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	(86*10^76128+121)/9	76129	Robert Price	03/2017
6752	22154*29^52050+9	76123	Curtis Bright	05/2015
6753	3^159530-112358	76116	Enzo Doria	06/2014
6754	11^73089-48	76115	Lelio R Paula	02/2015
6755	86^39337-85	76098	Norbert Schneider	10/2015
6756	(3^159505-7)/313297316	76095	Lelio R Paula	06/2012
6757	6^97783+77	76090	Lelio R Paula	01/2015
6758	2^252712-105	76074	Lelio R Paula	03/2012
6759	(10^76069-19)/9	76069	Robert Price	10/2017
6761	131^35927+2	76068	Lelio R Paula	05/2013
6760	(41*10^76067+373)/9	76068	Robert Price	04/2017
6762	2^252683-139	76066	Lelio R Paula	03/2012
6763	137^35597-136	76061	Norbert Schneider	05/2015
6764	3^159413+106	76060	Lelio R Paula	01/2015
6765	9^79677+38^79677-24^79677-3*2^79677	76032	Mike Oakes	12/2010
6766	(2^252557-9)/71	76026	Lelio R Paula	07/2012
6767	(85*10^76021-103)/9	76022	Robert Price	10/2017
6768	11^72989+80	76011	Lelio R Paula	02/2015
6769	99877!6-36	75996	Robert Price	11/2018
6770	2^252449-459523	75995	Enzo Doria	05/2015
6771	20^58408+73	75991	Lelio R Paula	01/2015
6772	2^252418-1421	75986	Yves Minet	01/2013
6773	(11*2^252396-1)/5	75980	Lelio R Paula	02/2014
6774	2^252365-110689	75970	Enzo Doria	05/2014
6775	11^72949-1020	75969	Enzo Doria	11/2012
6776	(2^252294+47)/6549	75945	Lelio R Paula	07/2012
6777	2^252261-110595	75939	Enzo Doria	05/2014
6778	7^89853+76	75935	Lelio R Paula	01/2015
6779	3^159132+56	75926	Lelio R Paula	01/2015
6780	730^26513+26513^730	75916	Norbert Schneider	11/2016
6781	(27*2^252163-1)/1945	75907	Lelio R Paula	01/2014
6782	5^108596-14846	75906	Enzo Doria	02/2013
6783	5^108560-14846	75881	Enzo Doria	02/2013
6784	2^252051-110359	75875	Enzo Doria	05/2014
6785	2^251971-110509	75851	Enzo Doria	05/2014
6786	(42457^16384+1)/327682	75819	Lelio R Paula	11/2011
6787	2^251842-4715	75812	Yves Minet	05/2019
6788	99655!6-2	75811	Robert Price	07/2017
6789	14*10^75798+1089	75800	Jens K. Andersen	11/2007
6790	2^251784-455	75795	Yves Minet	03/2012
6791	2^251780-1289	75794	Yves Minet	01/2013
6792	2^251760-215609	75788	Paul Bourdelais	03/2013
6793	99^37973+2	75781	Lelio R Paula	05/2013
6794	(185*10^75777+7)/3	75779	Robert Price	02/2017
6795	5*2^251690+3	75767	Lelio R Paula	06/2014
6796	6^97366+95	75766	Lelio R Paula	01/2015
6797	s(23010)	75760	Hans Havermann	11/2017
6798	8*6^97337-7	75744	Lelio R Paula	10/2014
6799	2^251588-111677	75736	Enzo Doria	05/2014
6800	5^108346-13256	75731	Enzo Doria	02/2013
6801	(31^50777+1)/32	75726	Robert Price	07/2013
6802	(10^75707+77)/3	75707	Robert Price	01/2017
6803	(174907#+1673)/(723915467899)	75700	Makoto Morimoto	10/2017
6804	2^251466+193	75699	Lelio R Paula	03/2012
6805	(5*2^251464+1)/9423	75695	Lelio R Paula	07/2012
6806	2^251422-109991	75686	Enzo Doria	04/2014
6807	91(10^23+1)(10^1721+1)*(10^118749+1)/(10^69+1)/(10^5163+1)/(10^39583+1)	75680	Makoto Kamada	03/2019
6808	4*5^108245-3	75661	Lelio R Paula	10/2014
6809	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
6810	12^70066+95	75614	Lelio R Paula	02/2015
6811	-E20534/2063	75607	Thomas Ritschel	02/2017
6812	19^59120-50	75600	Lelio R Paula	01/2015
6813	18^60222-4697	75596	Enzo Doria	03/2013
6814	18^60211-4355	75582	Enzo Doria	03/2013
6815	7*2^251014-9	75564	Lelio R Paula	06/2014
6816	6^97101-25	75560	Lelio R Paula	01/2015
6817	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
6818	3^158331-140	75544	Lelio R Paula	01/2015
6821	(37^48157-1)/36	75519	Robert Price	03/2012
6820	(19*10^75518-43)/3	75519	Robert Price	10/2017
6819	2^250868-4229	75519	Yves Minet	08/2018
6822	10^75516+31467	75517	Patrick De Geest	03/2016
6824	10^75516-10^2256-1	75516	Serge Batalov	01/2011
6823	10^75516-66591	75516	Patrick De Geest	03/2016
6825	2^250851-187	75514	Lelio R Paula	03/2012
6826	(43*10^75498-7)/9	75499	Robert Price	12/2014
6827	(3^158244-5)/247916	75497	Lelio R Paula	06/2012
6828	4*5^107971-3	75470	Lelio R Paula	10/2014
6829	(25*10^75465+71)/3	75466	Robert Price	01/2017
6830	(5*2^250681-1)/999	75461	Lelio R Paula	01/2014
6831	(182*10^75456+1)/3	75458	Robert Price	02/2017
6832	(2^250669-9)/98897729	75451	Lelio R Paula	07/2012
6833	10^75441+13	75442	Robert Price	01/2011
6834	10^75441-9923	75441	Patrick De Geest	05/2013
6835	(27*2^250546-1)/6457	75420	Lelio R Paula	01/2014
6836	5*7^89231-6	75410	Lelio R Paula	10/2014
6838	2^250503-16995	75409	Lelio R Paula	05/2013
6837	11^72411-28	75409	Lelio R Paula	02/2015
6839	3*5^107860-8	75392	Lelio R Paula	10/2014
6840	(34*10^75387-403)/9	75388	Robert Price	10/2017
6842	2^250426+29835	75386	Lelio R Paula	05/2013
6841	8*3^157999-7	75386	Lelio R Paula	05/2014
6843	(88*10^75381-43)/9	75382	Robert Price	11/2015
6844	2^250382-111755	75373	Enzo Doria	05/2014
6845	2^250374-2798051	75371	Eric Chen	03/2016
6846	(22*10^75368-1)/3	75369	Robert Price	12/2014
6847	2^250369-4543	75369	Yves Minet	03/2019
6848	(19*10^75338+119)/3	75339	Robert Price	02/2017
6849	2^250223-1859167	75325	Enzo Doria	03/2016
6850	(3^157854-7)/66025282	75308	Lelio R Paula	06/2012
6851	3^157831-98	75305	Lelio R Paula	01/2015
6852	(46^45281+11^45281)/57	75290	Serge Batalov	12/2016
6853	92^38335-91	75282	Norbert Schneider	01/2016
6854	2^250020+18915	75264	Lelio R Paula	05/2013
6855	2^250002+8193	75259	Lelio R Paula	05/2013
6856	(11*2^249977-7)/15	75251	Renaud Lifchitz	02/2011
6857	(2^249968+78557)/63	75247	Lelio R Paula	07/2012
6858	(5*10^75244+91)/3	75245	Robert Price	11/2016
6859	(10489!)^2+Prime(10489)	75242	Robert Price	08/2014
6860	14^65644+67	75237	Lelio R Paula	01/2015
6861	68383!4+32	75236	Robert Price	09/2019
6862	(2^249928-5)/11859059	75229	Lelio R Paula	06/2012
6863	129^35638+2	75218	Lelio R Paula	05/2013
6864	2^249853-110475	75214	Enzo Doria	05/2014
6865	2^249762+75409	75186	Enzo Doria	04/2016
6866	565^27318+27318^565	75181	Norbert Schneider	12/2016
6867	(2^249741-7)/685	75177	Lelio R Paula	06/2012
6868	2^249726-112181	75176	Enzo Doria	06/2014
6869	2^249721+11715	75174	Lelio R Paula	05/2013
6870	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
6871	2^249658-47355	75155	Lelio R Paula	05/2013
6872	155^34311+2	75153	Lelio R Paula	05/2013
6873	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
6874	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
6875	2^249522+8415	75114	Lelio R Paula	05/2013
6876	2^249489-110911	75104	Enzo Doria	05/2014
6877	(28*10^75078+131)/3	75079	Robert Price	02/2017
6878	(206*10^75073-17)/9	75075	Robert Price	03/2017
6879	2^249368-110573	75068	Enzo Doria	05/2014
6880	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
6881	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
6882	(26*10^75055-173)/3	75056	Robert Price	10/2017
6883	2^249272+193	75039	Lelio R Paula	03/2012
6884	14^65468+43	75035	Lelio R Paula	01/2015
6885	37^47844+36	75030	Norbert Schneider	05/2014
6886	(52*10^75027-7)/9	75028	Robert Price	12/2014
6887	20^57653+89	75009	Lelio R Paula	01/2015
6888	2^249061-1868353	74975	Enzo Doria	04/2016
6889	7^88713+2*3^88713	74972	Mike Oakes	07/2010
6890	2*6^96313+5	74947	Lelio R Paula	10/2014
6891	(8*10^74944+49)/3	74945	Robert Price	03/2016
6892	300^30247+30247^300	74926	Norbert Schneider	11/2014
6893	2^248866-171	74917	Lelio R Paula	03/2012
6894	6*5^107168-7	74908	Lelio R Paula	10/2014
6895	11^71926+78	74904	Lelio R Paula	02/2015
6896	2^248824+1869391	74904	Enzo Doria	05/2016
6897	2^248816+1111	74902	Lelio R Paula	01/2011
6898	V(388219)	74890	Serge Batalov	03/2015
6899	159^34017+158	74885	Norbert Schneider	12/2018
6900	2*F(358297)-1	74880	Henri Lifchitz	12/2009
6901	(22*10^74874-31)/9	74875	Robert Price	04/2015
6902	11^71892-76800000	74868	Enzo Doria	01/2013
6903	9*5^107107-4	74866	Lelio R Paula	10/2014
6904	2^248678-710111	74860	Paul Bourdelais	03/2013
6905	(14*10^74858+211)/9	74859	Robert Price	11/2017
6906	13^67194+12	74851	Lelio R Paula	01/2015
6907	(7*2^248634+1)/71	74846	Lelio R Paula	08/2012
6908	11^71867-3090	74842	Enzo Doria	12/2012
6909	68057!4-16	74841	Robert Price	11/2019
6910	2^248609+262145	74839	Lelio R Paula	05/2013
6911	3^156852+50	74838	Lelio R Paula	01/2015
6912	18^59607-11	74824	Lelio R Paula	01/2015
6913	2^248556-110507	74823	Enzo Doria	05/2014
6914	7^88531-36	74818	Lelio R Paula	01/2015
6915	p(15738)#/2+1024	74814	Robert Price	07/2017
6916	4*3^156740-5	74785	Lelio R Paula	05/2014
6917	(32*10^74773-41)/9	74774	Robert Price	05/2015
6918	(29*2^248384-1)/13	74772	Lelio R Paula	01/2014
6919	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
6920	2^248357-12797413	74763	Enzo Doria	03/2016
6921	42^46057+41	74762	Lelio R Paula	07/2012
6922	11^71784-3000	74756	Enzo Doria	12/2012
6923	19^58458+18	74754	Lelio R Paula	01/2015
6924	12^69265-35	74750	Lelio R Paula	02/2015
6926	11^71771-48000	74742	Enzo Doria	12/2012
6925	(7*10^74741+197)/3	74742	Robert Price	07/2017
6927	(2^248282-5)/50129	74736	Lelio R Paula	06/2012
6928	2^248252-110105	74732	Enzo Doria	04/2014
6929	(7*10^74729+71)/3	74730	Robert Price	03/2016
6930	3^156614-50	74724	Lelio R Paula	01/2015
6931	(7*2^248213+1)/135	74719	Lelio R Paula	07/2012
6932	(2^248173+78557)/767	74705	Lelio R Paula	07/2012
6933	125^35622+124	74697	Norbert Schneider	02/2015
6934	(19*2^248099-1)/29	74686	Lelio R Paula	01/2014
6935	(86*10^74676-41)/9	74677	Robert Price	11/2015
6936	(p(15711)#-4)/2	74672	Robert Price	09/2017
6937	10^74670+31	74671	Robert Price	01/2011
6938	10^74670-122463	74670	Patrick De Geest	05/2013
6939	2^248036-69	74667	Lelio R Paula	03/2012
6940	11^71698-6000	74666	Enzo Doria	12/2012
6941	58(10^(324887)-1)/111-1	74661	Robert Price	10/2014
6942	14^65139-45	74658	Lelio R Paula	01/2015
6943	6^95921-133	74642	Lelio R Paula	01/2015
6944	11^71675+78	74642	Lelio R Paula	02/2015
6945	18^59449-91	74625	Lelio R Paula	01/2015
6946	6^95864-16043	74597	Enzo Doria	02/2013
6947	5*7^88261+6	74590	Lelio R Paula	10/2014
6948	9*5^106710+4	74589	Lelio R Paula	10/2014
6949	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
6950	(265*10^74579+17)/3	74581	Robert Price	05/2016
6951	(2^247759-1017)/3318311717	74574	Lelio R Paula	07/2012
6952	5^106682-24	74568	Lelio R Paula	08/2014
6953	474^27863+27863^474	74556	Norbert Schneider	01/2017
6954	(14*10^74540+79)/3	74541	Robert Price	11/2017
6955	(35365^16384+1)/2	74524	Lelio R Paula	11/2011
6956	3^156161+2660	74508	Lelio R Paula	01/2015
6957	2^247474-58695	74498	Lelio R Paula	05/2013
6958	11^71519-90	74480	Enzo Doria	07/2012
6959	(19*2^247419-1)/23202983	74475	Lelio R Paula	01/2014
6961	(2^247394-7)/3	74473	Lelio R Paula	06/2012
6960	18^59328+17	74473	Lelio R Paula	01/2015
6962	2^247379-181	74469	Lelio R Paula	03/2012
6963	(15*2^247370-1)/479	74465	Lelio R Paula	01/2014
6964	2^247344+2047	74458	Lelio R Paula	05/2013
6965	2^247311-1017	74449	Lelio R Paula	05/2013
6966	2^247280+7	74439	Lelio R Paula	03/2012
6967	(68*10^74434+13)/9	74435	Ray Chandler	11/2010
6968	3^156004-62	74433	Lelio R Paula	01/2015
6969	36095!2-64	74416	Robert Price	06/2015
6970	67699!4+16	74409	Robert Price	09/2019
6971	2^247165-3	74405	M. Frind & P. Underwood	07/2002
6972	2^247150+32769	74400	Lelio R Paula	05/2013
6973	12^68911+73	74368	Lelio R Paula	01/2015
6974	2^246999+74903	74355	Enzo Doria	04/2016
6975	2^246989-110643	74352	Enzo Doria	05/2014
6976	10^74350+279439	74351	Patrick De Geest	07/2017
6979	(10^74350+11)/3	74350	Robert Price	11/2014
6977	10^74350-400000001	74350	Robert Price	07/2017
6978	10^74350-716241	74350	Patrick De Geest	07/2017
6980	67647!4-512	74346	Robert Price	11/2019
6981	10^74335+13659	74336	Patrick De Geest	05/2013
6982	10^74335-53	74335	Robert Price	05/2011
6983	2^246906-1215	74327	Lelio R Paula	05/2013
6984	2^246848+111	74309	Lelio R Paula	03/2012
6985	6^95490-18443	74306	Enzo Doria	03/2013
6986	18^59188-2369	74298	Enzo Doria	03/2013
6987	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
6988	2^246744+40755	74278	Lelio R Paula	05/2013
6989	(29*10^74276+91)/3	74277	Robert Price	03/2016
6990	6^95441+163	74268	Lelio R Paula	01/2015
6991	V(390863)	74258	Serge Batalov	03/2015
6992	10^74254+91	74255	Robert Price	03/2011
6994	(19*10^74253-1)/9	74254	Ray Chandler	02/2012
6993	10^74254-130569	74254	Patrick De Geest	05/2013
6995	771^25718+25718^771	74250	Norbert Schneider	10/2016
6996	2^246618+427	74240	Henri Lifchitz	02/2005
6997	88*10^74234+3	74236	Robert Price	11/2016
6998	8*10^74234-49	74235	Robert Price	04/2016
6999	2^246578+12285	74228	Lelio R Paula	05/2013
7000	(3^155569-5)/2	74225	Lelio R Paula	06/2012

Find by discoverer :

PRP Records

Probable Primes Top 10000

(255244 PRPs in the top)