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	31^78759-30	117459	Theodore Burton	02/2007
6752	(2^390176+1222)/2	117455	Stefano Morozzi	09/2020
6753	(2^390133+1242)/2	117442	Stefano Morozzi	09/2020
6754	(2^390013+2634)/2	117406	Stefano Morozzi	09/2020
6755	3*10^117402+61	117403	Robert Price	09/2020
6756	2^389998+37	117402	Lelio R Paula	03/2013
6757	(2^389977+314)/2	117395	Stefano Morozzi	09/2020
6758	(2^389921+342)/2	117378	Stefano Morozzi	01/2021
6759	71830^43+43^71830	117333	Hans Havermann	01/2021
6760	(2^389768+1582)/2	117332	Stefano Morozzi	09/2020
6761	33802^2951+2951^33802	117292	Hans Havermann	02/2021
6762	(2^561185)%L(561185)	117281	Henri Lifchitz	05/2025
6763	26789^23866+23866^26789	117277	Hans Havermann	02/2021
6764	29^80192-1*80192^29	117273	Dylan Delgado	12/2019
6765	(101*10^117260+7)/9	117262	Robert Price	02/2022
6766	(13*10^117249+161)/3	117250	Robert Price	11/2018
6767	2^389478+43	117245	Lelio R Paula	03/2013
6768	(298*10^117229-7)/3	117231	Robert Price	06/2020
6769	(2^389416+342)/2	117226	Stefano Morozzi	01/2021
6770	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
6771	5*10^117205+23	117206	Robert Price	03/2019
6772	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
6773	27272^19827+19827^27272	117195	Hans Havermann	01/2021
6774	(2^389276+2650)/2	117184	Stefano Morozzi	09/2020
6775	(844*10^117175-7)/9	117177	Robert Price	05/2021
6776	10^117142+209223	117143	Patrick De Geest	04/2018
6778	10^117142-1000000001	117142	Robert Price	03/2018
6777	10^117142-966057	117142	Patrick De Geest	04/2018
6779	10^117135+360577	117136	Patrick De Geest	07/2018
6780	10^117135-401	117135	Robert Price	01/2018
6781	26415^26488-26488^26415	117126	Norbert Schneider	05/2021
6782	4*10^117123+79	117124	Robert Price	08/2018
6783	2^389033-12797413	117111	Enzo Doria	04/2016
6784	(2^388987+2634)/2	117097	Stefano Morozzi	09/2020
6785	2^388960-109505	117089	Enzo Doria	04/2014
6786	7*10^117082-57	117083	Robert Price	06/2020
6787	791^40398-40398^791	117081	Norman Luhn	09/2024
6788	(2^388928-5)/569	117077	Lelio R Paula	03/2014
6789	2^388888-1529	117067	Yves Minet	01/2013
6790	10^117059+28879	117060	Patrick De Geest	05/2016
6791	(10^117059-71)/1	117059	Serge Batalov	12/2014
6792	(2^388854+3630)/2	117057	Stefano Morozzi	09/2020
6793	(2^388842+2098)/2	117053	Stefano Morozzi	09/2020
6794	(2^388789+3150)/2	117037	Stefano Morozzi	09/2020
6795	(2^388748+378)/2	117025	Stefano Morozzi	02/2021
6796	(693^41189-1)/692	117005	Michael Stocker	05/2020
6797	(26*10^116999-503)/9	117000	Robert Price	07/2018
6798	20^89917-21	116985	Anonymous	09/2024
6799	(2^388609+1554)/2	116983	Stefano Morozzi	09/2020
6800	38496^1093+1093^38496	116975	Hans Havermann	02/2021
6801	3^245154-6256	116969	Enzo Doria	05/2014
6802	5*10^116966-43	116967	Robert Price	01/2019
6803	(748^40699-1)/747	116963	Tom Wu	08/2025
6804	2^388536-113495	116961	Enzo Doria	08/2014
6805	(2^388512+382)/2	116954	Stefano Morozzi	02/2021
6806	(8*32^77701+271)/31	116952	Eric Chen	11/2023
6807	2^388469-43	116941	Lelio R Paula	03/2013
6808	27417^18416+18416^27417	116939	Hans Havermann	02/2021
6809	(2^388438+1842)/2	116932	Stefano Morozzi	02/2021
6810	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
6811	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
6812	2^388180+93	116854	Donovan Johnson	07/2008
6813	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
6814	(85*10^116842+293)/9	116843	Robert Price	12/2019
6815	35296^2043+2043^35296	116840	Hans Havermann	02/2021
6816	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
6817	38633^1056+1056^38633	116814	Hans Havermann	02/2021
6818	2^387946-113261	116784	Enzo Doria	07/2014
6819	28*36^75009+305	116739	Eric Chen	12/2022
6820	28363^13056+13056^28363	116737	Hans Havermann	02/2021
6821	2^387745+75557	116723	Enzo Doria	04/2016
6822	(29*10^116719+313)/9	116720	Robert Price	04/2021
6823	29622^8699+8699^29622	116695	Hans Havermann	02/2021
6824	(206*10^116687-17)/9	116689	Robert Price	01/2020
6825	(7*10^116684+179)/3	116685	Robert Price	09/2018
6826	2^387554+71455	116666	Enzo Doria	04/2016
6827	(602*10^116647-71)/9	116649	Robert Price	12/2021
6828	3^244461-10	116638	Tyler NeSmith	09/2022
6829	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
6830	(2*10^116620+43)/9	116620	Serge Batalov	11/2022
6831	(19*10^116617+287)/9/12893	116614	Alfred Reich	11/2022
6832	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
6833	(25*10^116601-331)/9	116602	Robert Price	08/2018
6834	25791^26428-26428^25791	116587	Frank Doornink	03/2024
6836	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
6835	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
6837	2^387211+111546435	116563	Paul Bourdelais	10/2021
6838	10^116557+987654321	116558	Robert Price	12/2019
6839	10^116557+9141	116558	Patrick De Geest	02/2020
6840	10^116557-609431	116557	Patrick De Geest	02/2020
6841	209^50234-50234^209	116551	Norman Luhn	09/2024
6842	(28*10^116546+41)/3	116547	Robert Price	07/2021
6843	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
6844	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
6845	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
6846	(7*10^116514-1)/3	116515	Robert Price	08/2022
6847	(26*32^77406-390071011)/31	116508	Eric Chen	11/2023
6848	28846^10931+10931^28846	116500	Hans Havermann	02/2021
6849	10^116496+3593037	116497	Paul Bourdelais	10/2021
6850	272^47851-47851^272	116497	Norman Luhn	09/2024
6851	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
6852	(944^39157+1)/945	116489	Jinyuan Wang	12/2024
6853	998^38840+997	116487	Alfred Reich	03/2026
6854	2^386947+1869143	116483	Enzo Doria	05/2016
6856	(30^78857-1)/29	116480	Robert Price	12/2011
6855	Phi(78857,5#)	116480	Henri Lifchitz	12/2025
6857	(2^386903-3)/5	116469	Lelio R Paula	03/2014
6858	28107^13892+13892^28107	116441	Hans Havermann	02/2021
6859	29110^9957+9957^29110	116386	Hans Havermann	02/2021
6860	26469^24838+24838^26469	116335	Hans Havermann	01/2021
6861	2^386389-1864783	116315	Enzo Doria	03/2016
6862	993^38799+992	116279	Alfred Reich	03/2026
6863	(8*32^77250-163)/31	116273	Eric Chen	11/2023
6864	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
6865	297^47012+47012^297	116250	Norbert Schneider	07/2018
6866	(35*10^116223-341)/9	116224	Robert Price	08/2021
6867	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
6868	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
6869	(10^116201+7)/39623	116197	Alfred Reich	06/2021
6870	2^385969-823	116189	Yves Minet	05/2012
6871	57^66162+2	116173	Lelio R Paula	08/2013
6872	2^385854+75049	116154	Enzo Doria	04/2016
6873	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
6874	2^385775-109587	116130	Enzo Doria	04/2014
6875	(14*10^116112-101)/3	116113	Robert Price	02/2019
6876	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
6877	3*10^116107+23	116108	Robert Price	03/2022
6878	28729^10990+10990^28729	116094	Hans Havermann	02/2021
6879	2^385622+71839	116084	Enzo Doria	04/2016
6881	2^385564+781	116067	Lelio R Paula	01/2012
6880	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
6882	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
6883	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
6884	29431^8776+8776^29431	116056	Hans Havermann	01/2021
6885	(266*10^116024-17)/3	116026	Robert Price	07/2020
6886	30263^6820+6820^30263	116022	Hans Havermann	02/2021
6887	2^385410+71893	116020	Enzo Doria	04/2016
6888	38225^1084+1084^38225	116014	Hans Havermann	02/2021
6889	26548^23433+23433^26548	116011	Hans Havermann	02/2021
6890	Phi(183801,-9)	115960	Henri Lifchitz	12/2025
6891	12^107422-11	115928	Riley Fisher	12/2023
6892	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
6893	(11*10^115910-131)/3	115911	Robert Price	09/2018
6894	2^384953-111943	115883	Paul Bourdelais	02/2012
6895	43^70942-2	115882	Lelio R Paula	04/2014
6896	(94*10^115879-7)/3	115881	Robert Price	03/2020
6897	7*10^115863+3	115864	Robert Price	08/2015
6898	2^384834+93	115847	Donovan Johnson	07/2008
6899	2^384809+71297	115840	Enzo Doria	04/2016
6900	(55*10^115829+323)/9	115830	Robert Price	10/2021
6901	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
6902	31348^4951+4951^31348	115822	Hans Havermann	02/2021
6903	(793*10^115810+53)/9	115812	Robert Price	01/2022
6904	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
6905	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
6906	31115^5266+5266^31115	115794	Hans Havermann	02/2021
6907	2*10^115784-27	115785	Robert Price	05/2018
6908	10^115773+126739	115774	Patrick De Geest	04/2018
6910	10^115773-1000000001	115773	Robert Price	03/2018
6909	10^115773-396221	115773	Patrick De Geest	04/2018
6911	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
6912	30537^6178+6178^30537	115762	Hans Havermann	01/2021
6913	2^384530+1874305	115756	Enzo Doria	06/2016
6914	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
6915	28275^12406+12406^28275	115748	Hans Havermann	01/2021
6916	(44*10^115697-413)/9	115698	Robert Price	03/2019
6917	31408^4825+4825^31408	115692	Hans Havermann	02/2021
6918	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
6919	2^384312+81091	115690	Yves Minet	02/2010
6920	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
6921	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
6922	(4*10^115668-79)/3	115669	Robert Price	02/2018
6923	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
6924	994^38584+993	115652	Alfred Reich	03/2026
6925	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
6926	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
6927	18^92125-92125^18	115642	Dylan Delgado	08/2019
6928	(25^82723+3^82723)/28	115641	Robert Price	09/2025
6929	3^242337-4042	115625	Enzo Doria	05/2014
6930	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
6931	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
6932	7*10^115561+79	115562	Robert Price	07/2019
6933	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
6934	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
6935	2^383780-3149	115530	Yves Minet	10/2014
6936	(41*10^115523-383)/9	115524	Robert Price	11/2018
6937	27316^16923+16923^27316	115506	Hans Havermann	02/2021
6938	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
6939	2^383560-455	115464	Yves Minet	03/2012
6940	(2^383544+5)/3	115458	Lelio R Paula	03/2014
6941	(22*10^115454+119)/3	115455	Robert Price	04/2021
6942	89^59221-88^59221	115445	Robert Price	06/2015
6943	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
6944	2^383347+1869413	115399	Enzo Doria	05/2016
6945	(103*10^115366+17)/3	115368	Robert Price	08/2020
6946	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
6947	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
6948	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
6949	29961^7060+7060^29961	115315	Hans Havermann	01/2021
6951	2^383039+1869509	115307	Enzo Doria	05/2016
6950	32918^3183+3183^32918	115307	Hans Havermann	01/2021
6952	(109^56597-1)/90183471012	115302	Paul Vanderveen	06/2025
6953	36964^1315+1315^36964	115288	Hans Havermann	02/2021
6954	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
6955	(22*10^115282+29)/3	115283	Robert Price	02/2021
6956	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
6957	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
6958	30416^6141+6141^30416	115224	Hans Havermann	02/2021
6959	6*10^115211+79	115212	Robert Price	09/2020
6960	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
6961	27987^13078+13078^27987	115210	Hans Havermann	02/2021
6962	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
6963	(22*10^115188-193)/9	115189	Robert Price	07/2022
6964	2^382633+73697	115185	Enzo Doria	04/2016
6965	2^382509-113593	115147	Enzo Doria	08/2014
6966	2^382502-2791721	115145	Enzo Doria	03/2016
6967	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
6968	2^382464+22741	115134	Enzo Doria	09/2023
6969	26752^20065+20065^26752	115099	Hans Havermann	02/2021
6970	26383^23008+23008^26383	115080	Hans Havermann	02/2021
6971	9^120590-120590	115073	Robert Price	03/2014
6972	28203^12016+12016^28203	115062	Hans Havermann	02/2021
6973	2^382198+9	115054	Lelio R Paula	03/2013
6974	18268*31^77131+22839	115035	Eric Chen	05/2024
6975	30101^6630+6630^30101	115032	Hans Havermann	01/2021
6976	(89*10^115030-179)/9	115031	Robert Price	12/2019
6977	25554^26089-26089^25554	114987	Frank Doornink	02/2024
6978	25142^26129-26129^25142	114979	Frank Doornink	12/2023
6979	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
6980	27300^16271+16271^27300	114972	Hans Havermann	02/2021
6981	(23*10^114962+7)/3	114963	Robert Price	05/2023
6982	2^381883-59197	114959	Enzo Doria	10/2015
6983	27423^15542+15542^27423	114944	Hans Havermann	02/2021
6984	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
6986	2^381806-4481	114936	Yves Minet	07/2011
6985	2^381808-1851507	114936	Enzo Doria	08/2015
6987	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
6988	2^381774-112373	114926	Enzo Doria	06/2014
6989	26341^22980+22980^26341	114883	Hans Havermann	01/2021
6990	(79^60539-1)/61747564999146	114867	Paul Vanderveen	05/2025
6991	2^381555-109051	114860	Enzo Doria	04/2014
6992	2^381551+213683	114859	Enzo Doria	09/2023
6993	2^381546-113501	114857	Enzo Doria	08/2014
6994	(7*10^114845-19)/3	114846	Robert Price	10/2020
6995	26675^20178+20178^26675	114833	Hans Havermann	02/2021
6996	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
6997	3^240644+16	114817	Robert Price	04/2020
6998	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
6999	2^381360-110429	114801	Enzo Doria	05/2014
7000	(17*10^114795+79)/3	114796	Robert Price	04/2019

Find by discoverer :

PRP Records

Probable Primes Top 10000

(302955 PRPs in the top)