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 (> 30000)	Who ?	When ?
6751	7*2^232381+3	69955	Lelio R Paula	04/2014
6752	2^232362-110541	69948	Enzo Doria	05/2014
6753	2^232326-112391	69938	Enzo Doria	06/2014
6754	3^146575+236	69935	Lelio R Paula	09/2013
6755	30^47341-29	69929	Norbert Schneider	02/2014
6756	5^100040-68	69925	Lelio R Paula	09/2013
6757	(35*10^69866-593)/9	69867	Robert Price	08/2017
6758	2^232045-17295	69853	Lelio R Paula	04/2012
6759	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
6760	2^231955+74243	69826	Yves Minet	03/2011
6761	2^231946-15873	69823	Enzo Doria	04/2013
6762	18^55618+95	69816	Lelio R Paula	09/2013
6763	6^89712+5^(89712-1)	69810	Robert Price	02/2016
6764	2^231870+135	69800	Lelio R Paula	02/2012
6765	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
6766	2^231778+54615	69773	Lelio R Paula	04/2012
6767	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
6768	14^60866+27	69761	Lelio R Paula	09/2013
6769	13^62619-44	69755	Lelio R Paula	09/2013
6770	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
6771	2^231711-110467	69752	Enzo Doria	05/2014
6772	(19^54547+18^54547)/37	69751	Robert Price	08/2013
6773	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
6774	2^231696-1861499	69748	Enzo Doria	03/2016
6775	2^231684-147	69744	Lelio R Paula	02/2012
6776	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
6777	2^231591-477397	69716	Paul Bourdelais	03/2013
6778	11^66916-420	69686	Enzo Doria	08/2012
6779	5^99680-13706	69674	Enzo Doria	02/2013
6780	(8*10^69674-53)/9	69674	Robert Price	11/2014
6781	(44*10^69663-413)/9	69664	Robert Price	10/2017
6782	(77*10^69656-23)/9	69657	Robert Price	10/2015
6783	6^89509+131	69652	Lelio R Paula	09/2013
6784	(78557*2^231349+1)/35	69647	Lelio R Paula	06/2014
6785	(11*10^69645+19)/3	69646	Robert Price	03/2016
6786	11^66875-28	69644	Lelio R Paula	09/2013
6787	2^231347+71483	69643	Enzo Doria	04/2016
6788	(14^60763+3^60763)/17	69641	Robert Price	04/2013
6789	(4*10^69626+173)/3	69627	Robert Price	01/2017
6790	2^231289+255	69625	Lelio R Paula	04/2012
6791	2^231234-112913	69609	Enzo Doria	06/2014
6792	(265*10^69602-7)/3	69604	Robert Price	07/2016
6793	2^231182-112841	69593	Enzo Doria	06/2014
6794	(15*2^231129+1)/23	69577	Lelio R Paula	08/2012
6795	3^145806-28	69568	Lelio R Paula	09/2013
6796	(265*10^69554-7)/3	69556	Robert Price	07/2016
6797	2^231052-113159	69554	Enzo Doria	07/2014
6798	11^66784-8	69549	Lelio R Paula	09/2013
6799	Phi(104409,10)/2296999	69546	Maksym Voznyy	07/2015
6800	2^231016-110523	69543	Enzo Doria	05/2014
6801	2^231014+577294575	69543	Lelio R Paula	02/2016
6802	14^60658+67	69522	Lelio R Paula	09/2013
6803	5^99418+36	69491	Lelio R Paula	06/2013
6804	7^82203-30	69470	Lelio R Paula	09/2013
6805	(63^38609-1)/62	69469	Paul Bourdelais	08/2017
6806	5^99359-2^99360	69449	Mike Oakes	12/2010
6807	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
6808	(19*10^69424+77)/3	69425	Robert Price	08/2016
6809	19^54287-96	69420	Lelio R Paula	09/2013
6810	2^230541+58905	69400	Lelio R Paula	04/2012
6811	2^230506+12705	69390	Lelio R Paula	02/2013
6812	8*6^89156-5	69378	Lelio R Paula	09/2014
6813	2^230438-111347	69369	Enzo Doria	05/2014
6814	2^230428-99	69366	Lelio R Paula	02/2012
6815	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
6816	3*10^69354+17	69355	Robert Price	03/2017
6817	(493*10^69340-7)/9	69342	Robert Price	07/2016
6818	(41*10^69321+373)/9	69322	Robert Price	04/2017
6819	6^89072+53	69312	Lelio R Paula	09/2013
6820	155^31639+2	69300	Lelio R Paula	05/2013
6821	3*7^81965-4	69269	Lelio R Paula	09/2014
6822	(16*10^69265+41)/3	69266	Robert Price	10/2017
6823	(86*10^69260-77)/9	69261	Robert Price	05/2016
6824	9*5^99087+4	69260	Lelio R Paula	09/2014
6825	3^145145+2660	69252	Lelio R Paula	09/2013
6826	11^66492-1140	69245	Enzo Doria	11/2012
6827	5*3^145129-4	69245	Lelio R Paula	04/2014
6828	7*3^145126+8	69244	Lelio R Paula	04/2014
6829	11^66480-2370	69232	Enzo Doria	12/2012
6830	2^229962-65	69226	Lelio R Paula	02/2012
6831	2^229958-110733	69225	Enzo Doria	05/2014
6832	V(332407)	69225	Serge Batalov	03/2015
6833	6^88959+7	69224	Lelio R Paula	09/2013
6834	15^58855-94	69219	Lelio R Paula	09/2013
6835	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
6836	3^144952+98	69160	Lelio R Paula	09/2013
6837	5^98941-72	69157	Lelio R Paula	06/2013
6838	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
6839	2^229585-1063	69112	Yves Minet	11/2012
6840	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
6841	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
6842	(53*10^69050-17)/9	69051	Robert Price	09/2015
6843	(43*10^69048+47)/9	69049	Robert Price	12/2017
6844	2^229305-1868533	69028	Enzo Doria	04/2016
6845	2^229297+1385	69026	Lelio R Paula	04/2012
6846	18^54986-2441	69023	Enzo Doria	03/2013
6847	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
6848	5^98736-14636	69014	Enzo Doria	02/2013
6849	(13^61949-5^61949)/8	69007	Robert Price	03/2013
6850	(2^229227+5)/611	69002	Lelio R Paula	04/2012
6851	2^229216-113279	69001	Enzo Doria	07/2014
6852	10^68994+51913	68995	Patrick De Geest	03/2016
6854	10^68994-10^5814-1	68994	Serge Batalov	01/2011
6853	10^68994-82947	68994	Patrick De Geest	03/2016
6855	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
6856	2^229113+107	68970	Lelio R Paula	02/2012
6857	11^66202-4410	68943	Enzo Doria	01/2013
6858	12^63883+5	68942	Lelio R Paula	07/2013
6859	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
6860	2^228962-111581	68925	Enzo Doria	05/2014
6861	2^228944+81	68920	Henri Lifchitz	01/2007
6862	11^66174-54	68914	Lelio R Paula	09/2013
6863	2^228913-111265	68910	Enzo Doria	05/2014
6864	2^228902+73519	68907	Enzo Doria	04/2016
6865	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
6866	2^228821+76427	68882	Enzo Doria	05/2016
6867	3^144340+50	68868	Lelio R Paula	09/2013
6868	2^228758-112967	68864	Enzo Doria	06/2014
6869	2^228743-111379	68859	Enzo Doria	05/2014
6870	2^228741-110911	68858	Enzo Doria	05/2014
6872	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
6871	3*5^98511-8	68857	Lelio R Paula	09/2014
6873	2^228717+467	68851	Lelio R Paula	02/2011
6874	Phi(153218,10)/2211855049/23592660859/497714117291	68849	Maksym Voznyy	10/2011
6875	(509203*2^228665-1)/35	68840	Lelio R Paula	04/2015
6876	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
6877	11^66074-1050	68809	Enzo Doria	11/2012
6878	(68*10^68798-11)/3	68800	Robert Price	10/2017
6879	2^228484+181	68781	Lelio R Paula	02/2012
6880	2^228479-58695	68780	Lelio R Paula	04/2012
6881	2^228465-15853	68775	Enzo Doria	04/2013
6882	11^66040-5400	68774	Enzo Doria	01/2013
6883	(13*2^228441-1)/575	68766	Lelio R Paula	01/2014
6884	(17*2^228393+1)/295	68752	Lelio R Paula	08/2012
6885	2*10^68744+41	68745	Robert Price	01/2017
6886	11^66011-150	68744	Enzo Doria	08/2012
6887	(13*2^228304-1)/81	68726	Lelio R Paula	01/2014
6888	2^228295-111079	68724	Enzo Doria	05/2014
6890	(3^144039+7)/22	68723	Lelio R Paula	04/2012
6889	(8*10^68722+49)/3	68723	Robert Price	03/2016
6891	(35*10^68718+1)/9	68719	Serge Batalov	11/2010
6892	2^228271-228271	68717	Henri Lifchitz	11/2004
6893	2^228257+82875	68713	Lelio R Paula	02/2013
6894	3^144013+40	68712	Lelio R Paula	09/2013
6895	13^61671-86	68699	Lelio R Paula	09/2013
6896	(46*10^68698+683)/9	68699	Robert Price	12/2017
6897	17^55828-72	68694	Lelio R Paula	09/2013
6898	6^88259+61	68679	Lelio R Paula	09/2013
6899	18^54699-5	68663	Lelio R Paula	09/2013
6900	33^45216+2	68662	Lelio R Paula	05/2013
6902	(2^228073-5)/3	68657	Lelio R Paula	04/2012
6901	(2^(6*38012+1)-5)/3	68657	Kevin Acres	11/2013
6903	2^228055-111607	68652	Enzo Doria	05/2014
6904	2^228054-114761	68652	Enzo Doria	05/2015
6905	2^228041+1185	68648	Lelio R Paula	04/2012
6906	2^228040-1037	68647	Yves Minet	11/2012
6907	2*F(328450)-1	68642	Henri Lifchitz	12/2009
6908	5^98201-34	68640	Lelio R Paula	06/2013
6909	9^71910+38^71910-24^71910-3*2^71910	68620	Mike Oakes	12/2010
6910	7*2^227780-3	68570	Lelio R Paula	04/2014
6911	2^227733-121	68555	Lelio R Paula	02/2012
6912	2^227702-16967	68546	Enzo Doria	05/2013
6913	2^227689-111655	68542	Enzo Doria	05/2014
6914	gcd(V(823915),5F(164783)(F(164783)-1)+1)	68536	Serge Batalov	04/2015
6915	5^98051+2	68535	Ray Chandler	07/2011
6916	5*10^68524+51	68525	Robert Price	01/2017
6917	(11*10^68520-149)/3	68521	Robert Price	01/2017
6918	19^53573-78	68507	Lelio R Paula	09/2013
6919	(68*10^68504+13)/9	68505	Ray Chandler	10/2010
6920	9*5^98003+4	68503	Lelio R Paula	09/2014
6921	2^227528+51	68493	Lelio R Paula	02/2012
6922	(146*28^47316+1)/3	68476	Karsten Bonath	06/2018
6923	3^143497+8	68466	Lelio R Paula	04/2012
6924	2^227430-95	68464	Lelio R Paula	02/2012
6925	(8*10^68455+13)/3	68456	Robert Price	11/2017
6926	3*5^97934-2	68454	Lelio R Paula	09/2014
6927	20^52613+77	68452	Lelio R Paula	09/2013
6928	2^227371+32769	68446	Lelio R Paula	04/2012
6929	(3^143465+4)/21270420067	68440	Lelio R Paula	04/2012
6930	CopelandErdos(68433)	68433	Eric W. Weisstein	08/2013
6931	2^227323+75431	68432	Enzo Doria	04/2016
6932	2^227314-1965	68429	Lelio R Paula	04/2012
6933	2^227303-110617	68426	Enzo Doria	05/2014
6934	7^80963+66	68422	Lelio R Paula	07/2013
6935	2^227290+73849	68422	Enzo Doria	04/2016
6936	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
6937	2^227256-2786249	68411	Enzo Doria	03/2016
6939	8*10^68400-7	68401	Dmitry Domanov	11/2010
6938	(15*2^227228-1)/583	68401	Lelio R Paula	01/2014
6940	2^227210+1869169	68398	Enzo Doria	05/2016
6941	2^227159-1838635	68382	Enzo Doria	05/2015
6942	44*10^68368+3	68370	Robert Price	08/2017
6943	2^227115-7807	68369	Lelio R Paula	10/2009
6944	2^227078-47355	68358	Lelio R Paula	04/2012
6945	(2^227063-1017)/349	68351	Lelio R Paula	04/2012
6946	2^227057+148091	68351	Lelio R Paula	04/2012
6947	2^227046+187	68348	Lelio R Paula	02/2012
6948	9*10^68331+59	68332	Robert Price	10/2017
6949	11^65608-720	68324	Enzo Doria	11/2012
6950	(32*10^68320+319)/9	68321	Robert Price	10/2017
6951	33408!2-2^33408-1	68315	Joe McLean	05/2017
6952	2^226894-123	68302	Lelio R Paula	02/2012
6953	10^68297+141559	68298	Patrick De Geest	05/2013
6954	10^68297-93	68297	Robert Price	05/2011
6955	680^24107-679^24107	68284	Jean-Louis Charton	07/2010
6956	12^63267+59	68277	Lelio R Paula	07/2013
6957	2^226785-1159	68270	Yves Minet	11/2012
6958	7^80769+90	68258	Lelio R Paula	07/2013
6959	(88*10^68256-1)/3	68258	Robert Price	10/2017
6960	2^226741+66587	68256	Yves Minet	10/2010
6961	2^226720-112403	68250	Enzo Doria	06/2014
6962	(78557*2^226694+1)/3	68247	Lelio R Paula	06/2014
6963	(83*10^68231+7)/9	68232	Robert Price	10/2015
6964	65^37636+16	68231	Lelio R Paula	01/2016
6965	5^97615-4^(97615+1)	68230	Robert Price	04/2016
6966	12^63200-43	68205	Lelio R Paula	07/2013
6967	-330*Bern(21940)/223790620733	68201	Serge Batalov	04/2015
6968	3^142925+8680	68193	Lelio R Paula	06/2013
6969	3*2^226512-7	68188	Lelio R Paula	04/2014
6970	14^59484+57	68177	Lelio R Paula	08/2013
6971	11^65438-2190	68147	Enzo Doria	12/2012
6972	91^34784-2	68144	Lelio R Paula	09/2013
6973	(2^226336-3)*6-7	68135	Gilbert Mozzo	06/2016
6974	(22*10^68133-37)/3	68134	Robert Price	05/2017
6975	5^97476+36	68133	Lelio R Paula	06/2013
6976	3*5^97474-2	68132	Lelio R Paula	09/2014
6977	12^63130+49	68129	Lelio R Paula	07/2013
6978	2^226281+5385	68118	Lelio R Paula	04/2012
6979	2^226257-3049	68111	Yves Minet	10/2014
6980	(28*10^68107-43)/3	68108	Robert Price	04/2016
6981	2^226243-2587	68106	Yves Minet	07/2014
6982	20^52346-11	68104	Lelio R Paula	09/2013
6983	2^226205-99	68095	Lelio R Paula	02/2012
6984	2^226187-49	68090	Lelio R Paula	02/2012
6985	3^142708+76	68090	Lelio R Paula	06/2013
6986	7*10^68088-89	68089	Robert Price	01/2017
6987	2^226154+71839	68080	Enzo Doria	04/2016
6988	(10^68078+59)/3	68078	Serge Batalov	12/2014
6990	14^59387+69	68066	Lelio R Paula	08/2013
6989	2^226108-113429	68066	Enzo Doria	07/2014
6991	(62*10^68059-197)/9	68060	Robert Price	10/2017
6992	(24^49307-1)/23	68053	Robert Price	04/2012
6993	15^57859-28	68048	Lelio R Paula	08/2013
6994	(509203*2^226003-1)/13	68039	Lelio R Paula	04/2015
6995	2^226015-111361	68038	Enzo Doria	05/2014
6996	(10^(234016+1)+7210^34016-1)/9	68033	Robert Price	09/2017
6997	4*10^68020+91	68021	Robert Price	11/2017
6998	156(10^(417000)-1)/101-1	68001	Robert Price	05/2014
6999	2^225878-1017	67997	Lelio R Paula	04/2012
7000	38^75289+5^75289-34^75289+3*2^75289	67994	Mike Oakes	11/2010

Find by discoverer :

PRP Records

Probable Primes Top 10000

(225451 PRPs in the top)