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 ?
7751	18917^4392+4392^18917	68909	Hans Havermann	09/2019
7752	2^228902+73519	68907	Enzo Doria	04/2016
7753	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
7754	16542^14591+14591^16542	68883	Hans Havermann	09/2019
7755	2^228821+76427	68882	Enzo Doria	05/2016
7756	3^144340+50	68868	Lelio R Paula	09/2013
7757	2^228758-112967	68864	Enzo Doria	06/2014
7758	2^228743-111379	68859	Enzo Doria	05/2014
7759	2^228741-110911	68858	Enzo Doria	05/2014
7761	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
7760	3*5^98511-8	68857	Lelio R Paula	09/2014
7762	2^228717+467	68851	Lelio R Paula	02/2011
7763	Phi(153218,10)/2211855049/23592660859/497714117291	68849	Maksym Voznyy	10/2011
7764	(509203*2^228665-1)/35	68840	Lelio R Paula	04/2015
7765	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
7766	11^66074-1050	68809	Enzo Doria	11/2012
7767	(68*10^68798-11)/3	68800	Robert Price	10/2017
7768	2^228484+181	68781	Lelio R Paula	02/2012
7769	2^228479-58695	68780	Lelio R Paula	04/2012
7770	2^228465-15853	68775	Enzo Doria	04/2013
7771	11^66040-5400	68774	Enzo Doria	01/2013
7772	(13*2^228441-1)/575	68766	Lelio R Paula	01/2014
7773	(17*2^228393+1)/295	68752	Lelio R Paula	08/2012
7774	17859^7072+7072^17859	68749	Hans Havermann	09/2019
7775	2*10^68744+41	68745	Robert Price	01/2017
7776	11^66011-150	68744	Enzo Doria	08/2012
7777	(13*2^228304-1)/81	68726	Lelio R Paula	01/2014
7778	2^228295-111079	68724	Enzo Doria	05/2014
7780	(3^144039+7)/22	68723	Lelio R Paula	04/2012
7779	(8*10^68722+49)/3	68723	Robert Price	03/2016
7781	(35*10^68718+1)/9	68719	Serge Batalov	11/2010
7782	2^228271-228271	68717	Henri Lifchitz	11/2004
7783	2^228257+82875	68713	Lelio R Paula	02/2013
7784	3^144013+40	68712	Lelio R Paula	09/2013
7785	13^61671-86	68699	Lelio R Paula	09/2013
7786	(46*10^68698+683)/9	68699	Robert Price	12/2017
7787	17^55828-72	68694	Lelio R Paula	09/2013
7788	18675^4762+4762^18675	68683	Hans Havermann	09/2019
7789	6^88259+61	68679	Lelio R Paula	09/2013
7790	18^54699-5	68663	Lelio R Paula	09/2013
7791	33^45216+2	68662	Lelio R Paula	05/2013
7793	(2^228073-5)/3	68657	Lelio R Paula	04/2012
7792	(2^(6*38012+1)-5)/3	68657	Kevin Acres	11/2013
7794	2^228055-111607	68652	Enzo Doria	05/2014
7795	2^228054-114761	68652	Enzo Doria	05/2015
7796	2^228041+1185	68648	Lelio R Paula	04/2012
7797	2^228040-1037	68647	Yves Minet	11/2012
7798	2*F(328450)-1	68642	Henri Lifchitz	12/2009
7799	5^98201-34	68640	Lelio R Paula	06/2013
7800	9^71910+38^71910-24^71910-3*2^71910	68620	Mike Oakes	12/2010
7801	18177^5948+5948^18177	68607	Hans Havermann	09/2019
7802	7*2^227780-3	68570	Lelio R Paula	04/2014
7803	15327^16382-16382^15327	68567	Norbert Schneider	11/2018
7804	2^227733-121	68555	Lelio R Paula	02/2012
7805	16460^14607+14607^16460	68549	Hans Havermann	09/2019
7806	2^227702-16967	68546	Enzo Doria	05/2013
7807	2^227689-111655	68542	Enzo Doria	05/2014
7808	gcd(V(823915),5F(164783)(F(164783)-1)+1)	68536	Serge Batalov	04/2015
7809	5^98051+2	68535	Ray Chandler	07/2011
7810	5*10^68524+51	68525	Robert Price	01/2017
7811	(11*10^68520-149)/3	68521	Robert Price	01/2017
7812	16624^13235+13235^16624	68520	Hans Havermann	09/2019
7813	16359^15430+15430^16359	68518	Hans Havermann	08/2019
7814	19^53573-78	68507	Lelio R Paula	09/2013
7815	(68*10^68504+13)/9	68505	Ray Chandler	10/2010
7816	9*5^98003+4	68503	Lelio R Paula	09/2014
7817	21121^1750+1750^21121	68497	Hans Havermann	10/2019
7818	2^227528+51	68493	Lelio R Paula	02/2012
7819	(146*28^47316+1)/3	68476	Karsten Bonath	06/2018
7820	3^143497+8	68466	Lelio R Paula	04/2012
7821	2^227430-95	68464	Lelio R Paula	02/2012
7822	(8*10^68455+13)/3	68456	Robert Price	11/2017
7823	3*5^97934-2	68454	Lelio R Paula	09/2014
7824	20^52613+77	68452	Lelio R Paula	09/2013
7825	2^227371+32769	68446	Lelio R Paula	04/2012
7826	(3^143465+4)/21270420067	68440	Lelio R Paula	04/2012
7827	CopelandErdos(68433)	68433	Eric W. Weisstein	08/2013
7828	2^227323+75431	68432	Enzo Doria	04/2016
7829	2^227314-1965	68429	Lelio R Paula	04/2012
7830	2^227303-110617	68426	Enzo Doria	05/2014
7832	7^80963+66	68422	Lelio R Paula	07/2013
7831	2^227290+73849	68422	Enzo Doria	04/2016
7833	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
7834	2^227256-2786249	68411	Enzo Doria	03/2016
7836	8*10^68400-7	68401	Dmitry Domanov	11/2010
7835	(15*2^227228-1)/583	68401	Lelio R Paula	01/2014
7837	2^227210+1869169	68398	Enzo Doria	05/2016
7838	2^227159-1838635	68382	Enzo Doria	05/2015
7839	44*10^68368+3	68370	Robert Price	08/2017
7840	2^227115-7807	68369	Lelio R Paula	10/2009
7841	18469^5032+5032^18469	68368	Hans Havermann	08/2019
7842	2^227078-47355	68358	Lelio R Paula	04/2012
7843	16927^10920+10920^16927	68355	Hans Havermann	10/2019
7844	(2^227063-1017)/349	68351	Lelio R Paula	04/2012
7845	2^227057+148091	68351	Lelio R Paula	04/2012
7846	2^227046+187	68348	Lelio R Paula	02/2012
7847	2^227009-4693	68337	Yves Minet	05/2019
7848	9*10^68331+59	68332	Robert Price	10/2017
7849	11^65608-720	68324	Enzo Doria	11/2012
7850	(32*10^68320+319)/9	68321	Robert Price	10/2017
7851	33408!2-2^33408-1	68315	Joe McLean	05/2017
7852	2^226894-123	68302	Lelio R Paula	02/2012
7853	10^68297+141559	68298	Patrick De Geest	05/2013
7854	10^68297-93	68297	Robert Price	05/2011
7855	680^24107-679^24107	68284	Jean-Louis Charton	07/2010
7856	12^63267+59	68277	Lelio R Paula	07/2013
7857	2^226785-1159	68270	Yves Minet	11/2012
7858	7^80769+90	68258	Lelio R Paula	07/2013
7859	(88*10^68256-1)/3	68258	Robert Price	10/2017
7860	2^226741+66587	68256	Yves Minet	10/2010
7861	2^226720-112403	68250	Enzo Doria	06/2014
7862	(78557*2^226694+1)/3	68247	Lelio R Paula	06/2014
7863	(83*10^68231+7)/9	68232	Robert Price	10/2015
7864	65^37636+16	68231	Lelio R Paula	01/2016
7865	5^97615-4^(97615+1)	68230	Robert Price	04/2016
7866	12^63200-43	68205	Lelio R Paula	07/2013
7867	-330*Bern(21940)/223790620733	68201	Serge Batalov	04/2015
7868	3^142925+8680	68193	Lelio R Paula	06/2013
7869	3*2^226512-7	68188	Lelio R Paula	04/2014
7870	14^59484+57	68177	Lelio R Paula	08/2013
7871	11^65438-2190	68147	Enzo Doria	12/2012
7872	91^34784-2	68144	Lelio R Paula	09/2013
7873	16589^12810+12810^16589	68141	Hans Havermann	10/2019
7874	(2^226336-3)*6-7	68135	Gilbert Mozzo	06/2016
7875	(22*10^68133-37)/3	68134	Robert Price	05/2017
7876	5^97476+36	68133	Lelio R Paula	06/2013
7877	3*5^97474-2	68132	Lelio R Paula	09/2014
7878	12^63130+49	68129	Lelio R Paula	07/2013
7879	2^226281+5385	68118	Lelio R Paula	04/2012
7880	2^226257-3049	68111	Yves Minet	10/2014
7881	(28*10^68107-43)/3	68108	Robert Price	04/2016
7882	2^226243-2587	68106	Yves Minet	07/2014
7883	20^52346-11	68104	Lelio R Paula	09/2013
7884	2^226205-99	68095	Lelio R Paula	02/2012
7885	2^226187-49	68090	Lelio R Paula	02/2012
7886	3^142708+76	68090	Lelio R Paula	06/2013
7887	7*10^68088-89	68089	Robert Price	01/2017
7888	18562^4653+4653^18562	68081	Hans Havermann	09/2019
7889	2^226154+71839	68080	Enzo Doria	04/2016
7890	(10^68078+59)/3	68078	Serge Batalov	12/2014
7892	14^59387+69	68066	Lelio R Paula	08/2013
7891	2^226108-113429	68066	Enzo Doria	07/2014
7893	(62*10^68059-197)/9	68060	Robert Price	10/2017
7894	(24^49307-1)/23	68053	Robert Price	04/2012
7895	15^57859-28	68048	Lelio R Paula	08/2013
7896	(509203*2^226003-1)/13	68039	Lelio R Paula	04/2015
7897	2^226015-111361	68038	Enzo Doria	05/2014
7898	(10^(234016+1)+7210^34016-1)/9	68033	Robert Price	09/2017
7899	4*10^68020+91	68021	Robert Price	11/2017
7900	16181^15948+15948^16181	68004	Hans Havermann	09/2019
7901	156(10^(417000)-1)/101-1	68001	Robert Price	05/2014
7902	2^225878-1017	67997	Lelio R Paula	04/2012
7903	38^75289+5^75289-34^75289+3*2^75289	67994	Mike Oakes	11/2010
7904	3*2^225865+5	67993	Lelio R Paula	04/2014
7905	11^65284-5820	67987	Enzo Doria	01/2013
7906	19^53166+70	67987	Lelio R Paula	08/2013
7907	2^225837+75407	67984	Enzo Doria	04/2016
7908	3^142464-112654	67973	Enzo Doria	06/2014
7909	16851^10802+10802^16851	67969	Hans Havermann	09/2019
7910	2^225777+95	67966	Lelio R Paula	02/2012
7911	(2^225641-1017)/138815	67920	Lelio R Paula	04/2012
7912	2^225609-18445	67916	Enzo Doria	05/2013
7913	2^225542-177	67895	Lelio R Paula	02/2012
7914	2^225536-29	67894	Henri Lifchitz	05/2005
7915	11^65190-3390	67889	Enzo Doria	12/2012
7916	62271!4-1024	67878	Robert Price	11/2019
7917	16971^9986+9986^16971	67874	Hans Havermann	09/2019
7918	3^142249-2^(142249-1)	67871	Robert Price	01/2016
7919	11^65168-4830	67866	Enzo Doria	01/2013
7920	10^67863+58627	67864	Patrick De Geest	01/2016
7921	16258^14933+14933^16258	67864	Hans Havermann	09/2019
7922	10^67863-11	67863	Robert Price	05/2011
7923	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
7924	(19*2^225357-1)/11	67840	Lelio R Paula	01/2014
7925	9*6^87164-7	67828	Lelio R Paula	09/2014
7926	131^32034+130	67825	Norbert Schneider	03/2015
7927	(29*2^225314+1)/10881	67824	Lelio R Paula	08/2012
7928	17761^6586+6586^17761	67823	Hans Havermann	09/2019
7929	(134*10^67816+7)/3	67818	Robert Price	02/2017
7930	2^225261+855	67811	Lelio R Paula	04/2012
7931	(29*2^225252-1)/2933	67806	Lelio R Paula	01/2014
7932	(4*10^67796+23)/9	67796	Robert Price	11/2014
7933	15477^16180-16180^15477	67790	Norbert Schneider	09/2018
7934	(23*2^225177+1)/31	67785	Lelio R Paula	08/2012
7935	(4*10^67784+149)/9	67784	Robert Price	03/2017
7936	8177^17322+17322^8177	67774	Norbert Schneider	03/2019
7937	2^225120+151	67768	Lelio R Paula	02/2012
7938	(44^41233+1)/45	67763	Robert Price	11/2013
7939	89933!6-16	67747	Robert Price	08/2018
7940	8*10^67742+9	67743	Dmitry Domanov	11/2010
7941	2^224977+1089	67725	Lelio R Paula	04/2012
7942	(2^224950+5)/19509	67713	Lelio R Paula	04/2012
7943	11^65011-5970	67702	Enzo Doria	01/2013
7944	88*10^67691+7	67693	Robert Price	11/2016
7945	11^65000-7140	67691	Enzo Doria	01/2013
7946	2^224841+59	67684	Lelio R Paula	02/2012
7947	33129!2+2^33129	67684	Robert Price	09/2015
7948	2^224827+8415	67680	Lelio R Paula	02/2013
7949	(9913*2^224821-1)/19825	67678	Lelio R Paula	04/2015
7950	2^224815-49789	67677	Henri Lifchitz	04/2005
7951	7257^17528+17528^7257	67672	Norbert Schneider	08/2019
7952	(43*10^67664+11)/9	67665	Robert Price	06/2015
7953	(292*10^67659-1)/3	67661	Robert Price	01/2017
7954	(17*2^224766+1)/29007	67659	Lelio R Paula	06/2012
7955	2^224744+577294575	67655	Lelio R Paula	02/2016
7956	((1+sqrt(7)+sqrt(6))^45863-1)((1+sqrt(7)-sqrt(6))^45863-1)((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(7	67653	Mike Oakes	05/2009
7957	(2^224721+78557)/1739	67645	Lelio R Paula	05/2012
7958	2^224700+1915	67642	Lelio R Paula	04/2012
7959	(29*2^224694-1)/198905	67636	Lelio R Paula	01/2014
7960	2^224658-93	67629	Lelio R Paula	02/2012
7961	2^224624-13077	67619	Enzo Doria	10/2012
7962	18^53860-3319	67609	Enzo Doria	03/2013
7963	(21181*2^224570+1)/5	67606	Lelio R Paula	06/2014
7964	89762!6-3	67606	Robert Price	08/2018
7965	2^224578-111041	67605	Enzo Doria	05/2014
7966	2^224569-113233	67603	Enzo Doria	07/2014
7967	2^224562-113171	67600	Enzo Doria	07/2014
7968	2^224556-113129	67599	Enzo Doria	07/2014
7969	6*7^79980-5	67592	Lelio R Paula	09/2014
7970	(6883*2^224523-1)/16031	67588	Lelio R Paula	04/2015
7971	10^67579+164779	67580	Patrick De Geest	07/2017
7973	(52*10^67578-61)/9	67579	Robert Price	09/2015
7972	10^67579-401	67579	Robert Price	06/2017
7974	(17^54919-1)/16	67574	Paul Bourdelais	03/2010
7975	22115^1134+1134^22115	67553	Hans Havermann	08/2019
7976	((10^33771-1)10000/9+6389)10^33771+(10^33771-1)/9	67546	Hans Havermann	05/2019
7977	(2^224363-9)/1951	67537	Lelio R Paula	04/2012
7978	(709*10^67517-7)/9	67519	Robert Price	09/2017
7979	47719!3-59049	67516	Robert Price	12/2015
7980	16356^13411+13411^16356	67509	Hans Havermann	09/2019
7981	(22^50287+1)/23	67506	Robert Price	06/2013
7982	16671^11198+11198^16671	67504	Hans Havermann	09/2019
7983	3*10^67499+67	67500	Robert Price	11/2017
7984	11^64811-5820	67494	Enzo Doria	01/2013
7985	131^31870+31870^131	67478	Serge Batalov	05/2014
7986	9*10^67468+7	67469	Dmitry Domanov	11/2010
7987	(31*2^224115-1)/47723	67463	Lelio R Paula	01/2014
7988	128^32001+32001^128	67433	Serge Batalov	05/2014
7989	(89*10^67431-17)/9	67432	Robert Price	11/2015
7990	2^223912-111059	67405	Enzo Doria	05/2014
7992	2^223913+73697	67405	Enzo Doria	04/2016
7991	(2*10^67405-23)/3	67405	Robert Price	09/2017
7994	(10^67404+179)/9	67404	Serge Batalov	12/2014
7993	18738^3955+3955^18738	67404	Hans Havermann	09/2016
7995	9*7^79728-2	67379	Lelio R Paula	09/2014
7996	(28*10^67378-43)/3	67379	Robert Price	04/2016
7997	(3^141234-7)/430241282	67378	Lelio R Paula	04/2012
7998	211^28988-2	67377	Lelio R Paula	09/2013
7999	4*10^67375+91	67376	Robert Price	11/2017
8000	2^223793-18069	67369	Enzo Doria	05/2013

Find by discoverer :

PRP Records

Probable Primes Top 10000

(255312 PRPs in the top)