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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
6752	2^388180+93	116854	Donovan Johnson	07/2008
6753	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
6754	(85*10^116842+293)/9	116843	Robert Price	12/2019
6755	35296^2043+2043^35296	116840	Hans Havermann	02/2021
6756	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
6757	38633^1056+1056^38633	116814	Hans Havermann	02/2021
6758	2^387946-113261	116784	Enzo Doria	07/2014
6759	28*36^75009+305	116739	Eric Chen	12/2022
6760	28363^13056+13056^28363	116737	Hans Havermann	02/2021
6761	2^387745+75557	116723	Enzo Doria	04/2016
6762	(29*10^116719+313)/9	116720	Robert Price	04/2021
6763	29622^8699+8699^29622	116695	Hans Havermann	02/2021
6764	(206*10^116687-17)/9	116689	Robert Price	01/2020
6765	(7*10^116684+179)/3	116685	Robert Price	09/2018
6766	2^387554+71455	116666	Enzo Doria	04/2016
6767	(602*10^116647-71)/9	116649	Robert Price	12/2021
6768	3^244461-10	116638	Tyler NeSmith	09/2022
6769	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
6770	(2*10^116620+43)/9	116620	Serge Batalov	11/2022
6771	(19*10^116617+287)/9/12893	116614	Alfred Reich	11/2022
6772	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
6773	(25*10^116601-331)/9	116602	Robert Price	08/2018
6774	25791^26428-26428^25791	116587	Frank Doornink	03/2024
6776	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
6775	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
6777	2^387211+111546435	116563	Paul Bourdelais	10/2021
6778	10^116557+987654321	116558	Robert Price	12/2019
6779	10^116557+9141	116558	Patrick De Geest	02/2020
6780	10^116557-609431	116557	Patrick De Geest	02/2020
6781	209^50234-50234^209	116551	Norman Luhn	09/2024
6782	(28*10^116546+41)/3	116547	Robert Price	07/2021
6783	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
6784	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
6785	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
6786	(7*10^116514-1)/3	116515	Robert Price	08/2022
6787	(26*32^77406-390071011)/31	116508	Eric Chen	11/2023
6788	28846^10931+10931^28846	116500	Hans Havermann	02/2021
6789	10^116496+3593037	116497	Paul Bourdelais	10/2021
6790	272^47851-47851^272	116497	Norman Luhn	09/2024
6791	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
6792	(944^39157+1)/945	116489	Jinyuan Wang	12/2024
6793	2^386947+1869143	116483	Enzo Doria	05/2016
6795	(30^78857-1)/29	116480	Robert Price	12/2011
6794	Phi(78857,5#)	116480	Henri Lifchitz	12/2025
6796	(2^386903-3)/5	116469	Lelio R Paula	03/2014
6797	28107^13892+13892^28107	116441	Hans Havermann	02/2021
6798	29110^9957+9957^29110	116386	Hans Havermann	02/2021
6799	26469^24838+24838^26469	116335	Hans Havermann	01/2021
6800	2^386389-1864783	116315	Enzo Doria	03/2016
6801	(8*32^77250-163)/31	116273	Eric Chen	11/2023
6802	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
6803	297^47012+47012^297	116250	Norbert Schneider	07/2018
6804	(35*10^116223-341)/9	116224	Robert Price	08/2021
6805	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
6806	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
6807	(10^116201+7)/39623	116197	Alfred Reich	06/2021
6808	2^385969-823	116189	Yves Minet	05/2012
6809	57^66162+2	116173	Lelio R Paula	08/2013
6810	2^385854+75049	116154	Enzo Doria	04/2016
6811	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
6812	2^385775-109587	116130	Enzo Doria	04/2014
6813	(14*10^116112-101)/3	116113	Robert Price	02/2019
6814	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
6815	3*10^116107+23	116108	Robert Price	03/2022
6816	28729^10990+10990^28729	116094	Hans Havermann	02/2021
6817	2^385622+71839	116084	Enzo Doria	04/2016
6819	2^385564+781	116067	Lelio R Paula	01/2012
6818	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
6820	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
6821	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
6822	29431^8776+8776^29431	116056	Hans Havermann	01/2021
6823	(266*10^116024-17)/3	116026	Robert Price	07/2020
6824	30263^6820+6820^30263	116022	Hans Havermann	02/2021
6825	2^385410+71893	116020	Enzo Doria	04/2016
6826	38225^1084+1084^38225	116014	Hans Havermann	02/2021
6827	26548^23433+23433^26548	116011	Hans Havermann	02/2021
6828	Phi(183801,-9)	115960	Henri Lifchitz	12/2025
6829	12^107422-11	115928	Riley Fisher	12/2023
6830	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
6831	(11*10^115910-131)/3	115911	Robert Price	09/2018
6832	2^384953-111943	115883	Paul Bourdelais	02/2012
6833	43^70942-2	115882	Lelio R Paula	04/2014
6834	(94*10^115879-7)/3	115881	Robert Price	03/2020
6835	7*10^115863+3	115864	Robert Price	08/2015
6836	2^384834+93	115847	Donovan Johnson	07/2008
6837	2^384809+71297	115840	Enzo Doria	04/2016
6838	(55*10^115829+323)/9	115830	Robert Price	10/2021
6839	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
6840	31348^4951+4951^31348	115822	Hans Havermann	02/2021
6841	(793*10^115810+53)/9	115812	Robert Price	01/2022
6842	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
6843	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
6844	31115^5266+5266^31115	115794	Hans Havermann	02/2021
6845	2*10^115784-27	115785	Robert Price	05/2018
6846	10^115773+126739	115774	Patrick De Geest	04/2018
6848	10^115773-1000000001	115773	Robert Price	03/2018
6847	10^115773-396221	115773	Patrick De Geest	04/2018
6849	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
6850	30537^6178+6178^30537	115762	Hans Havermann	01/2021
6851	2^384530+1874305	115756	Enzo Doria	06/2016
6852	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
6853	28275^12406+12406^28275	115748	Hans Havermann	01/2021
6854	(44*10^115697-413)/9	115698	Robert Price	03/2019
6855	31408^4825+4825^31408	115692	Hans Havermann	02/2021
6856	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
6857	2^384312+81091	115690	Yves Minet	02/2010
6858	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
6859	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
6860	(4*10^115668-79)/3	115669	Robert Price	02/2018
6861	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
6862	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
6863	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
6864	18^92125-92125^18	115642	Dylan Delgado	08/2019
6865	(25^82723+3^82723)/28	115641	Robert Price	09/2025
6866	3^242337-4042	115625	Enzo Doria	05/2014
6867	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
6868	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
6869	7*10^115561+79	115562	Robert Price	07/2019
6870	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
6871	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
6872	2^383780-3149	115530	Yves Minet	10/2014
6873	(41*10^115523-383)/9	115524	Robert Price	11/2018
6874	27316^16923+16923^27316	115506	Hans Havermann	02/2021
6875	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
6876	2^383560-455	115464	Yves Minet	03/2012
6877	(2^383544+5)/3	115458	Lelio R Paula	03/2014
6878	(22*10^115454+119)/3	115455	Robert Price	04/2021
6879	89^59221-88^59221	115445	Robert Price	06/2015
6880	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
6881	2^383347+1869413	115399	Enzo Doria	05/2016
6882	(103*10^115366+17)/3	115368	Robert Price	08/2020
6883	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
6884	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
6885	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
6886	29961^7060+7060^29961	115315	Hans Havermann	01/2021
6888	2^383039+1869509	115307	Enzo Doria	05/2016
6887	32918^3183+3183^32918	115307	Hans Havermann	01/2021
6889	(109^56597-1)/90183471012	115302	Paul Vanderveen	06/2025
6890	36964^1315+1315^36964	115288	Hans Havermann	02/2021
6891	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
6892	(22*10^115282+29)/3	115283	Robert Price	02/2021
6893	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
6894	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
6895	30416^6141+6141^30416	115224	Hans Havermann	02/2021
6896	6*10^115211+79	115212	Robert Price	09/2020
6897	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
6898	27987^13078+13078^27987	115210	Hans Havermann	02/2021
6899	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
6900	(22*10^115188-193)/9	115189	Robert Price	07/2022
6901	2^382633+73697	115185	Enzo Doria	04/2016
6902	2^382509-113593	115147	Enzo Doria	08/2014
6903	2^382502-2791721	115145	Enzo Doria	03/2016
6904	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
6905	2^382464+22741	115134	Enzo Doria	09/2023
6906	26752^20065+20065^26752	115099	Hans Havermann	02/2021
6907	26383^23008+23008^26383	115080	Hans Havermann	02/2021
6908	9^120590-120590	115073	Robert Price	03/2014
6909	28203^12016+12016^28203	115062	Hans Havermann	02/2021
6910	2^382198+9	115054	Lelio R Paula	03/2013
6911	18268*31^77131+22839	115035	Eric Chen	05/2024
6912	30101^6630+6630^30101	115032	Hans Havermann	01/2021
6913	(89*10^115030-179)/9	115031	Robert Price	12/2019
6914	25554^26089-26089^25554	114987	Frank Doornink	02/2024
6915	25142^26129-26129^25142	114979	Frank Doornink	12/2023
6916	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
6917	27300^16271+16271^27300	114972	Hans Havermann	02/2021
6918	(23*10^114962+7)/3	114963	Robert Price	05/2023
6919	2^381883-59197	114959	Enzo Doria	10/2015
6920	27423^15542+15542^27423	114944	Hans Havermann	02/2021
6921	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
6923	2^381806-4481	114936	Yves Minet	07/2011
6922	2^381808-1851507	114936	Enzo Doria	08/2015
6924	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
6925	2^381774-112373	114926	Enzo Doria	06/2014
6926	26341^22980+22980^26341	114883	Hans Havermann	01/2021
6927	(79^60539-1)/61747564999146	114867	Paul Vanderveen	05/2025
6928	2^381555-109051	114860	Enzo Doria	04/2014
6929	2^381551+213683	114859	Enzo Doria	09/2023
6930	2^381546-113501	114857	Enzo Doria	08/2014
6931	(7*10^114845-19)/3	114846	Robert Price	10/2020
6932	26675^20178+20178^26675	114833	Hans Havermann	02/2021
6933	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
6934	3^240644+16	114817	Robert Price	04/2020
6935	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
6936	2^381360-110429	114801	Enzo Doria	05/2014
6937	(17*10^114795+79)/3	114796	Robert Price	04/2019
6938	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
6939	2^381252-115079	114769	Enzo Doria	06/2015
6940	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
6941	2^381209-29323	114756	Enzo Doria	07/2015
6942	2^381207-111546435	114755	Paul Bourdelais	10/2021
6943	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
6944	2^381201+1873205	114753	Enzo Doria	06/2016
6946	(85*10^114737+293)/9	114738	Robert Price	12/2019
6947	(265*10^114736+17)/3	114738	Robert Price	03/2020
6945	379*10^114735+9	114738	Jason Yuen	01/2025
6948	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
6949	2^380974-112991	114685	Enzo Doria	07/2014
6950	37097^1234+1234^37097	114679	Hans Havermann	02/2021
6951	(26*10^114658-119)/3	114659	Robert Price	07/2023
6952	88^58949-87	114626	Norbert Schneider	11/2015
6953	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
6954	Phi(155285,10)/242674820198201	114610	Makoto Kamada	02/2024
6955	(10^155285-1)(10^2389-1)(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201	114610	Anonymous	04/2025
6956	29913^6782+6782^29913	114608	Hans Havermann	02/2021
6957	(331*10^114605-7)/9	114607	Robert Price	04/2022
6958	2^380700+91	114603	Lelio R Paula	03/2013
6959	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
6960	7*10^114577+27	114578	Robert Price	11/2020
6962	10^114575+3^114576	114576	Mike Oakes	09/2010
6961	10^114575+66561	114576	Patrick De Geest	02/2017
6963	10^114575-581081	114575	Patrick De Geest	02/2017
6964	2^380587-115315	114569	Enzo Doria	06/2015
6965	31874^3927+3927^31874	114558	Hans Havermann	02/2021
6966	2^380513-216925	114546	Enzo Doria	05/2014
6967	2^380451-1840087	114528	Enzo Doria	06/2015
6968	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
6969	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
6970	2^380279-461347	114476	Enzo Doria	07/2015
6971	(331*10^114454-7)/9	114456	Robert Price	04/2022
6972	27121^16590+16590^27121	114447	Hans Havermann	01/2021
6973	25966^25555+25555^25966	114445	Hans Havermann	01/2021
6974	(611*32^76029-53)/31	114437	Eric Chen	11/2023
6975	(11*10^114400+529)/9	114401	Robert Price	09/2021
6976	2^380021+1871147	114398	Enzo Doria	05/2016
6977	2^380005+1869707	114393	Enzo Doria	05/2016
6978	2^379958-113297	114379	Enzo Doria	07/2014
6979	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
6980	2^379881-109105	114356	Enzo Doria	04/2014
6981	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
6982	(4*10^114340+83)/3	114341	Robert Price	02/2018
6983	(26*10^114317-77)/3	114318	Robert Price	11/2019
6984	(4*10^114296+149)/9	114296	Robert Price	04/2018
6985	88^58773-87	114284	Norbert Schneider	11/2015
6986	27764^13065+13065^27764	114280	Hans Havermann	01/2021
6987	(132^53891-1)/131	114278	Anonymous	06/2024
6988	2^379529-2790283	114250	Enzo Doria	03/2016
6989	2^379522+1869115	114248	Enzo Doria	05/2016
6990	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
6991	2^379317-115033	114186	Enzo Doria	06/2015
6992	(22*10^114178+47)/3	114179	Robert Price	06/2021
6993	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
6994	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
6995	(228^48407-1)/227	114139	Alexander Zhirkov	03/2023
6996	6*10^114091+23	114092	Robert Price	09/2020
6997	(4*10^114076+143)/3	114077	Robert Price	03/2018
6998	332*25^81584+12357	114053	Eric Chen	10/2023
6999	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
7000	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020

Find by discoverer :

PRP Records

Probable Primes Top 10000

(302588 PRPs in the top)