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	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
6752	2^368641-460303	110972	Enzo Doria	06/2015
6753	2^368619-109087	110966	Enzo Doria	04/2014
6754	(74*10^110961+313)/9	110962	Robert Price	06/2019
6755	25258^24711+24711^25258	110956	Hans Havermann	11/2020
6756	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
6757	3*2^368489+7	110927	Lelio R Paula	09/2014
6758	(14*10^110922+61)/3	110923	Robert Price	12/2018
6759	97411!4-2	110913	Robert Price	07/2017
6760	(301*10^110903+23)/9	110905	Robert Price	06/2021
6761	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
6762	25830^19619+19619^25830	110880	Hans Havermann	10/2020
6763	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
6764	26022^18191+18191^26022	110850	Hans Havermann	10/2020
6765	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
6766	(37*10^110813+251)/9	110814	Robert Price	09/2021
6767	2^368050-64875	110795	Lelio R Paula	05/2017
6768	2^368048+25	110794	Lelio R Paula	02/2013
6769	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
6770	69^60239-2	110771	Lelio R Paula	10/2013
6771	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
6772	2^367924-69	110757	Lelio R Paula	02/2013
6773	(23*10^110738+61)/3	110739	Robert Price	01/2022
6774	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
6775	2^367709-109723	110692	Enzo Doria	04/2014
6776	2^367687+213413	110685	Enzo Doria	09/2023
6777	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
6778	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
6779	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
6780	379*10^110616+9	110619	Jason Yuen	01/2025
6781	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
6782	140^51515-139	110558	Norbert Schneider	04/2019
6783	2^367215+1879223	110543	Enzo Doria	09/2016
6784	25782^19375+19375^25782	110534	Hans Havermann	10/2020
6785	26117^17058+17058^26117	110526	Hans Havermann	10/2020
6786	2^367141+41	110521	Lelio R Paula	02/2013
6787	2^367126+29835	110516	Lelio R Paula	05/2017
6788	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
6789	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
6790	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
6791	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
6792	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
6793	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
6794	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
6795	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
6796	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
6797	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
6798	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
6799	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
6800	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
6801	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
6802	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
6803	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
6804	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
6805	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
6806	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
6807	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
6808	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
6809	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
6810	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
6811	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
6812	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
6813	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
6814	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
6815	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
6816	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
6817	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
6818	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
6819	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
6820	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
6821	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
6822	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
6823	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
6824	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
6825	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
6826	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020
6827	(10^110503-1)-710^100712-710^9790	110503	Makoto Morimoto	09/2020
6828	(10^110503-1)-710^76427-710^34075	110503	Makoto Morimoto	09/2020
6829	(10^110503-1)-710^90451-710^20051	110503	Makoto Morimoto	09/2020
6830	(10^110503-1)-810^106252-810^4250	110503	Makoto Morimoto	09/2020
6831	(11*10^110496+49)/3	110497	Robert Price	07/2018
6832	25447^21958+21958^25447	110481	Hans Havermann	11/2020
6833	(31*2^366976+1)/7	110472	Lelio R Paula	03/2014
6834	7*10^110468-23	110469	Robert Price	07/2019
6835	5*3^231464-2^231464	110438	Jon Grantham	08/2023
6836	2^366853+5711	110434	Lelio R Paula	05/2017
6837	(21181*2^366833+1)/3	110432	Lelio R Paula	07/2014
6838	2^366816+315	110423	Lelio R Paula	05/2017
6839	2^366775-2787037	110411	Enzo Doria	03/2016
6840	(112*10^110405-1)/3	110407	Serge Batalov	12/2014
6841	2^366751+2797553	110404	Enzo Doria	03/2016
6842	25276^23331+23331^25276	110404	Hans Havermann	10/2020
6843	2^366748+255	110403	Lelio R Paula	05/2017
6844	2^366738-2985	110400	Yves Minet	09/2014
6845	(23*2^366739+1)/74575	110396	Lelio R Paula	03/2014
6846	(2^366722+1314)/2	110395	Stefano Morozzi	02/2021
6847	2^366716+1871791	110393	Enzo Doria	05/2016
6848	(239*23^81066-349)/22	110391	Eric Chen	08/2023
6849	2^366695+1334025	110387	Henri Lifchitz	10/2024
6850	2^366649+1871687	110373	Enzo Doria	05/2016
6851	2^366629-351205	110367	Enzo Doria	06/2015
6852	(31*10^110363+257)/9	110364	Robert Price	12/2021
6853	(17*19^86292-215)/18	110347	Eric Chen	01/2023
6855	2^366558+1874479	110345	Enzo Doria	06/2016
6854	25132^24581+24581^25132	110345	Hans Havermann	10/2020
6856	(2^366539+770)/2	110339	Stefano Morozzi	09/2020
6857	26368^15285+15285^26368	110331	Hans Havermann	10/2020
6858	(23*10^110290+19)/3	110291	Robert Price	07/2019
6859	18^87853-4409	110280	Enzo Doria	03/2013
6860	28490^7419+7419^28490	110267	Hans Havermann	11/2020
6861	2^366218-23	110243	Lelio R Paula	02/2013
6862	(21*2^366193-1)/197	110235	Lelio R Paula	03/2014
6863	2^366178-343991	110231	Enzo Doria	07/2015
6864	12^102123-11	110210	Riley Fisher	09/2023
6865	(725*35^71368+16649)/34	110199	Eric Chen	05/2025
6866	25777^18798+18798^25777	110174	Hans Havermann	10/2020
6867	2^365944+1871341	110161	Enzo Doria	05/2016
6868	2^365838-461267	110129	Enzo Doria	07/2015
6869	30152^4491+4491^30152	110126	Hans Havermann	11/2020
6870	2^365802+23359	110118	Enzo Doria	10/2023
6871	10^110111+464019	110112	Patrick De Geest	05/2021
6872	10^110111-40001	110111	Robert Price	01/2021
6873	2^365763-6555	110106	Lelio R Paula	04/2017
6874	(2^365689+2^182845+1)/5	110083		11/2006
6875	2^365666-459161	110077	Enzo Doria	05/2015
6876	3*10^110076-7	110077	Robert Price	08/2015
6877	13^98785-72	110041	Lelio R Paula	03/2017
6879	(25^78707+1)/26	110027	Robert Price	06/2013
6878	(7*10^110027-277)/9	110027	Robert Price	02/2022
6880	(16*10^110014-73)/3	110015	Robert Price	07/2020
6881	(7*10^110006-151)/9	110006	Robert Price	02/2018
6882	6^141361-7	110001	Lelio R Paula	11/2014
6883	10^110000+8029681	110001	Hayden Chesnut	11/2024
6884	10^110000+2044477	110001	Hayden Chesnut	11/2024
6885	10^110000+76407	110001	Hayden Chesnut	11/2024
6886	10^110000+167311	110001	Hayden Chesnut	11/2024
6887	20^84536+81	109984	Lelio R Paula	03/2017
6888	5*2^365347-9	109982	Lelio R Paula	09/2014
6889	9*6^141303+7	109957	Lelio R Paula	11/2014
6890	27635^9522+9522^27635	109953	Hans Havermann	11/2020
6891	78^58099+77	109929	Norbert Schneider	02/2015
6892	2*10^109928-7	109929	Robert Price	10/2015
6893	30580^3933+3933^30580	109927	Hans Havermann	11/2020
6894	26380^14689+14689^26380	109926	Hans Havermann	11/2020
6895	(2^365161+1130)/2	109925	Stefano Morozzi	09/2020
6896	(27*2^365137-1)/2021	109916	Lelio R Paula	03/2014
6897	29^75157-30	109910	Anonymous	09/2024
6898	(4441*29^75152-24)/7	109905	Curtis Bright	05/2015
6899	(2^365087+7)/6015	109899	Lelio R Paula	01/2014
6900	(2^365069+3774)/2	109897	Stefano Morozzi	02/2021
6901	29652^5083+5083^29652	109894	Mark Rodenkirch	10/2020
6902	(2^365049+722)/2	109891	Stefano Morozzi	09/2020
6903	(35*10^109888-89)/9	109889	Robert Price	02/2022
6904	18^87533-11	109878	Lelio R Paula	04/2017
6905	2^364982-5	109871	Henri Lifchitz	04/2006
6906	3*10^109861+59	109862	Robert Price	08/2018
6907	5*10^109860-69	109861	Robert Price	02/2021
6908	2^364936-1867979	109857	Enzo Doria	04/2016
6909	27013^11652+11652^27013	109846	Hans Havermann	10/2020
6910	2^364867-112087	109836	Enzo Doria	06/2014
6911	4^182415-85061	109825	Mike Oakes	06/2011
6912	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
6913	24972^24972-8323^8323	109814	Henri Lifchitz	10/2024
6914	(53*10^109809-287)/9	109810	Robert Price	02/2022
6915	(52*10^109807-133)/9	109808	Robert Price	09/2021
6916	25708^18675+18675^25708	109806	Hans Havermann	10/2020
6917	(17^89227+16^89227)/33	109788	Robert Price	08/2013
6918	2^364687-187	109782	Lelio R Paula	01/2012
6919	2^364644+67	109769	Lelio R Paula	01/2012
6920	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
6921	(2^364616+5)/9	109760	Lelio R Paula	01/2014
6922	(55*10^109759+89)/9	109760	Robert Price	03/2019
6923	(14*32^72921+4171)/31	109757	Eric Chen	04/2023
6924	12^101694+73	109747	Lelio R Paula	03/2017
6925	13^98518-66	109744	Lelio R Paula	03/2017
6926	(35^71069+2^71069)/37	109734	Robert Price	01/2025
6927	(8*10^109721-269)/9	109721	Robert Price	09/2021
6928	2^364478-113261	109719	Enzo Doria	07/2014
6929	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
6930	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
6931	27814^8777+8777^27814	109681	Hans Havermann	10/2020
6932	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
6933	3^229824+340	109654	Lelio R Paula	03/2017
6934	(16623*33^72206-8095)/16	109649	Eric Chen	05/2023
6935	(2*10^109645-71)/3	109645	Robert Price	12/2017
6936	V(786978)	109644	Serge Batalov	07/2024
6937	2^364169-112813	109626	Enzo Doria	06/2014
6938	28822^6359+6359^28822	109622	Hans Havermann	11/2020
6939	10^109615+21	109616	Lelio R Paula	03/2017
6940	10^109615-456267	109615	Patrick De Geest	03/2017
6941	522^40331-40331^522	109607	Norman Luhn	09/2024
6942	2^364094-113	109604	Lelio R Paula	01/2012
6943	25251^21898+21898^25251	109600	Hans Havermann	11/2020
6944	(4^182026+11)/3	109591	Robert Price	02/2017
6945	2^364041-6883	109588	Lelio R Paula	09/2011
6946	12^101545+11	109586	Lelio R Paula	03/2017
6947	26536^13475+13475^26536	109582	Hans Havermann	11/2020
6948	2^363842-2787101	109528	Enzo Doria	03/2016
6949	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
6950	(996^36527+1)/997	109515	Jinyuan Wang	12/2024
6951	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
6952	2^363769+5711	109506	Lelio R Paula	04/2017
6953	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
6954	26^77372+25	109480	Anonymous	09/2024
6955	(2^363670+100280245065)	109476	Paul Bourdelais	05/2022
6956	p(22245)#/2-8	109462	Robert Price	01/2017
6957	2^363556+55	109442	Lelio R Paula	01/2012
6958	(509*10^109414+31)/9	109416	Robert Price	08/2022
6959	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
6960	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
6961	2^363406+1871569	109397	Enzo Doria	05/2016
6962	(129^51829-1)/128	109388	Anonymous	06/2024
6963	(2^363370+1338)/2	109385	Stefano Morozzi	02/2021
6964	(2^363349+7)/9	109378	Lelio R Paula	01/2014
6965	(13869^26569-1)/(13869^163-1)	109375	Ryan Propper	11/2023
6966	3^229236+100	109374	Lelio R Paula	03/2017
6967	(2^363315+3258)/2	109369	Stefano Morozzi	02/2021
6968	2^363268-58695	109355	Lelio R Paula	04/2017
6969	2^363191-112321	109332	Enzo Doria	06/2014
6970	26231^14718+14718^26231	109327	Hans Havermann	10/2020
6971	25461^19672+19672^25461	109326	Hans Havermann	10/2020
6972	4*10^109316-63	109317	Robert Price	10/2018
6973	2^363120+3	109311	Donovan Johnson	04/2006
6974	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
6975	2^363042-114641	109287	Enzo Doria	04/2015
6976	2^363020-112793	109280	Enzo Doria	06/2014
6977	(8732^27889-1)/(8732^167-1)	109256	Ryan Propper	11/2023
6978	(85*10^109253+203)/9	109254	Robert Price	09/2020
6979	24990^23431+23431^24990	109202	Hans Havermann	10/2020
6980	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
6981	(2^362716+1282)/2	109189	Stefano Morozzi	01/2021
6982	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
6983	25060^22737+22737^25060	109180	Hans Havermann	10/2020
6984	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
6985	5^156181+38	109166	Lelio R Paula	02/2017
6986	(2^362623+3618)/2	109161	Stefano Morozzi	09/2020
6987	25138^21993+21993^25138	109157	Hans Havermann	10/2020
6988	4*10^109142+91	109143	Robert Price	08/2018
6989	3^228750+68	109142	Lelio R Paula	03/2017
6990	(2^362561+786)/2	109142	Stefano Morozzi	09/2020
6991	(23*10^109113+61)/3	109114	Robert Price	01/2022
6992	2*10^109100-49	109101	Robert Price	09/2020
6993	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
6994	65^60167-64^60167	109078	Robert Price	08/2013
6995	7*3^228589-2	109066	Lelio R Paula	09/2014
6996	24874^24243+24243^24874	109063	Hans Havermann	11/2020
6997	(17*10^109059-161)/9	109060	Robert Price	02/2021
6998	29158^5495+5495^29158	109050	Hans Havermann	11/2020
6999	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
7000	2*7^129008+9	109025	Lelio R Paula	11/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301429 PRPs in the top)