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 (> 30000)	Who ?	When ?
7501	Phi(193404,10)/386809/8122969	63268	Maksym Voznyy	10/2011
7502	96^31913-95	63261	Norbert Schneider	04/2016
7503	3^132572+280	63253	Lelio R Paula	04/2013
7504	3^132570-2^(132570-1)	63252	Robert Price	01/2016
7505	11^60734-4920	63248	Enzo Doria	01/2013
7507	2^210061+21	63235	Donovan Johnson	06/2006
7506	18^50375+95	63235	Lelio R Paula	05/2013
7508	85^32773-2	63233	Lelio R Paula	08/2013
7509	(-lucasV(1,2,420115)-2)/(3*5^3)	63232	Mike Oakes	02/2017
7510	(2^210054-1017)/671	63230	Lelio R Paula	04/2012
7511	3*2^210022+5	63224	Lelio R Paula	04/2014
7512	15^53756+32	63222	Lelio R Paula	05/2013
7513	17^51380+22	63221	Lelio R Paula	05/2013
7514	(lucasV(1,2,420045)+2)/257	63221	Mike Oakes	02/2017
7515	43^38700+42	63216	Norbert Schneider	06/2014
7516	5^90431-96	63209	Lelio R Paula	04/2013
7517	(172*10^63202-1)/9	63204	Serge Batalov	12/2014
7518	(43*10^63200+83)/9	63201	Robert Price	08/2017
7519	2^209914-16005	63191	Enzo Doria	04/2013
7520	3*6^81190-5	63179	Lelio R Paula	09/2014
7521	2^209820+4257	63163	Lelio R Paula	10/2011
7522	99^31648+2	63158	Lelio R Paula	05/2013
7523	16976^5253+5253^16976	63158	Hans Havermann	01/2017
7524	2^209790+67	63154	Lelio R Paula	08/2011
7525	2^209759+90195	63144	Lelio R Paula	02/2013
7526	145823#+211507	63142	Arkadiusz Wesolowski	03/2013
7528	2^209707+513	63129	Lelio R Paula	10/2011
7527	(3^132314-8)/17	63129	Lelio R Paula	04/2012
7529	(2*10^63117+7)/9	63117	Erik Branger	03/2011
7530	9*2^209654-7	63114	Lelio R Paula	04/2014
7531	11^60598-14	63107	Lelio R Paula	05/2013
7532	15103^15078+15078^15103	63106	Hans Havermann	01/2017
7533	15346^12941+12941^15346	63103	Hans Havermann	01/2017
7535	3^132253+76	63101	Lelio R Paula	04/2013
7534	(56*10^63100+403)/9	63101	Robert Price	10/2017
7536	17549^3936+3936^17549	63090	Hans Havermann	01/2017
7537	(55459*2^209553+1)/423	63084	Lelio R Paula	06/2014
7538	(331^25033-1)/330	63077	Eric Chen	09/2017
7539	20^48480+31	63074	Lelio R Paula	06/2013
7540	(26*10^63073-23)/3	63074	Robert Price	08/2016
7541	2^209499+76253	63066	Enzo Doria	04/2016
7542	11^60546-11340	63053	Enzo Doria	12/2012
7543	2^209426+57889	63044	Yves Minet	02/2010
7544	(22699*2^209405+1)/21	63041	Lelio R Paula	06/2014
7545	5^90189+54	63040	Lelio R Paula	04/2013
7546	(22*10^63034-73)/3	63035	Robert Price	09/2017
7547	(314021^11467+1)/314022	63029	Faysal YAtim	05/2008
7548	V(301486)	63007	Henri Lifchitz	05/2003
7549	(31*2^209298+1)/95	63005	Lelio R Paula	08/2012
7550	(27*2^209245+1)/5	62990	Lelio R Paula	08/2012
7551	6^80946-5^(80946-1)	62989	Robert Price	05/2016
7552	467^23596+23596^467	62986	Norbert Schneider	08/2016
7553	(7*2^209212-1)/3	62980	Lelio R Paula	01/2014
7554	(27*2^209206-1)/11	62978	Lelio R Paula	01/2014
7555	1456^19909+19909^1456	62976	Serge Batalov	05/2014
7557	(3^131964-5)/185212396	62955	Lelio R Paula	04/2012
7556	35^40772-1466	62955	Enzo Doria	03/2013
7558	5^90064-13706	62953	Enzo Doria	02/2013
7559	(22*10^62926+257)/9	62927	Robert Price	11/2017
7560	(13*10^62914+401)/9	62915	Robert Price	10/2017
7561	2^208993+107	62914	Lelio R Paula	08/2011
7562	2^208993+77	62914	Lelio R Paula	08/2011
7563	189^27636-2	62913	Lelio R Paula	10/2017
7564	(2^208948-7)/261	62898	Lelio R Paula	03/2012
7565	(151*10^62879-1)/3	62881	Robert Price	04/2017
7566	15^53464-82	62879	Lelio R Paula	05/2013
7567	2^208843-112921	62869	Enzo Doria	06/2014
7568	2^208779+81	62849	Henri Lifchitz	01/2007
7569	(21181*2^208780+1)/8993838841	62844	Lelio R Paula	06/2014
7570	(73*10^62824+17)/9	62825	Robert Price	10/2015
7571	3^131670-82	62823	Lelio R Paula	04/2013
7572	19^49128-90	62823	Lelio R Paula	05/2013
7573	11^60314-4410	62811	Enzo Doria	01/2013
7574	(17*2^208614-1)/53	62799	Lelio R Paula	01/2014
7575	2^208594+93	62794	Donovan Johnson	06/2008
7576	(-lucasV(1,2,417184)+2)/(3*104297)	62788	Mike Oakes	02/2017
7577	(2^208534+7)/9059	62772	Lelio R Paula	03/2012
7578	(13^56333+1)/14	62751	Paul Bourdelais	03/2010
7579	10^62750+57	62751	Robert Price	01/2011
7580	10^62750-267429	62750	Patrick De Geest	01/2013
7581	2^208427-69	62743	Lelio R Paula	08/2011
7582	2^208421-111775	62741	Enzo Doria	05/2014
7583	2^208404-112079	62736	Enzo Doria	06/2014
7584	2^208343-2221	62718	Yves Minet	08/2013
7585	2^208335+513	62716	Lelio R Paula	10/2011
7587	(2^208328+47)/3	62713	Lelio R Paula	03/2012
7586	11^60220-2040	62713	Enzo Doria	12/2012
7588	2^208292+81	62703	Henri Lifchitz	10/2005
7589	15013^15012-15012	62698	Henri Lifchitz	10/2014
7590	2^208271-112747	62696	Enzo Doria	06/2014
7591	11^60202-4380	62694	Enzo Doria	01/2013
7592	(3^131403-4)/157	62693	Lelio R Paula	04/2012
7593	2^208127-126667	62653	Paul Bourdelais	01/2012
7594	71^33843+2	62653	Lelio R Paula	05/2013
7595	(3^131325+7)/1066850	62652	Lelio R Paula	04/2012
7596	2^208019+119	62620	Lelio R Paula	08/2011
7597	(-lucasV(1,2,416078)+2)/(11*190717)	62620	Mike Oakes	02/2017
7598	11^60126-11370	62615	Enzo Doria	12/2012
7599	2^207976-2489	62608	Yves Minet	07/2014
7600	(22699*2^207945+1)/281709	62597	Lelio R Paula	06/2014
7601	4*21^47335+205	62588	Curtis Bright	05/2015
7602	15^53210+8	62580	Lelio R Paula	05/2013
7603	2^207865+29	62574	Henri Lifchitz	08/2005
7604	15^53199-38	62567	Lelio R Paula	05/2013
7605	(F(24947)^13-F(24946)^13)/F(24945)	62560	Wayne Halsdorf	03/2012
7606	2^207782+58905	62549	Lelio R Paula	10/2011
7607	(2^207748-3)/8437	62535	Lelio R Paula	03/2012
7608	(2^207711+5)/13	62527	Lelio R Paula	03/2012
7609	(268*10^62523-1)/3	62525	Robert Price	10/2017
7610	10^62523+63	62524	Robert Price	01/2011
7611	10^62523-292373	62523	Patrick De Geest	01/2013
7612	2^207691+1155*207691	62522	Henri Lifchitz	02/2005
7613	(lucasV(1,2,415410)+2)/(17*653)	62522	Mike Oakes	02/2017
7614	2^207626-112157	62502	Enzo Doria	06/2014
7615	3^130987+52	62497	Lelio R Paula	04/2013
7616	8*6^80299-7	62486	Lelio R Paula	09/2014
7617	11^59997-2670	62481	Enzo Doria	12/2012
7618	93^31740+2	62480	Lelio R Paula	05/2013
7619	(10^62451+119)/3	62451	Serge Batalov	12/2014
7620	(2^207443+47)/7645	62443	Lelio R Paula	03/2012
7621	2^207364+115	62423	Lelio R Paula	08/2011
7622	3^130815-46	62415	Lelio R Paula	04/2013
7623	(F(182)^1657-F(181)^1657)/F(180)	62409	Wayne Halsdorf	03/2012
7624	20^47968-9483	62408	Enzo Doria	03/2013
7625	(10^62402+101)/3	62402	Robert Price	04/2016
7626	(13*2^207264-1)/3	62394	Lelio R Paula	01/2014
7627	(79*10^62387-61)/9	62388	Robert Price	10/2015
7628	5^89244+3*2^89244	62379	Mike Oakes	02/2010
7629	6^80160-13	62377	Lelio R Paula	04/2013
7630	(7*10^62362+53)/3	62363	Robert Price	10/2017
7631	(1000121^10391+1)/1000122	62341	Faysal YAtim	07/2008
7632	(17*10^62328-11)/3	62329	Robert Price	07/2015
7633	2^207023+11715	62321	Lelio R Paula	09/2011
7634	(265*10^62298+11)/3	62300	Robert Price	03/2017
7635	2^206947-69	62298	Lelio R Paula	08/2011
7636	2^206938+29835	62295	Lelio R Paula	02/2013
7637	2^206911-726877	62287	Paul Bourdelais	03/2013
7638	(6883*2^206884-1)/3	62282	Lelio R Paula	04/2015
7639	2^206892-112817	62281	Enzo Doria	06/2014
7640	(7*10^62278+113)/3	62279	Robert Price	10/2017
7641	3^130523+46	62276	Lelio R Paula	04/2013
7642	2^206872-113453	62275	Enzo Doria	07/2014
7643	2^206840-93	62266	Lelio R Paula	08/2011
7644	(1017*2^206815-1)/635	62258	Lelio R Paula	04/2015
7645	96^31406+95	62256	Norbert Schneider	03/2016
7646	(2^206824+7)/646213	62255	Lelio R Paula	03/2012
7647	2^206765-941683	62243	Paul Bourdelais	11/2012
7648	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
7649	2^206755-1579	62240	Yves Minet	03/2013
7650	11^59764-5820	62238	Enzo Doria	01/2013
7651	5*10^62233+3	62234	Dmitry Domanov	11/2010
7652	8*3^130421+7	62228	Lelio R Paula	04/2014
7653	19^48661+10	62226	Lelio R Paula	05/2013
7655	(17*2^206705+1)/5	62225	Lelio R Paula	08/2012
7654	2^206705-112635	62225	Enzo Doria	06/2014
7656	3^130403+8680	62219	Lelio R Paula	04/2013
7657	11^59740-7110	62213	Enzo Doria	01/2013
7659	2^206596-167	62192	Lelio R Paula	08/2011
7658	2^206597+18915	62192	Lelio R Paula	02/2013
7660	6^79918+137	62189	Lelio R Paula	04/2013
7661	lucasU(2408,1,18390)-lucasU(2408,1,18389)	62186	Mike Oakes	05/2009
7662	2^206574+613	62185	Jason Earls	04/2008
7663	3^130328+80	62183	Lelio R Paula	04/2013
7664	(lucasV(1,2,413270)-2)/(11^2234431871200337571687961)	62181	Mike Oakes	02/2017
7665	2^206550+76819	62178	Enzo Doria	05/2016
7666	11^59703-24	62175	Lelio R Paula	05/2013
7667	2^206524+75781	62170	Enzo Doria	04/2016
7668	2^206506+427	62165	Henri Lifchitz	01/2005
7669	2^206465+7695	62153	Lelio R Paula	02/2013
7670	2^206464-1649	62152	Yves Minet	03/2013
7671	5^88917+56	62151	Lelio R Paula	04/2013
7672	2^206444-111569	62146	Enzo Doria	05/2014
7673	5^88908-42	62145	Lelio R Paula	04/2013
7674	18^49495-29	62130	Lelio R Paula	05/2013
7675	3*6^79842-5	62130	Lelio R Paula	09/2014
7676	7*10^62127-17	62128	Robert Price	01/2017
7677	2^206373+8415	62125	Lelio R Paula	02/2013
7678	20^47745-9583	62118	Enzo Doria	03/2013
7679	41^38516-2	62118	Lelio R Paula	08/2013
7680	2^206332-58695	62113	Lelio R Paula	09/2011
7681	11^59639-1260	62108	Enzo Doria	11/2012
7682	2^206232-15893	62083	Enzo Doria	04/2013
7683	(115*10^62073-1)/3	62075	Serge Batalov	12/2014
7684	2^206206+75799	62075	Enzo Doria	04/2016
7685	(74*10^62072+43)/9	62073	Robert Price	10/2015
7686	2^206194-185	62071	Lelio R Paula	08/2011
7687	6^79757-103	62064	Lelio R Paula	04/2013
7688	p(13285)#/2-64	62063	Robert Price	04/2017
7689	(29*10^62030-41)/3	62031	Robert Price	07/2016
7690	20^47675-81	62027	Lelio R Paula	06/2013
7691	3^129972+98	62013	Lelio R Paula	04/2013
7692	2^205962+3	62001	Donovan Johnson	02/2006
7693	2^205933-205933^2	61993	Henri Lifchitz	05/2005
7694	(68*10^61991+7)/3	61993	Robert Price	03/2016
7695	20^47641-663	61983	Enzo Doria	03/2013
7696	3^129861+2660	61960	Lelio R Paula	04/2013
7697	(55459*2^205800+1)/1345	61954	Lelio R Paula	06/2014
7698	18^49354-97	61953	Lelio R Paula	05/2013
7699	(209*10^61947-17)/3	61949	Robert Price	05/2017
7701	14*10^61937+1089	61939	Jens K. Andersen	11/2007
7700	(11*2^205758-1)/53	61939	Lelio R Paula	01/2014
7702	20^47600+63	61930	Lelio R Paula	06/2013
7703	(16384!+1185)/(3579*10705361)	61926	Makoto Morimoto	09/2017
7704	44117!3+243	61918	Robert Price	09/2014
7705	(31*2^205677-1)/59	61915	Lelio R Paula	01/2014
7706	(lucasV(1,2,411332)-2)/(139713792940507)	61900	Mike Oakes	02/2017
7707	20^47575-81	61897	Lelio R Paula	06/2013
7708	(58695*2^205593-1)/727	61892	Lelio R Paula	04/2015
7709	87^31909+86	61889	Norbert Schneider	10/2015
7710	2^205568+141	61883	Lelio R Paula	08/2011
7711	10^61868+58927	61869	Patrick De Geest	12/2012
7712	10^61868-39	61868	Robert Price	05/2011
7714	5^88505-88	61863	Lelio R Paula	04/2013
7713	(-lucasV(1,2,411034)-2)/14639	61863	Mike Oakes	02/2017
7715	13^55528-98	61856	Lelio R Paula	05/2013
7716	(55^35543-1)/54	61856	Paul Bourdelais	08/2017
7717	30535!2-8	61844	Robert Price	06/2015
7718	11^59371-1200	61829	Enzo Doria	11/2012
7719	7*2^205370-5	61824	Lelio R Paula	04/2014
7720	(47*10^61821+403)/9	61822	Robert Price	04/2017
7721	2^205275+7695	61794	Lelio R Paula	02/2013
7722	2^205269+12915	61793	Lelio R Paula	02/2013
7723	(47*2^205265+1)/35	61792	Lelio R Paula	04/2015
7724	19^48309+40	61776	Lelio R Paula	05/2013
7725	(424*10^61770-1)/9	61772	Robert Price	11/2017
7726	2^205192-4079	61769	Yves Minet	06/2011
7727	2^205184+16095	61767	Lelio R Paula	09/2011
7728	20^47472-3423	61763	Enzo Doria	03/2013
7729	(17*10^61760-89)/9	61761	Robert Price	11/2017
7730	2^205149-1795	61757	Lelio R Paula	09/2011
7731	2^205110-17	61745	Lelio R Paula	08/2011
7732	(373^24007+1)/374	61737	Eric Chen	10/2017
7733	(2^205025-7)/25	61718	Lelio R Paula	03/2012
7734	27^43117-26^43117	61717	Robert Price	08/2012
7735	2^205016+37	61716	Lelio R Paula	08/2011
7736	gcd(V(738275),5F(147655)(F(147655)-1)+1)	61715	Serge Batalov	04/2015
7737	1263^19898+19898^1263	61712	Serge Batalov	05/2014
7738	135^28963-134	61701	Norbert Schneider	04/2015
7739	(33*2^204966+1)/234341	61698	Michael Porter	01/2015
7740	(7*10^61696+167)/3	61696	Robert Kinser	10/2017
7741	(46*10^61693+17)/9	61694	Robert Price	06/2015
7742	((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768	61684	Phil Carmody	09/2004
7743	1850^18879+18879^1850	61681	Serge Batalov	05/2014
7745	2^204891-1005	61679	Lelio R Paula	09/2011
7744	151^28306-2	61679	Lelio R Paula	10/2017
7746	(3^129271-5)/41506	61674	Lelio R Paula	03/2012
7747	15937^7408+7408^15937	61672	Hans Havermann	02/2017
7748	5^88216-12	61661	Lelio R Paula	04/2013
7749	18185^2454+2454^18185	61645	Hans Havermann	01/2017
7750	(lucasV(1,2,409560)+2)/3079	61642	Mike Oakes	01/2017

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Probable Primes Top 10000

(212140 PRPs in the top)