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	26383^23008+23008^26383	115080	Hans Havermann	02/2021
6752	9^120590-120590	115073	Robert Price	03/2014
6753	28203^12016+12016^28203	115062	Hans Havermann	02/2021
6754	2^382198+9	115054	Lelio R Paula	03/2013
6755	18268*31^77131+22839	115035	Eric Chen	05/2024
6756	30101^6630+6630^30101	115032	Hans Havermann	01/2021
6757	(89*10^115030-179)/9	115031	Robert Price	12/2019
6758	25554^26089-26089^25554	114987	Frank Doornink	02/2024
6759	25142^26129-26129^25142	114979	Frank Doornink	12/2023
6760	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
6761	27300^16271+16271^27300	114972	Hans Havermann	02/2021
6762	(23*10^114962+7)/3	114963	Robert Price	05/2023
6763	2^381883-59197	114959	Enzo Doria	10/2015
6764	27423^15542+15542^27423	114944	Hans Havermann	02/2021
6765	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
6767	2^381806-4481	114936	Yves Minet	07/2011
6766	2^381808-1851507	114936	Enzo Doria	08/2015
6768	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
6769	2^381774-112373	114926	Enzo Doria	06/2014
6770	26341^22980+22980^26341	114883	Hans Havermann	01/2021
6771	(79^60539-1)/61747564999146	114867	Paul Vanderveen	05/2025
6772	2^381555-109051	114860	Enzo Doria	04/2014
6773	2^381551+213683	114859	Enzo Doria	09/2023
6774	2^381546-113501	114857	Enzo Doria	08/2014
6775	(7*10^114845-19)/3	114846	Robert Price	10/2020
6776	26675^20178+20178^26675	114833	Hans Havermann	02/2021
6777	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
6778	3^240644+16	114817	Robert Price	04/2020
6779	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
6780	2^381360-110429	114801	Enzo Doria	05/2014
6781	(17*10^114795+79)/3	114796	Robert Price	04/2019
6782	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
6783	2^381252-115079	114769	Enzo Doria	06/2015
6784	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
6785	2^381209-29323	114756	Enzo Doria	07/2015
6786	2^381207-111546435	114755	Paul Bourdelais	10/2021
6787	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
6788	2^381201+1873205	114753	Enzo Doria	06/2016
6790	(85*10^114737+293)/9	114738	Robert Price	12/2019
6791	(265*10^114736+17)/3	114738	Robert Price	03/2020
6789	379*10^114735+9	114738	Jason Yuen	01/2025
6792	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
6793	2^380974-112991	114685	Enzo Doria	07/2014
6794	37097^1234+1234^37097	114679	Hans Havermann	02/2021
6795	(26*10^114658-119)/3	114659	Robert Price	07/2023
6796	88^58949-87	114626	Norbert Schneider	11/2015
6797	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
6798	Phi(155285,10)/242674820198201	114610	Makoto Kamada	02/2024
6799	(10^155285-1)(10^2389-1)(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201	114610	Anonymous	04/2025
6800	29913^6782+6782^29913	114608	Hans Havermann	02/2021
6801	(331*10^114605-7)/9	114607	Robert Price	04/2022
6802	2^380700+91	114603	Lelio R Paula	03/2013
6803	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
6804	7*10^114577+27	114578	Robert Price	11/2020
6806	10^114575+3^114576	114576	Mike Oakes	09/2010
6805	10^114575+66561	114576	Patrick De Geest	02/2017
6807	10^114575-581081	114575	Patrick De Geest	02/2017
6808	2^380587-115315	114569	Enzo Doria	06/2015
6809	31874^3927+3927^31874	114558	Hans Havermann	02/2021
6810	2^380513-216925	114546	Enzo Doria	05/2014
6811	2^380451-1840087	114528	Enzo Doria	06/2015
6812	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
6813	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
6814	2^380279-461347	114476	Enzo Doria	07/2015
6815	(331*10^114454-7)/9	114456	Robert Price	04/2022
6816	27121^16590+16590^27121	114447	Hans Havermann	01/2021
6817	25966^25555+25555^25966	114445	Hans Havermann	01/2021
6818	(611*32^76029-53)/31	114437	Eric Chen	11/2023
6819	(11*10^114400+529)/9	114401	Robert Price	09/2021
6820	2^380021+1871147	114398	Enzo Doria	05/2016
6821	2^380005+1869707	114393	Enzo Doria	05/2016
6822	2^379958-113297	114379	Enzo Doria	07/2014
6823	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
6824	2^379881-109105	114356	Enzo Doria	04/2014
6825	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
6826	(4*10^114340+83)/3	114341	Robert Price	02/2018
6827	(26*10^114317-77)/3	114318	Robert Price	11/2019
6828	(4*10^114296+149)/9	114296	Robert Price	04/2018
6829	88^58773-87	114284	Norbert Schneider	11/2015
6830	27764^13065+13065^27764	114280	Hans Havermann	01/2021
6831	(132^53891-1)/131	114278	Anonymous	06/2024
6832	2^379529-2790283	114250	Enzo Doria	03/2016
6833	2^379522+1869115	114248	Enzo Doria	05/2016
6834	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
6835	2^379317-115033	114186	Enzo Doria	06/2015
6836	(22*10^114178+47)/3	114179	Robert Price	06/2021
6837	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
6838	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
6839	(228^48407-1)/227	114139	Alexander Zhirkov	03/2023
6840	6*10^114091+23	114092	Robert Price	09/2020
6841	(4*10^114076+143)/3	114077	Robert Price	03/2018
6842	332*25^81584+12357	114053	Eric Chen	10/2023
6843	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
6844	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
6845	13643^27572-27572^13643	114008	Norbert Schneider	12/2022
6847	(46*10^113969+683)/9	113970	Robert Price	03/2019
6846	(83*10^113969+133)/9	113970	Robert Price	08/2021
6848	32226^3439+3439^32226	113966	Hans Havermann	02/2021
6849	(77*10^113963-149)/9	113964	Robert Price	03/2022
6850	78*10^113954-7	113956	Robert Price	10/2020
6851	2*10^113941+9	113942	Dmitry Domanov	11/2010
6852	10^113933+145897	113934	Patrick De Geest	02/2021
6855	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
6853	10^113933-8000000001	113933	Robert Price	11/2020
6854	10^113933-66167	113933	Patrick De Geest	02/2021
6856	2339662057597*10^113903+9	113916	Robert Price	03/2021
6857	4*10^113905+91	113906	Robert Price	08/2018
6858	10^113894+76609	113895	Patrick De Geest	02/2021
6860	10^113894-10000001	113894	Robert Price	09/2020
6859	10^113894-373947	113894	Patrick De Geest	02/2021
6861	33933^2270+2270^33933	113881	Hans Havermann	02/2021
6862	4*10^113874-21	113875	Robert Price	09/2018
6863	2^378272-16565	113872	Enzo Doria	04/2013
6864	2^378217-109075	113855	Enzo Doria	04/2014
6865	2^378198+67	113849	Lelio R Paula	03/2013
6866	2^378173-3249	113842	Yves Minet	12/2014
6867	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
6868	2^378137+1334025	113831	Henri Lifchitz	10/2024
6869	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
6870	30030^6173+6173^30030	113829	Hans Havermann	01/2021
6871	2^378128-262977	113828	Enzo Doria	05/2014
6872	2^378123-113215	113827	Enzo Doria	07/2014
6873	6^146274-18893	113824	Enzo Doria	03/2013
6874	34596^1949+1949^34596	113815	Hans Havermann	02/2021
6875	2^378078+75	113813	Lelio R Paula	03/2013
6876	(28*10^113810+449)/9	113811	Robert Price	11/2021
6877	26273^21448+21448^26273	113799	Hans Havermann	02/2021
6878	2^377966+255255	113780	Paul Bourdelais	10/2021
6879	2^377940+63	113772	Lelio R Paula	03/2013
6880	2^377941-2785843	113772	Enzo Doria	04/2016
6881	(7*10^113757+11)/9	113757	Tyler Busby	01/2023
6882	2^377810+1875109	113733	Enzo Doria	09/2016
6883	2^377803-1838635	113731	Enzo Doria	05/2015
6884	2^377799+52223	113729	Yves Minet	08/2010
6885	(2^377791+3258)/2	113727	Stefano Morozzi	02/2021
6886	11^109190-270	113710	Enzo Doria	12/2012
6887	28206^10739+10739^28206	113698	Hans Havermann	01/2021
6888	7*10^113693+9	113694	Robert Price	09/2015
6889	13899^27442+27442^13899	113692	Norbert Schneider	12/2020
6890	(82*10^113681+161)/9	113682	Robert Price	10/2019
6891	26121^22478+22478^26121	113673	Hans Havermann	01/2021
6892	4*10^113658+49	113659	Robert Price	01/2019
6893	(10^113656+7)/40231/6439001	113645	Alfred Reich	06/2021
6894	(2*10^113631+529)/9	113631	Robert Price	01/2018
6895	2^377408-2798279	113612	Enzo Doria	04/2016
6896	(292^46336+1)/(292^256+1)	113605	Martin Hopf	12/2023
6897	13706^27459+27459^13706	113596	Norbert Schneider	12/2020
6898	5*10^113586+57	113587	Robert Price	12/2018
6899	(2^377242+2794)/2	113561	Stefano Morozzi	02/2021
6900	2^377222+93679	113556	Yves Minet	02/2011
6902	262147#+316847	113552	Makoto Morimoto	02/2016
6901	27172^15101+15101^27172	113552	Hans Havermann	01/2021
6903	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
6904	2^377026-458903	113497	Enzo Doria	04/2015
6905	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
6906	34791^1828+1828^34791	113488	Hans Havermann	02/2021
6907	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
6908	(29*10^113468-17)/3	113469	Robert Price	09/2019
6909	35^73477-34^73477	113454	Robert Price	05/2012
6910	(14*10^113451-89)/3	113452	Robert Price	05/2020
6911	2^376790+27	113426	Lelio R Paula	03/2013
6912	2^376786-112701	113424	Enzo Doria	06/2014
6913	2^376731+21	113408	Lelio R Paula	03/2013
6914	9*10^113394-73	113395	Robert Price	01/2021
6915	29660^6651+6651^29660	113387	Hans Havermann	01/2021
6917	2^376634+1871245	113379	Enzo Doria	05/2016
6916	(4^188318+17)/3	113379	Robert Price	02/2017
6918	E(29532)/492842728006750534663978950979381235	113367	Thomas Ritschel	01/2021
6919	2^376576-344369	113361	Enzo Doria	07/2015
6920	2^376549-4543	113353	Yves Minet	03/2019
6921	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
6922	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
6923	(2^376350+3538)/2	113293	Stefano Morozzi	09/2020
6924	27265^14272+14272^27265	113273	Hans Havermann	02/2021
6925	32174^3315+3315^32174	113269	Hans Havermann	02/2021
6926	(2*10^113248+73)/3	113248	Robert Price	09/2020
6927	2^376128-21237	113226	Enzo Doria	06/2013
6928	5*10^113224-81	113225	Robert Price	01/2019
6929	10^113220+51409	113221	Patrick De Geest	02/2021
6931	10^113220-1000001	113220	Robert Price	08/2020
6930	10^113220-61779	113220	Patrick De Geest	02/2021
6932	(2^376102+1578)/2	113218	Stefano Morozzi	09/2020
6933	(2^375996+3102)/2	113186	Stefano Morozzi	09/2020
6934	37258^1091+1091^37258	113184	Hans Havermann	02/2021
6935	(94*10^113176+11)/3	113178	Robert Price	04/2020
6936	(46*10^113162+521)/9	113163	Robert Price	02/2019
6937	14*29^77375+17875	113155	Eric Chen	06/2025
6938	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
6939	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
6940	3*10^113137+23	113138	Robert Price	03/2022
6941	(8*10^113135-269)/9	113135	Robert Price	09/2021
6942	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
6943	26050^21959+21959^26050	113100	Hans Havermann	02/2021
6944	2^375638-1787171	113079	Enzo Doria	03/2016
6945	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
6946	2^375537+4847	113048	Yves Minet	02/2011
6947	(17^91837+16^91837)/33	113000	Robert Price	08/2013
6948	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
6949	2^375350-3221	112992	Yves Minet	07/2011
6950	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
6951	2^375305+76757	112979	Enzo Doria	05/2016
6952	2^375258+1874989	112964	Enzo Doria	07/2016
6953	(29^77237-1)/28	112950	Robert Price	04/2012
6954	26620^17483+17483^26620	112939	Hans Havermann	01/2021
6955	2^375154+74959	112933	Enzo Doria	04/2016
6956	(266*10^112930-17)/3	112932	Robert Price	07/2020
6957	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
6958	(85*10^112919+293)/9	112920	Robert Price	12/2019
6959	29412^6899+6899^29412	112907	Hans Havermann	02/2021
6960	(191*10^112903-17)/3	112905	Robert Price	11/2021
6961	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
6962	25992^22039+22039^25992	112889	Hans Havermann	02/2021
6963	2^374993-2787163	112885	Enzo Doria	11/2015
6964	(697*10^112869+23)/9	112871	Robert Price	04/2021
6965	(19*10^112851+377)/9	112852	Alfred Reich	11/2022
6966	30420^5111+5111^30420	112813	Hans Havermann	02/2021
6967	13699^27268+27268^13699	112800	Norbert Schneider	12/2020
6968	123^53970+2	112793	Lelio R Paula	06/2013
6969	12308*27^78796+23	112790	Eric Chen	07/2023
6970	28942^7887+7887^28942	112785	Hans Havermann	01/2021
6971	2^374640-4685	112778	Yves Minet	05/2019
6972	12^104501-11	112776	Riley Fisher	12/2023
6973	57290^93+93^57290	112775	Hans Havermann	01/2021
6974	115^54726-54726^115	112774	Norman Luhn	09/2024
6975	13608^27277-27277^13608	112758	Norbert Schneider	12/2022
6976	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
6977	p(22852)#/2+512	112745	Robert Price	05/2017
6978	(11*10^112742-131)/3	112743	Robert Price	09/2018
6979	2^374441-21049	112718	Enzo Doria	06/2013
6980	(15056!^2+1)/(30113*454287444157)	112711	Michael Porter	09/2025
6981	4*10^112706-93	112707	Robert Price	07/2020
6982	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
6983	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
6984	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
6985	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
6986	3^236011-8828	112606	Enzo Doria	05/2014
6987	31854^3427+3427^31854	112602	Hans Havermann	02/2021
6988	(85*10^112530-373)/9	112531	Robert Price	05/2021
6989	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
6990	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
6991	27618^11821+11821^27618	112479	Hans Havermann	01/2021
6992	U(602921)/4823369	112479	Serge Batalov	07/2024
6993	26343^18580+18580^26343	112460	Hans Havermann	01/2021
6994	39^70666+2	112435	Lelio R Paula	11/2013
6995	(134*10^112400+7)/3	112402	Robert Price	02/2020
6996	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
6997	(2^373350-7)/3	112390	Lelio R Paula	03/2014
6998	3^235532-235532	112378	Anonymous	09/2025
6999	2^373306-1840931	112377	Enzo Doria	06/2015
7000	8*10^112371-37	112372	Robert Price	03/2022

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