108624-49	108625	Robert Price	07/2018
6781	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
6782	(134*10^108610+7)/3	108612	Robert Price	02/2020
6783	2*10^108609+29	108610	Robert Price	02/2021
6784	(10^108604+7)/71/191	108600	Alfred Reich	06/2021
6785	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
6786	2^360706-458903	108584	Enzo Doria	04/2015
6787	31112^3087+3087^31112	108567	Hans Havermann	11/2020
6788	2^360641-113185	108564	Enzo Doria	07/2014
6789	(29*10^108559-71)/3	108560	Robert Price	07/2021
6791	2^360618+75019	108557	Enzo Doria	04/2016
6790	2^360618+2025	108557	Henri Lifchitz	01/2025
6792	2^360607-216367	108554	Harrison Mesh	06/2022
6793	(14*10^108545-221)/9	108546	Robert Price	04/2018
6794	(44*10^108544-233)/9	108545	Robert Price	01/2019
6795	3*5^155286+2	108541	Lelio R Paula	11/2014
6796	7^128422+4	108530	Lelio R Paula	11/2014
6797	7^128421-80	108529	Lelio R Paula	03/2017
6798	2^360497+53807	108521	Yves Minet	07/2010
6799	2^360468-4559	108512	Yves Minet	03/2019
6800	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
6801	2^360366+1459	108481	Lelio R Paula	09/2011
6802	2^360364-1499	108481	Yves Minet	05/2013
6803	25662^16871+16871^25662	108477	Hans Havermann	10/2020
6804	25009^21748+21748^25009	108475	Hans Havermann	10/2020
6805	14^94642-23	108472	Lelio R Paula	05/2017
6806	(197*10^108446-11)/3	108448	Robert Price	03/2020
6807	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
6808	4*10^108412+9	108413	Robert Price	05/2015
6809	(259*10^108409-1)/3	108411	Robert Price	12/2020
6810	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
6811	133^51042-132	108406	Norbert Schneider	02/2019
6812	2^360093-351103	108399	Enzo Doria	06/2015
6813	2^360042+723	108384	Lelio R Paula	01/2012
6814	85^56164-2	108364	Lelio R Paula	10/2013
6815	2^359937-29323	108352	Enzo Doria	07/2015
6816	22^80712-23	108350	Anonymous	09/2024
6817	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
6818	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
6819	2^359898-19997	108341	Enzo Doria	06/2013
6820	(2^359886+2122)/2	108337	Stefano Morozzi	09/2020
6821	2*5^154948-7	108305	Lelio R Paula	11/2014
6822	10^108303+13	108304	Lelio R Paula	02/2017
6823	10^108303-207959	108303	Patrick De Geest	03/2017
6824	7*10^108300+69	108301	Robert Price	07/2019
6825	198^47155-47155^198	108300	Norman Luhn	09/2024
6826	2^359730+753	108290	Lelio R Paula	12/2011
6827	(8*10^108273+13)/3	108274	Robert Price	06/2018
6828	2^359650-19797	108266	Enzo Doria	06/2013
6829	(47*10^108261+259)/9	108262	Robert Price	03/2022
6830	91^55259-90^55259	108255	Robert Price	07/2015
6831	10^108251+85749	108252	Patrick De Geest	02/2021
6832	10^108251-50000000001	108251	Robert Price	12/2020
6833	10^108251-252081	108251	Patrick De Geest	02/2021
6834	4*10^108238-71	108239	Robert Price	12/2018
6835	3^226845+68	108233	Lelio R Paula	03/2017
6836	31836^2509+2509^31836	108227	Hans Havermann	10/2020
6837	5^154822-12866	108216	Enzo Doria	05/2014
6838	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
6839	2^359454-177	108207	Lelio R Paula	12/2011
6840	(19*10^108184+191)/3	108185	Robert Price	05/2019
6841	6^139022-59	108181	Lelio R Paula	02/2017
6842	(19*10^108176-43)/3	108177	Robert Price	05/2019
6843	2^359352-179	108176	Lelio R Paula	12/2011
6844	2^359338-1858781	108172	Enzo Doria	04/2016
6845	12^100230-97	108167	Lelio R Paula	03/2017
6846	27028^10043+10043^27028	108163	Hans Havermann	11/2020
6847	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
6848	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
6849	26583^11702+11702^26583	108147	Hans Havermann	11/2020
6850	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
6851	6^138956-59	108129	Lelio R Paula	02/2017
6852	2^359184+30285	108126	Lelio R Paula	04/2017
6853	13^97059+10	108119	Lelio R Paula	03/2017
6854	2^359137-81	108112	Lelio R Paula	12/2011
6856	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
6855	2^359110-11655	108103	Lelio R Paula	04/2017
6857	2^359069-933075	108091	Paul Bourdelais	06/2021
6858	26227^13222+13222^26227	108090	Hans Havermann	10/2020
6859	8*6^138875+5	108067	Lelio R Paula	11/2014
6860	2^358987-216919	108066	Enzo Doria	05/2014
6861	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
6862	39^67918-67918^39	108062	Norbert Schneider	02/2017
6863	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
6864	25282^18767+18767^25282	108040	Hans Havermann	11/2020
6865	2^358785-16933	108006	Enzo Doria	05/2013
6866	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
6867	6^138770-77	107985	Lelio R Paula	02/2017
6868	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
6869	10^107976+19	107977	Lelio R Paula	02/2017
6870	10^107976-202103	107976	Patrick De Geest	03/2017
6871	2^358684+75781	107975	Enzo Doria	04/2016
6872	24928^21411+21411^24928	107955	Hans Havermann	10/2020
6873	99^54094+2	107952	Lelio R Paula	06/2013
6874	(2^358583-9)/391	107942	Lelio R Paula	12/2013
6875	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
6876	2^358538+55	107931	Lelio R Paula	12/2011
6877	2^358517-109009	107925	Enzo Doria	03/2014
6878	26395^12258+12258^26395	107914	Hans Havermann	10/2020
6879	3^226159+104	107906	Lelio R Paula	03/2017
6880	7*10^107870+39	107871	Robert Price	01/2023
6881	2^358310-11655	107863	Lelio R Paula	03/2017
6882	(68*10^107852-329)/9	107853	Robert Price	03/2021
6883	2^358275-112987	107852	Enzo Doria	07/2014
6884	3^226038+4	107848	Tyler NeSmith	01/2021
6885	2^358233-20005	107839	Enzo Doria	06/2013
6886	2^358194+175	107828	Lelio R Paula	12/2011
6887	107^53125-106	107812	Norbert Schneider	12/2016
6888	(25*10^107804+161)/3	107805	Robert Price	09/2019
6889	3^225922-2	107793	Lelio R Paula	10/2013
6890	12^99874-95	107783	Lelio R Paula	03/2017
6891	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
6892	2^358030-171	107778	Lelio R Paula	12/2011
6893	11^103488-4170	107772	Enzo Doria	12/2012
6894	2^357930-4547	107748	Yves Minet	03/2019
6895	2^357911-20089	107742	Enzo Doria	06/2013
6896	2^357885+12857	107735	Yves Minet	07/2010
6897	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
6898	7^127473+40	107728	Lelio R Paula	03/2017
6899	5*2^357850+9	107725	Lelio R Paula	09/2014
6900	2^357786-291191	107705	Enzo Doria	06/2015
6901	28907^5320+5320^28907	107705	Hans Havermann	10/2020
6902	18^85798-23	107700	Lelio R Paula	04/2017
6903	3*10^107697+61	107698	Robert Price	09/2020
6904	(14*10^107694-83)/3	107695	Robert Price	12/2018
6905	2^357688-1854269	107675	Enzo Doria	09/2015
6906	2^357671-112225	107670	Enzo Doria	06/2014
6907	34323^1370+1370^34323	107662	Hans Havermann	11/2020
6908	2^357618-21005	107654	Enzo Doria	06/2013
6909	2^357615-17505	107653	Enzo Doria	05/2013
6910	26350^12171+12171^26350	107649	Hans Havermann	11/2020
6911	(30^72871-1)/29	107638	Robert Price	12/2011
6912	25021^20026+20026^25021	107631	Hans Havermann	11/2020
6913	2^357521+1870217	107625	Enzo Doria	05/2016
6914	2^357477-1203	107612	Lelio R Paula	03/2017
6915	26008^13693+13693^26008	107583	Hans Havermann	10/2020
6916	25432^16991+16991^25432	107583	Hans Havermann	10/2020
6917	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
6918	5^153894-18	107568	Lelio R Paula	02/2017
6919	2^357324-69059	107566	Enzo Doria	11/2015
6920	467^40296+40296^467	107563	Norbert Schneider	03/2019
6921	29446^4495+4495^29446	107559	Hans Havermann	10/2020
6922	(8*10^107556-149)/3	107557	Robert Price	12/2021
6923	2^357283-869688105	107553	Lelio R Paula	01/2017
6924	2^357280-16805	107552	Enzo Doria	05/2013
6925	10^107547+481719	107548	Patrick De Geest	03/2017
6926	10^107547-47	107547	Lelio R Paula	02/2017
6927	(23*10^107540+37)/3	107541	Robert Price	02/2022
6928	17^87396-32	107537	Lelio R Paula	04/2017
6929	(746*10^107505+1)/9	107507	Robert Price	03/2020
6930	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
6931	2^357081+107	107493	Lelio R Paula	12/2011
6932	2^357058-3911	107486	Yves Minet	04/2017
6933	3^225274+64	107484	Lelio R Paula	03/2017
6934	5*10^107482-57	107483	Robert Price	03/2021
6935	18^85619-95	107476	Lelio R Paula	04/2017
6936	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
6937	3^225248-130	107471	Lelio R Paula	03/2017
6938	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
6939	27029^9448+9448^27029	107450	Hans Havermann	11/2020
6940	2^356935-18085	107449	Enzo Doria	05/2013
6941	55396^87+87^55396	107442	Hans Havermann	10/2020
6942	(14*10^107439-137)/3	107440	Robert Price	04/2021
6943	164^48505-48505^164	107432	Norman Luhn	09/2024
6944	10^107409+37	107410	Lelio R Paula	02/2017
6945	10^107409-329633	107409	Patrick De Geest	03/2017
6946	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
6947	2^356787-109027	107404	Enzo Doria	04/2014
6948	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
6949	3*10^107389+77	107390	Robert Price	09/2018
6950	(11*10^107385+61)/9	107386	Tyler Busby	01/2023
6951	5^153622-42	107378	Lelio R Paula	02/2017
6952	2^356699-97305	107378	Lelio R Paula	03/2017
6953	13129^26072-26072^13129	107371	Norbert Schneider	09/2022
6954	2^356654+85	107364	Lelio R Paula	11/2011
6955	2^356641-19921	107360	Enzo Doria	06/2013
6956	5*10^107355+11	107356	Robert Price	08/2019
6957	2^356623-465	107355	Lelio R Paula	03/2017
6958	19^83945-92	107345	Lelio R Paula	02/2017
6959	25491^16246+16246^25491	107337	Hans Havermann	11/2020
6960	10^107334+28149	107335	Patrick De Geest	03/2017
6961	10^107334-83	107334	Lelio R Paula	02/2017
6962	2^356518+885	107323	Lelio R Paula	03/2017
6963	(59*10^107322+391)/9	107323	Robert Price	03/2021
6964	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
6965	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
6966	2^356442-114713	107300	Enzo Doria	04/2015
6967	2^356425+72257	107295	Enzo Doria	04/2016
6968	2^356351-112237	107273	Enzo Doria	06/2014
6970	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
6969	2^356322+74539	107264	Enzo Doria	04/2016
6971	2^356274+1874479	107250	Enzo Doria	06/2016
6972	24606^22819+22819^24606	107241	Hans Havermann	10/2020
6973	(2^356243+3686)/2	107240	Stefano Morozzi	09/2020
6974	20^82422-93	107234	Lelio R Paula	02/2017
6975	2^356157-20365	107214	Enzo Doria	06/2013
6976	8*10^107209+99	107210	Robert Price	03/2021
6977	2^356129-18949	107206	Enzo Doria	05/2013
6978	2^356100-109587	107197	Enzo Doria	04/2014
6979	2*10^107173-37	107174	Robert Price	11/2021
6980	(2^355978+3262)/2	107160	Stefano Morozzi	02/2021
6981	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
6982	2^355968-64875	107158	Lelio R Paula	01/2017
6983	2^355952+1870321	107153	Enzo Doria	05/2016
6984	27069^9088+9088^27069	107152	Hans Havermann	11/2020
6985	2^355915-117	107142	Lelio R Paula	11/2011
6986	(16*10^107140+77)/3	107141	Robert Price	03/2019
6987	24628^22369+22369^24628	107124	Hans Havermann	11/2020
6988	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
6989	3^224495-8	107112	Lelio R Paula	12/2013
6990	3*10^107096+23	107097	Robert Price	03/2022
6991	25077^18632+18632^25077	107086	Hans Havermann	10/2020
6992	7^126691-44	107067	Lelio R Paula	03/2017
6993	4^177830-8243	107065	Mike Oakes	02/2011
6994	(509*10^107057+13)/9	107059	Robert Price	05/2022
6995	2^355604+214051	107048	Enzo Doria	10/2023
6996	(2^355562+1702)/2	107035	Stefano Morozzi	09/2020
6997	10^107028+3593037	107029	Paul Bourdelais	10/2021
6998	10^107028-43301	107028	Alfred Reich	08/2024
6999	2^355524-21237	107024	Enzo Doria	06/2013
7000	24843^20320+20320^24843	107022	Hans Havermann	10/2020

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Probable Primes Top 10000

(300835 PRPs in the top)