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	24874^24243+24243^24874	109063	Hans Havermann	11/2020
7752	(17*10^109059-161)/9	109060	Robert Price	02/2021
7753	29158^5495+5495^29158	109050	Hans Havermann	11/2020
7754	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
7755	2*7^129008+9	109025	Lelio R Paula	11/2014
7756	88*10^109022+7	109024	Robert Price	03/2020
7757	28194^7337+7337^28194	108985	Hans Havermann	10/2020
7758	(5*10^108960+91)/3	108961	Robert Price	04/2018
7759	2^361957+76367	108960	Enzo Doria	05/2016
7760	(11*29^74504-245655)/28	108955	Eric Chen	06/2025
7761	2^361873-1411	108935	Yves Minet	01/2013
7762	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
7763	216^216^216+91^91^91	108917	Henri Lifchitz	03/2025
7764	47^65132-65132^47	108908	Norman Luhn	09/2024
7765	115^52842-114	108892	Norbert Schneider	07/2018
7766	13^97745-24	108883	Lelio R Paula	03/2017
7767	(2^361696+2562)/2	108882	Stefano Morozzi	09/2020
7768	17^88475+8	108864	Lelio R Paula	04/2017
7769	2^361567+51	108843	Lelio R Paula	01/2012
7770	2^361563-109501	108842	Enzo Doria	04/2014
7771	12^100852+83	108838	Lelio R Paula	03/2017
7772	2^361497+767	108822	Lelio R Paula	01/2012
7773	L(520691)/78103651/1057002731/42794551909	108791	Serge Batalov	07/2024
7774	28019^7630+7630^28019	108785	Hans Havermann	10/2020
7775	24723^24758-24758^24723	108765	Norbert Schneider	11/2020
7776	2^361280-112349	108757	Enzo Doria	06/2014
7777	2^361271-5955	108754	Lelio R Paula	04/2017
7778	12^100757+19	108736	Lelio R Paula	03/2017
7779	25368^19333+19333^25368	108735	Hans Havermann	11/2020
7780	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
7781	2^361153-111546435	108718	Paul Bourdelais	10/2021
7782	14^94849-61	108710	Lelio R Paula	05/2017
7783	27267^9700+9700^27267	108708	Hans Havermann	11/2020
7784	(19^85009-5^85009)/14	108705	Robert Price	07/2013
7785	24832^23853+23853^24832	108704	Hans Havermann	11/2020
7786	27502^8963+8963^27502	108701	Hans Havermann	11/2020
7787	(130^51419-1)/129	108695	Anonymous	06/2024
7788	25807^16278+16278^25807	108689	Hans Havermann	11/2020
7789	39^68306+38	108680	Alfred Reich	03/2026
7790	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
7791	2^360973+1299	108664	Lelio R Paula	04/2017
7792	24^78728+23	108662	Anonymous	09/2024
7793	2^360959-109101	108660	Enzo Doria	04/2014
7794	6*5^155454+7	108659	Lelio R Paula	11/2014
7795	10^108656+79	108657	Lelio R Paula	02/2017
7796	10^108656-50001	108656	Patrick De Geest	03/2017
7797	2^360918-35	108648	Lelio R Paula	01/2012
7798	4*10^108646-47	108647	Robert Price	10/2021
7799	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
7800	3*10^108624-49	108625	Robert Price	07/2018
7801	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
7802	(134*10^108610+7)/3	108612	Robert Price	02/2020
7803	2*10^108609+29	108610	Robert Price	02/2021
7804	(10^108604+7)/71/191	108600	Alfred Reich	06/2021
7805	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
7806	2^360706-458903	108584	Enzo Doria	04/2015
7807	31112^3087+3087^31112	108567	Hans Havermann	11/2020
7808	2^360641-113185	108564	Enzo Doria	07/2014
7809	(29*10^108559-71)/3	108560	Robert Price	07/2021
7811	2^360618+75019	108557	Enzo Doria	04/2016
7810	2^360618+2025	108557	Henri Lifchitz	01/2025
7812	2^360607-216367	108554	Harrison Mesh	06/2022
7813	29^74228+556	108551	Eric Chen	06/2025
7814	(14*10^108545-221)/9	108546	Robert Price	04/2018
7815	(44*10^108544-233)/9	108545	Robert Price	01/2019
7816	3*5^155286+2	108541	Lelio R Paula	11/2014
7817	7^128422+4	108530	Lelio R Paula	11/2014
7818	7^128421-80	108529	Lelio R Paula	03/2017
7819	2^360497+53807	108521	Yves Minet	07/2010
7820	2^360468-4559	108512	Yves Minet	03/2019
7821	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
7822	2^360366+1459	108481	Lelio R Paula	09/2011
7823	2^360364-1499	108481	Yves Minet	05/2013
7824	25662^16871+16871^25662	108477	Hans Havermann	10/2020
7825	25009^21748+21748^25009	108475	Hans Havermann	10/2020
7826	14^94642-23	108472	Lelio R Paula	05/2017
7827	(197*10^108446-11)/3	108448	Robert Price	03/2020
7828	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
7829	4*10^108412+9	108413	Robert Price	05/2015
7830	(259*10^108409-1)/3	108411	Robert Price	12/2020
7831	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
7832	133^51042-132	108406	Norbert Schneider	02/2019
7833	2^360093-351103	108399	Enzo Doria	06/2015
7834	2^360042+723	108384	Lelio R Paula	01/2012
7835	85^56164-2	108364	Lelio R Paula	10/2013
7836	2^359937-29323	108352	Enzo Doria	07/2015
7837	22^80712-23	108350	Anonymous	09/2024
7838	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
7839	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
7840	2^359898-19997	108341	Enzo Doria	06/2013
7841	(2^359886+2122)/2	108337	Stefano Morozzi	09/2020
7842	2*5^154948-7	108305	Lelio R Paula	11/2014
7843	10^108303+13	108304	Lelio R Paula	02/2017
7844	10^108303-207959	108303	Patrick De Geest	03/2017
7845	7*10^108300+69	108301	Robert Price	07/2019
7846	198^47155-47155^198	108300	Norman Luhn	09/2024
7847	2^359730+753	108290	Lelio R Paula	12/2011
7848	(8*10^108273+13)/3	108274	Robert Price	06/2018
7849	2^359650-19797	108266	Enzo Doria	06/2013
7850	(47*10^108261+259)/9	108262	Robert Price	03/2022
7851	91^55259-90^55259	108255	Robert Price	07/2015
7852	10^108251+85749	108252	Patrick De Geest	02/2021
7853	10^108251-50000000001	108251	Robert Price	12/2020
7854	10^108251-252081	108251	Patrick De Geest	02/2021
7855	4*10^108238-71	108239	Robert Price	12/2018
7856	3^226845+68	108233	Lelio R Paula	03/2017
7857	31836^2509+2509^31836	108227	Hans Havermann	10/2020
7858	5^154822-12866	108216	Enzo Doria	05/2014
7859	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
7860	2^359454-177	108207	Lelio R Paula	12/2011
7861	(19*10^108184+191)/3	108185	Robert Price	05/2019
7862	6^139022-59	108181	Lelio R Paula	02/2017
7863	(19*10^108176-43)/3	108177	Robert Price	05/2019
7864	2^359352-179	108176	Lelio R Paula	12/2011
7865	2^359338-1858781	108172	Enzo Doria	04/2016
7866	12^100230-97	108167	Lelio R Paula	03/2017
7867	27028^10043+10043^27028	108163	Hans Havermann	11/2020
7868	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
7869	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
7870	26583^11702+11702^26583	108147	Hans Havermann	11/2020
7871	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
7872	6^138956-59	108129	Lelio R Paula	02/2017
7873	2^359184+30285	108126	Lelio R Paula	04/2017
7874	13^97059+10	108119	Lelio R Paula	03/2017
7875	2^359137-81	108112	Lelio R Paula	12/2011
7877	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
7876	2^359110-11655	108103	Lelio R Paula	04/2017
7878	2^359069-933075	108091	Paul Bourdelais	06/2021
7879	26227^13222+13222^26227	108090	Hans Havermann	10/2020
7880	8*6^138875+5	108067	Lelio R Paula	11/2014
7881	2^358987-216919	108066	Enzo Doria	05/2014
7882	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
7883	39^67918-67918^39	108062	Norbert Schneider	02/2017
7884	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
7885	25282^18767+18767^25282	108040	Hans Havermann	11/2020
7886	(918^36457-1)/917	108014	Tom Wu	08/2025
7887	2^358785-16933	108006	Enzo Doria	05/2013
7888	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
7889	6^138770-77	107985	Lelio R Paula	02/2017
7890	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
7891	10^107976+19	107977	Lelio R Paula	02/2017
7892	10^107976-202103	107976	Patrick De Geest	03/2017
7893	2^358684+75781	107975	Enzo Doria	04/2016
7894	24928^21411+21411^24928	107955	Hans Havermann	10/2020
7895	99^54094+2	107952	Lelio R Paula	06/2013
7896	(2^358583-9)/391	107942	Lelio R Paula	12/2013
7897	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
7898	2^358538+55	107931	Lelio R Paula	12/2011
7899	2^358517-109009	107925	Enzo Doria	03/2014
7900	26395^12258+12258^26395	107914	Hans Havermann	10/2020
7901	3^226159+104	107906	Lelio R Paula	03/2017
7902	7*10^107870+39	107871	Robert Price	01/2023
7903	2^358310-11655	107863	Lelio R Paula	03/2017
7904	(68*10^107852-329)/9	107853	Robert Price	03/2021
7905	2^358275-112987	107852	Enzo Doria	07/2014
7906	3^226038+4	107848	Tyler NeSmith	01/2021
7907	2^358233-20005	107839	Enzo Doria	06/2013
7908	2^358194+175	107828	Lelio R Paula	12/2011
7909	107^53125-106	107812	Norbert Schneider	12/2016
7910	(25*10^107804+161)/3	107805	Robert Price	09/2019
7911	3^225922-2	107793	Lelio R Paula	10/2013
7912	12^99874-95	107783	Lelio R Paula	03/2017
7913	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
7914	2^358030-171	107778	Lelio R Paula	12/2011
7915	11^103488-4170	107772	Enzo Doria	12/2012
7916	2^357930-4547	107748	Yves Minet	03/2019
7917	2^357911-20089	107742	Enzo Doria	06/2013
7918	2^357885+12857	107735	Yves Minet	07/2010
7919	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
7920	7^127473+40	107728	Lelio R Paula	03/2017
7921	5*2^357850+9	107725	Lelio R Paula	09/2014
7922	2^357786-291191	107705	Enzo Doria	06/2015
7923	28907^5320+5320^28907	107705	Hans Havermann	10/2020
7924	18^85798-23	107700	Lelio R Paula	04/2017
7925	3*10^107697+61	107698	Robert Price	09/2020
7926	(14*10^107694-83)/3	107695	Robert Price	12/2018
7927	2^357688-1854269	107675	Enzo Doria	09/2015
7928	2^357671-112225	107670	Enzo Doria	06/2014
7929	34323^1370+1370^34323	107662	Hans Havermann	11/2020
7930	2^357618-21005	107654	Enzo Doria	06/2013
7931	2^357615-17505	107653	Enzo Doria	05/2013
7932	26350^12171+12171^26350	107649	Hans Havermann	11/2020
7934	(30^72871-1)/29	107638	Robert Price	12/2011
7933	Phi(72871,5#)	107638	Henri Lifchitz	12/2025
7935	25021^20026+20026^25021	107631	Hans Havermann	11/2020
7936	2^357521+1870217	107625	Enzo Doria	05/2016
7937	2^357477-1203	107612	Lelio R Paula	03/2017
7938	26008^13693+13693^26008	107583	Hans Havermann	10/2020
7939	25432^16991+16991^25432	107583	Hans Havermann	10/2020
7940	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
7941	5^153894-18	107568	Lelio R Paula	02/2017
7942	2^357324-69059	107566	Enzo Doria	11/2015
7943	467^40296+40296^467	107563	Norbert Schneider	03/2019
7944	29446^4495+4495^29446	107559	Hans Havermann	10/2020
7945	(8*10^107556-149)/3	107557	Robert Price	12/2021
7946	2^357283-869688105	107553	Lelio R Paula	01/2017
7947	2^357280-16805	107552	Enzo Doria	05/2013
7948	10^107547+481719	107548	Patrick De Geest	03/2017
7949	10^107547-47	107547	Lelio R Paula	02/2017
7950	(23*10^107540+37)/3	107541	Robert Price	02/2022
7951	17^87396-32	107537	Lelio R Paula	04/2017
7952	(746*10^107505+1)/9	107507	Robert Price	03/2020
7953	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
7954	2^357081+107	107493	Lelio R Paula	12/2011
7955	2^357058-3911	107486	Yves Minet	04/2017
7956	3^225274+64	107484	Lelio R Paula	03/2017
7957	5*10^107482-57	107483	Robert Price	03/2021
7958	18^85619-95	107476	Lelio R Paula	04/2017
7959	Phi(118283,10)/102584248160709208281690489429805181088536061161	107473	Anonymous	01/2026
7960	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
7961	3^225248-130	107471	Lelio R Paula	03/2017
7962	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
7963	27029^9448+9448^27029	107450	Hans Havermann	11/2020
7964	2^356935-18085	107449	Enzo Doria	05/2013
7965	55396^87+87^55396	107442	Hans Havermann	10/2020
7966	(14*10^107439-137)/3	107440	Robert Price	04/2021
7967	164^48505-48505^164	107432	Norman Luhn	09/2024
7968	10^107409+37	107410	Lelio R Paula	02/2017
7969	10^107409-329633	107409	Patrick De Geest	03/2017
7970	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
7971	2^356787-109027	107404	Enzo Doria	04/2014
7972	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
7973	3*10^107389+77	107390	Robert Price	09/2018
7974	(11*10^107385+61)/9	107386	Tyler Busby	01/2023
7975	5^153622-42	107378	Lelio R Paula	02/2017
7976	2^356699-97305	107378	Lelio R Paula	03/2017
7977	13129^26072-26072^13129	107371	Norbert Schneider	09/2022
7978	2^356654+85	107364	Lelio R Paula	11/2011
7979	2^356641-19921	107360	Enzo Doria	06/2013
7980	5*10^107355+11	107356	Robert Price	08/2019
7981	2^356623-465	107355	Lelio R Paula	03/2017
7982	19^83945-92	107345	Lelio R Paula	02/2017
7983	25491^16246+16246^25491	107337	Hans Havermann	11/2020
7984	10^107334+28149	107335	Patrick De Geest	03/2017
7985	10^107334-83	107334	Lelio R Paula	02/2017
7986	2^356518+885	107323	Lelio R Paula	03/2017
7987	(59*10^107322+391)/9	107323	Robert Price	03/2021
7988	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
7989	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
7990	2^356442-114713	107300	Enzo Doria	04/2015
7991	2^356425+72257	107295	Enzo Doria	04/2016
7992	2^356351-112237	107273	Enzo Doria	06/2014
7994	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
7993	2^356322+74539	107264	Enzo Doria	04/2016
7995	2^356274+1874479	107250	Enzo Doria	06/2016
7996	24606^22819+22819^24606	107241	Hans Havermann	10/2020
7997	(2^356243+3686)/2	107240	Stefano Morozzi	09/2020
7998	20^82422-93	107234	Lelio R Paula	02/2017
7999	2^356157-20365	107214	Enzo Doria	06/2013
8000	8*10^107209+99	107210	Robert Price	03/2021

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Probable Primes Top 10000

(303264 PRPs in the top)