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	(191*10^112903-17)/3	112905	Robert Price	11/2021
6752	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
6753	25992^22039+22039^25992	112889	Hans Havermann	02/2021
6754	2^374993-2787163	112885	Enzo Doria	11/2015
6755	(697*10^112869+23)/9	112871	Robert Price	04/2021
6756	(19*10^112851+377)/9	112852	Alfred Reich	11/2022
6757	30420^5111+5111^30420	112813	Hans Havermann	02/2021
6758	13699^27268+27268^13699	112800	Norbert Schneider	12/2020
6759	123^53970+2	112793	Lelio R Paula	06/2013
6760	12308*27^78796+23	112790	Eric Chen	07/2023
6761	28942^7887+7887^28942	112785	Hans Havermann	01/2021
6762	2^374640-4685	112778	Yves Minet	05/2019
6763	12^104501-11	112776	Riley Fisher	12/2023
6764	57290^93+93^57290	112775	Hans Havermann	01/2021
6765	115^54726-54726^115	112774	Norman Luhn	09/2024
6766	13608^27277-27277^13608	112758	Norbert Schneider	12/2022
6767	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
6768	p(22852)#/2+512	112745	Robert Price	05/2017
6769	(11*10^112742-131)/3	112743	Robert Price	09/2018
6770	2^374441-21049	112718	Enzo Doria	06/2013
6771	4*10^112706-93	112707	Robert Price	07/2020
6772	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
6773	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
6774	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
6775	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
6776	3^236011-8828	112606	Enzo Doria	05/2014
6777	31854^3427+3427^31854	112602	Hans Havermann	02/2021
6778	(85*10^112530-373)/9	112531	Robert Price	05/2021
6779	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
6780	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
6781	27618^11821+11821^27618	112479	Hans Havermann	01/2021
6782	U(602921)/4823369	112479	Serge Batalov	07/2024
6783	26343^18580+18580^26343	112460	Hans Havermann	01/2021
6784	39^70666+2	112435	Lelio R Paula	11/2013
6785	(134*10^112400+7)/3	112402	Robert Price	02/2020
6786	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
6787	(2^373350-7)/3	112390	Lelio R Paula	03/2014
6788	2^373306-1840931	112377	Enzo Doria	06/2015
6789	8*10^112371-37	112372	Robert Price	03/2022
6790	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
6791	6*10^112359-79	112360	Robert Price	03/2022
6792	34409^1842+1842^34409	112356	Hans Havermann	02/2021
6793	(142*10^112352-7)/9	112354	Robert Price	12/2019
6794	25580^24633+24633^25580	112336	Hans Havermann	01/2021
6795	2^373117+1872107	112320	Enzo Doria	05/2016
6796	(2^373083+2226)/2	112309	Stefano Morozzi	01/2021
6797	(35*10^112308+37)/9	112309	Robert Price	05/2022
6798	27963^10376+10376^27963	112301	Hans Havermann	01/2021
6799	2^373040+2792761	112297	Enzo Doria	03/2016
6800	(156^51203-1)/155	112293	Anonymous	06/2024
6801	EPrime(112280)	112280	Eric W. Weisstein	10/2010
6802	2^372950+7	112270	Lelio R Paula	03/2013
6803	2^372945+1872167	112268	Enzo Doria	05/2016
6804	36274^1243+1243^36274	112249	Hans Havermann	02/2021
6805	(55*10^112246+629)/9	112247	Robert Price	01/2022
6806	(2^372872+3798)/2	112246	Stefano Morozzi	02/2021
6807	25513^25060+25060^25513	112232	Hans Havermann	02/2021
6808	(53*10^112229-611)/9	112230	Robert Price	02/2022
6809	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020
6810	6*10^112208+43	112209	Robert Price	07/2020
6811	(2^372728+3058)/2	112203	Stefano Morozzi	09/2020
6812	32061^3158+3158^32061	112195	Hans Havermann	02/2021
6813	2^372695+72113	112193	Enzo Doria	04/2016
6814	2^372689-2563	112191	Yves Minet	07/2014
6815	2^372638-1859441	112176	Enzo Doria	03/2016
6816	3^235074-113056	112159	Enzo Doria	07/2014
6817	-E(29242)/489848365125303139750087	112140	Thomas Ritschel	01/2021
6818	(2^372514+1822)/2	112138	Stefano Morozzi	02/2021
6819	29468^6387+6387^29468	112135	Hans Havermann	02/2021
6820	(2^372428+3742)/2	112112	Stefano Morozzi	01/2021
6821	25375^25454-25454^25375	112110	Norbert Schneider	01/2021
6822	131^52949-130	112108	Norbert Schneider	02/2019
6823	(91*10^112098-1)/9	112100	Robert Price	04/2015
6824	(68*10^112087-149)/9	112088	Robert Price	07/2022
6825	2^372314+212419	112078	Enzo Doria	08/2023
6826	2^372310-85061	112077	Paul Bourdelais	02/2012
6827	(10^112067+53)/9	112067	Serge Batalov	07/2015
6828	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
6829	75^59760+2	112054	Lelio R Paula	08/2013
6830	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
6831	(10^112048+7)/8747/373157	112039	Alfred Reich	06/2021
6832	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
6833	F(536233)/825798821/1102495049/5641839306317	112036	Serge Batalov	07/2024
6834	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
6835	8*10^112018-49	112019	Robert Price	08/2019
6837	2^372108+74221	112016	Enzo Doria	04/2016
6836	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
6838	8*10^112011-73	112012	Robert Price	01/2022
6839	(184*10^112007-1)/3	112009	Robert Price	02/2020
6840	5*10^112003+81	112004	Robert Price	03/2019
6841	215^48018+48018^215	112000	Norbert Schneider	10/2018
6842	25549^24148+24148^25549	111979	Hans Havermann	02/2021
6843	2^371970-459491	111975	Enzo Doria	05/2015
6844	41^69427-40^69427	111971	Robert Price	07/2012
6845	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
6846	15*25^80056+446	111915	Eric Chen	10/2023
6847	(34*10^111902-547)/9	111903	Robert Price	03/2021
6848	(10^111902+71)/9	111902	Serge Batalov	07/2015
6849	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
6850	29080^7027+7027^29080	111865	Hans Havermann	01/2021
6851	31307^3730+3730^31307	111820	Hans Havermann	02/2021
6852	2^371440-112865	111815	Enzo Doria	06/2014
6853	2^371426-459161	111811	Enzo Doria	05/2015
6854	25768^21771+21771^25768	111779	Hans Havermann	02/2021
6855	28022^9747+9747^28022	111777	Hans Havermann	02/2021
6856	(94*10^111770+11)/3	111772	Robert Price	04/2020
6857	2^371276-461267	111766	Enzo Doria	07/2015
6858	6*10^111760+43	111761	Robert Price	07/2020
6859	98079!4-1024	111747	Robert Price	11/2019
6860	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
6861	10^(255862+1)-410^55862-1	111725	Robert Price	07/2023
6862	2^371098-113261	111712	Enzo Doria	07/2014
6863	(7*10^111706-61)/9	111706	Erik Branger	01/2011
6864	2^371044+1869391	111696	Enzo Doria	05/2016
6865	26310^17581+17581^26310	111688	Hans Havermann	01/2021
6866	88^57416+87	111645	Norbert Schneider	11/2015
6867	2^370829-109693	111631	Enzo Doria	04/2014
6868	15^94906-2	111619	Lelio R Paula	11/2013
6869	25835^20904+20904^25835	111614	Hans Havermann	02/2021
6870	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
6871	27758^10479+10479^27758	111597	Hans Havermann	02/2021
6872	2^370695-4627	111591	Yves Minet	05/2019
6873	7*10^111579-87	111580	Robert Price	06/2020
6874	2^370643-37	111575	Yves Minet	01/2012
6875	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
6876	2^370610-3911	111565	Yves Minet	04/2017
6877	(154*10^111549+17)/9	111551	Robert Price	06/2022
6878	26200^18097+18097^26200	111550	Hans Havermann	01/2021
6879	286^45405+45405^286	111532	Norbert Schneider	04/2015
6880	4*5^159563-9	111531	Lelio R Paula	11/2014
6881	5*10^111528-21	111529	Robert Price	12/2021
6882	(4^185225+23)/3	111517	Robert Price	10/2018
6883	2^370393-2797093	111500	Enzo Doria	03/2016
6884	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
6885	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
6886	6^143273-5	111489	Paul Bourdelais	01/2021
6887	2^370292-2791979	111469	Enzo Doria	03/2016
6888	(14*10^111443-11)/3	111444	Robert Price	08/2022
6889	2^370177-461551	111435	Enzo Doria	07/2015
6890	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
6891	109^54683-108	111413	Norbert Schneider	02/2017
6893	(83*10^111406-173)/9	111407	Robert Price	04/2021
6892	959^37362-37362^959	111407	Henri Lifchitz	10/2024
6894	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
6895	32961^2396+2396^32961	111392	Hans Havermann	10/2020
6896	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
6897	(19*10^111385+11)/3	111386	Robert Price	07/2023
6898	(23*10^111380-29)/3	111381	Robert Price	03/2022
6899	2^369974+733	111374	Lelio R Paula	05/2013
6900	121^53470+120	111367	Norbert Schneider	10/2018
6901	2^369915-286267	111356	Enzo Doria	07/2015
6902	(62*10^111347-629)/9	111348	Robert Price	07/2021
6903	2^369855-1615	111338	Lelio R Paula	05/2017
6904	7*10^111325+3	111326	Robert Price	08/2015
6905	51^65176+2	111293	Lelio R Paula	08/2013
6906	Phi(43329,-43329)	111283	Henri Lifchitz	06/2025
6907	2^369643-1865767	111274	Enzo Doria	03/2016
6908	2^369603+885	111262	Lelio R Paula	05/2017
6909	25555^22564+22564^25555	111252	Hans Havermann	10/2020
6910	F(532391)/89441689/1425422598617	111243	Serge Batalov	07/2024
6911	L(532277)	111240	Renaud Lifchitz	03/2004
6912	105^55033-2	111233	Lelio R Paula	10/2017
6913	(35*10^111232-737)/9	111233	Robert Price	07/2018
6914	26970^13307+13307^26970	111227	Hans Havermann	10/2020
6915	25419^23716+23716^25419	111210	Hans Havermann	10/2020
6916	(26^78593-3^78593)/23	111206	Robert Price	02/2025
6917	9*10^111201-29	111202	Robert Price	09/2019
6918	2^369392+29835	111199	Lelio R Paula	05/2017
6919	3^233059+16	111198	Robert Price	03/2020
6920	2^369354-3413	111187	Yves Minet	12/2016
6921	2^369296-27	111170	Lelio R Paula	02/2013
6922	(2468^40960+1)/(2468^8192+1)	111161	Martin Hopf	08/2024
6923	2^369239-109837	111153	Enzo Doria	05/2014
6924	2^369224-291839	111148	Enzo Doria	07/2015
6925	2^369216+2798881	111146	Enzo Doria	04/2016
6926	26842^13817+13817^26842	111137	Hans Havermann	11/2020
6927	(5*10^111119-191)/3	111120	Robert Price	05/2021
6928	(29*10^111112-23)/3	111113	Robert Price	03/2022
6929	10^111111+163849	111112	Patrick De Geest	03/2017
6930	10^111111-312911	111111	Patrick De Geest	03/2017
6931	2^369092-216923	111108	Enzo Doria	05/2014
6932	2^369081-55	111105	Lelio R Paula	02/2013
6933	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
6934	88^57124-87	111077	Norbert Schneider	11/2015
6935	2^368980+753	111075	Lelio R Paula	05/2013
6936	2^368946-3623	111064	Yves Minet	03/2017
6937	2^368929+29835	111059	Lelio R Paula	05/2017
6938	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
6939	111^54298+110	111057	Norbert Schneider	04/2017
6940	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
6941	(29*10^111020-41)/3	111021	Tyler Busby	03/2024
6942	35799^1262+1262^35799	111015	Hans Havermann	10/2020
6943	(298*10^111004+11)/3	111006	Robert Price	11/2020
6944	27648^10349+10349^27648	111004	Hans Havermann	11/2020
6945	28899^6932+6932^28899	110997	Hans Havermann	11/2020
6946	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
6947	2^368641-460303	110972	Enzo Doria	06/2015
6948	2^368619-109087	110966	Enzo Doria	04/2014
6949	(74*10^110961+313)/9	110962	Robert Price	06/2019
6950	25258^24711+24711^25258	110956	Hans Havermann	11/2020
6951	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
6952	3*2^368489+7	110927	Lelio R Paula	09/2014
6953	(14*10^110922+61)/3	110923	Robert Price	12/2018
6954	97411!4-2	110913	Robert Price	07/2017
6955	(301*10^110903+23)/9	110905	Robert Price	06/2021
6956	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
6957	25830^19619+19619^25830	110880	Hans Havermann	10/2020
6958	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
6959	26022^18191+18191^26022	110850	Hans Havermann	10/2020
6960	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
6961	(37*10^110813+251)/9	110814	Robert Price	09/2021
6962	2^368050-64875	110795	Lelio R Paula	05/2017
6963	2^368048+25	110794	Lelio R Paula	02/2013
6964	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
6965	69^60239-2	110771	Lelio R Paula	10/2013
6966	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
6967	2^367924-69	110757	Lelio R Paula	02/2013
6968	(23*10^110738+61)/3	110739	Robert Price	01/2022
6969	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
6970	2^367709-109723	110692	Enzo Doria	04/2014
6971	2^367687+213413	110685	Enzo Doria	09/2023
6972	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
6973	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
6974	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
6975	379*10^110616+9	110619	Jason Yuen	01/2025
6976	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
6977	140^51515-139	110558	Norbert Schneider	04/2019
6978	2^367215+1879223	110543	Enzo Doria	09/2016
6979	25782^19375+19375^25782	110534	Hans Havermann	10/2020
6980	26117^17058+17058^26117	110526	Hans Havermann	10/2020
6981	2^367141+41	110521	Lelio R Paula	02/2013
6982	2^367126+29835	110516	Lelio R Paula	05/2017
6983	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
6984	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
6985	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
6986	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
6987	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
6988	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
6989	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
6990	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
6991	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
6992	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
6993	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
6994	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
6995	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
6996	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
6997	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
6998	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
6999	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
7000	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020

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Probable Primes Top 10000

(301723 PRPs in the top)