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) !!!

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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 ?
7752	2^218897-111889	65895	Enzo Doria	05/2014
7751	2^218896+1869451	65895	Enzo Doria	05/2016
7753	63^36616+2	65885	Lelio R Paula	05/2013
7754	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
7755	2^218796-113297	65865	Enzo Doria	07/2014
7756	2^218797+73727	65865	Enzo Doria	04/2016
7757	3^138040-110	65862	Lelio R Paula	06/2013
7758	11^63240-1950	65858	Enzo Doria	12/2012
7759	2^218764-111873	65855	Enzo Doria	05/2014
7760	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
7761	3^137988+26	65838	Lelio R Paula	06/2013
7762	2^218680-719	65830	Yves Minet	05/2012
7763	18^52424+17	65807	Lelio R Paula	08/2013
7764	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
7765	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
7766	(5*10^65773+1)/3	65774	Erik Branger	12/2013
7767	160^29839-159	65769	Norbert Schneider	12/2018
7768	2^218457-17329	65763	Enzo Doria	05/2013
7769	151703#+223381	65759	Nicolas PALAU	10/2016
7770	2^218436+40755	65756	Lelio R Paula	10/2011
7771	2^218399-4627	65745	Yves Minet	05/2019
7772	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
7773	157^29934+29934^157	65733	Serge Batalov	05/2014
7774	211^28273-2	65715	Lelio R Paula	09/2013
7775	(59*10^65712+31)/9	65713	Robert Price	09/2015
7777	611^23586+23586^611	65712	Norbert Schneider	08/2016
7776	p(13991)#/2+32	65712	Robert Price	12/2016
7778	2^218282-18485	65710	Enzo Doria	05/2013
7779	2^218274-111251	65708	Enzo Doria	05/2014
7780	2*F(314335)-1	65693	Henri Lifchitz	12/2009
7781	2^218200+427	65685	Henri Lifchitz	01/2005
7782	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
7783	(10199^(2^14)+(10197)^(2^14))/2	65676	Robert Price	05/2018
7784	46532!3+3	65667	Robert Price	10/2014
7785	2^218120-147	65661	Lelio R Paula	08/2011
7786	452^24729+24729^452	65659	Norbert Schneider	09/2016
7787	2^218102-114893	65656	Enzo Doria	05/2015
7788	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
7789	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
7790	(306^26407-1)/305	65638	Eric Chen	09/2017
7792	19^51326+36	65634	Lelio R Paula	08/2013
7791	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
7793	2^217989-33	65622	Lelio R Paula	08/2011
7794	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
7795	4*6^84315-5	65611	Lelio R Paula	09/2014
7796	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
7797	6^84303+55	65601	Lelio R Paula	07/2013
7798	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
7799	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
7800	5*2^217858+3	65583	Lelio R Paula	04/2014
7801	(19*10^65572+119)/3	65573	Robert Price	02/2017
7802	20^50399+51	65571	Lelio R Paula	08/2013
7803	7162^17009+17009^7162	65571	Norbert Schneider	07/2018
7804	11^62946-5670	65552	Enzo Doria	01/2013
7805	2^217742-3911	65547	Yves Minet	08/2009
7806	(19*10^65545+77)/3	65546	Robert Price	08/2016
7807	2^217731+131	65544	Lelio R Paula	08/2011
7808	2^217720-111287	65541	Enzo Doria	05/2014
7809	(365^25579+1)/366	65539	Eric Chen	10/2017
7810	10^65537+27	65538	Robert Price	01/2011
7811	10^65537-76859	65537	Patrick De Geest	05/2013
7812	(28*10^65532+359)/9	65533	Robert Price	11/2017
7813	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
7814	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
7815	5*10^65509+23	65510	Robert Price	11/2017
7816	(8*10^65507-83)/3	65508	Robert Price	10/2017
7817	7*10^65492-47	65493	Robert Price	02/2017
7818	2^217547-1868407	65489	Enzo Doria	04/2016
7819	2^217531-111769	65484	Enzo Doria	05/2014
7820	7^77484-18	65482	Lelio R Paula	06/2013
7821	5754^17413+17413^5754	65473	Norbert Schneider	05/2019
7822	2^217488-113285	65471	Enzo Doria	07/2014
7823	151153#/30-30	65468	Henri Lifchitz	12/2011
7824	2^217466+4257	65464	Lelio R Paula	10/2011
7825	46396!3-81	65455	Robert Price	09/2014
7826	2^217421-113185	65451	Enzo Doria	07/2014
7827	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
7828	2^217408-2145	65447	Lelio R Paula	10/2011
7829	2^217398-16947	65444	Enzo Doria	05/2013
7830	8*5^93613+3	65434	Lelio R Paula	09/2014
7831	11^62828-5310	65429	Enzo Doria	01/2013
7832	10^65426+13	65427	Robert Price	01/2011
7833	2^217341-6555	65427	Lelio R Paula	10/2011
7834	10^65426-54849	65426	Patrick De Geest	05/2013
7835	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
7836	30011^14608-108	65405	Enzo Doria	07/2012
7837	119^31504-2	65389	Lelio R Paula	10/2017
7838	(43^40031-1)/42	65388	Robert Price	04/2014
7839	2^217190+94395	65381	Henri Lifchitz	02/2005
7840	15^55587+46	65376	Lelio R Paula	08/2013
7841	2^217088-111833	65350	Enzo Doria	05/2014
7842	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
7843	(10^65340+47)/3	65340	Robert Price	11/2017
7844	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
7845	2^216947-111351	65308	Enzo Doria	05/2014
7846	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
7847	(13*10^65297+83)/3	65298	Robert Price	09/2016
7848	5^93400-8	65284	Lelio R Paula	06/2013
7849	2^216802-165	65264	Lelio R Paula	08/2011
7850	2^216799-28635	65264	Lelio R Paula	10/2011
7851	5*10^65255+51	65256	Robert Price	01/2017
7852	2^216762-167	65252	Lelio R Paula	08/2011
7853	11^62657-5790	65251	Enzo Doria	01/2013
7854	3^136756-112880	65250	Enzo Doria	06/2014
7855	2^216752+21	65249	Lelio R Paula	08/2011
7856	3*10^65247+11	65248	Robert Price	11/2017
7857	11^62651-2700	65245	Enzo Doria	12/2012
7858	15130^15609-15609^15130	65244	Norbert Schneider	07/2018
7860	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
7859	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
7861	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
7862	2^216652-2327	65219	Yves Minet	10/2013
7863	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
7864	(5*10^65203-119)/3	65204	Robert Price	04/2016
7865	2^216555-113269	65190	Enzo Doria	07/2014
7866	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
7867	2^216474+12915	65166	Lelio R Paula	02/2013
7868	19^50958-32	65163	Lelio R Paula	08/2013
7869	2^216442-112133	65156	Enzo Doria	06/2014
7870	2^216437-112213	65155	Enzo Doria	06/2014
7871	2^216435-112767	65154	Enzo Doria	06/2014
7872	2^216420+12705	65149	Lelio R Paula	02/2013
7873	8*3^136507-7	65132	Lelio R Paula	04/2014
7874	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
7875	15132^15575-15575^15132	65102	Norbert Schneider	07/2018
7876	5*10^65086-51	65087	Robert Price	10/2017
7877	2^216197-111769	65082	Enzo Doria	05/2014
7878	6^83631-79	65078	Lelio R Paula	07/2013
7879	572^23601+23601^572	65078	Norbert Schneider	08/2016
7880	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
7881	2^216154-1421	65069	Yves Minet	01/2013
7882	2^216145-112663	65067	Enzo Doria	06/2014
7883	(7*10^65064+53)/3	65065	Robert Price	10/2017
7884	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7885	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7886	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7887	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7888	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
7891	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
7890	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7889	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7892	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
7893	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
7894	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
7895	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
7896	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
7897	p(13861)#/2+256	65039	Robert Price	05/2017
7898	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
7899	11^62439-4380	65024	Enzo Doria	01/2013
7900	3^136244+2	65005	Mike Oakes	11/2009
7901	13^58343-50	64991	Lelio R Paula	07/2013
7902	331^25791-10002	64989	Enzo Doria	07/2012
7903	2^215877+131	64986	Lelio R Paula	08/2011
7904	4*5^92959+9	64977	Lelio R Paula	09/2014
7905	2^215789-18825	64959	Lelio R Paula	09/2011
7906	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
7907	U(315311)	64954	Serge Batalov	03/2015
7908	46072!3-59049	64951	Robert Price	12/2015
7909	2^215750-5955	64948	Lelio R Paula	09/2011
7910	13^58281+46	64922	Lelio R Paula	07/2013
7911	2^215623+183	64909	Lelio R Paula	08/2011
7912	(46*10^64904+521)/9	64905	Robert Price	08/2017
7913	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
7914	5*2^215554+3	64889	Lelio R Paula	04/2014
7915	2^215541-112075	64885	Enzo Doria	06/2014
7916	2*10^64882-3	64883	Dmitry Domanov	11/2010
7917	10^64862+342339	64863	Patrick De Geest	05/2013
7918	10^64862-47	64862	Robert Price	05/2011
7919	19^50718-84	64856	Lelio R Paula	08/2013
7920	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
7921	86413!6-12	64846	Robert Price	08/2018
7923	10^64843+4278697839	64844	Robert Price	05/2015
7922	10^64843+21967	64844	Patrick De Geest	03/2016
7924	10^64843-340073	64843	Patrick De Geest	03/2016
7925	11^62254+70	64831	Lelio R Paula	07/2013
7926	2^215351-111925	64828	Enzo Doria	05/2014
7927	2^215310-117	64815	Lelio R Paula	08/2011
7928	124^30958-123	64809	Norbert Schneider	02/2015
7929	(7*10^64807+17)/3	64808	Erik Branger	03/2014
7930	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
7931	2^215243-15949	64795	Enzo Doria	04/2013
7932	23^47581-22^47581	64793	Robert Price	08/2012
7933	(62*10^64783-17)/9	64784	Robert Price	09/2015
7934	5*3^135747-4	64769	Lelio R Paula	04/2014
7935	(59*10^64767-41)/9	64768	Robert Price	09/2015
7936	(2^215140+3)/19	64763	Lelio R Paula	04/2012
7937	2^215135-17169	64763	Enzo Doria	05/2013
7938	2^215115-111277	64757	Enzo Doria	05/2014
7939	9*5^92641+2	64755	Lelio R Paula	09/2014
7940	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
7941	5791^17200+17200^5791	64720	Norbert Schneider	12/2018
7942	(5*10^64715-23)/9	64715	Robert Price	11/2014
7943	2^214938-1781	64703	Yves Minet	03/2013
7944	11^62111-420	64682	Enzo Doria	08/2012
7945	5^92525+42	64673	Lelio R Paula	06/2013
7946	2^214824+71893	64669	Enzo Doria	04/2016
7947	2^214799-2221	64661	Yves Minet	08/2013
7948	5939^17128+17128^5939	64637	Norbert Schneider	10/2018
7949	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
7950	92^32907+32907^92	64623	Serge Batalov	05/2014
7951	(89*10^64608-539)/9	64609	Robert Price	11/2017
7952	6^83013+101	64597	Lelio R Paula	07/2013
7953	p(13775)#/2+8	64594	Robert Price	01/2017
7954	(7*10^64568-43)/9	64568	Robert Price	10/2014
7955	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
7956	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
7957	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
7958	2^214458+54615	64559	Lelio R Paula	10/2011
7959	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
7960	2^214389-683113	64538	Paul Bourdelais	03/2013
7961	(76*10^64534+113)/9	64535	Robert Price	11/2017
7962	2^214369-111241	64532	Enzo Doria	05/2014
7963	(19^50461+3^50461)/22	64526	Robert Price	07/2013
7964	11^61954-3660	64519	Enzo Doria	12/2012
7965	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
7966	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
7967	2^214300-4547	64511	Yves Minet	03/2019
7968	35^41779-34	64510	Norbert Schneider	04/2014
7969	(159^29303+1)/160	64506	Eric Chen	12/2017
7970	(89*10^64504-179)/9	64505	Robert Price	11/2017
7971	11^61939-5220	64503	Enzo Doria	01/2013
7972	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
7973	L(308604)+P(308604)	64495	Robert Price	12/2017
7974	126^30706-125	64494	Norbert Schneider	02/2015
7975	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
7976	2^214215+12909	64486	Lelio R Paula	10/2011
7977	5^92225+66	64463	Lelio R Paula	06/2013
7978	2^214126-240551	64459	Paul Bourdelais	03/2013
7979	8*6^82827+5	64453	Lelio R Paula	09/2014
7980	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
7981	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
7982	14^56227+89	64444	Lelio R Paula	08/2013
7985	2^214055-159	64437	Lelio R Paula	08/2011
7983	10^64436+2667	64437	Patrick De Geest	05/2013
7984	65^35543-64^35543	64437	Robert Price	08/2013
7986	10^64436-53	64436	Robert Price	05/2011
7987	(3^135043-lucasV(1,3,135043)+1)/3	64432	Paul Vanderveen	11/2017
7988	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
7989	3^135027+100	64425	Lelio R Paula	05/2013
7990	(3^134972-7)/2	64398	Lelio R Paula	04/2012
7991	6*10^64387+7	64388	Dmitry Domanov	11/2010
7992	2^213864-18377	64380	Enzo Doria	05/2013
7993	(2^213821+9)/209	64365	Lelio R Paula	04/2012
7994	2^213788+135	64357	Lelio R Paula	08/2011
7995	17703^4316+4316^17703	64352	Hans Havermann	06/2019
7996	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
7997	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
7998	(11^61781+2^61781)/13	64338	Robert Price	02/2013
7999	6^82670+37	64330	Lelio R Paula	07/2013
8000	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012

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Probable Primes Top 10000

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