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	(-lucasV(1,2,417184)+2)/(3*104297)	62788	Mike Oakes	02/2017
7502	(2^208534+7)/9059	62772	Lelio R Paula	03/2012
7503	(13^56333+1)/14	62751	Paul Bourdelais	03/2010
7504	10^62750+57	62751	Robert Price	01/2011
7505	10^62750-267429	62750	Patrick De Geest	01/2013
7506	2^208427-69	62743	Lelio R Paula	08/2011
7507	2^208421-111775	62741	Enzo Doria	05/2014
7508	2^208404-112079	62736	Enzo Doria	06/2014
7509	2^208343-2221	62718	Yves Minet	08/2013
7510	2^208335+513	62716	Lelio R Paula	10/2011
7512	(2^208328+47)/3	62713	Lelio R Paula	03/2012
7511	11^60220-2040	62713	Enzo Doria	12/2012
7513	2^208292+81	62703	Henri Lifchitz	10/2005
7514	15013^15012-15012	62698	Henri Lifchitz	10/2014
7515	2^208271-112747	62696	Enzo Doria	06/2014
7516	11^60202-4380	62694	Enzo Doria	01/2013
7517	(3^131403-4)/157	62693	Lelio R Paula	04/2012
7518	2^208127-126667	62653	Paul Bourdelais	01/2012
7519	71^33843+2	62653	Lelio R Paula	05/2013
7520	(3^131325+7)/1066850	62652	Lelio R Paula	04/2012
7521	2^208019+119	62620	Lelio R Paula	08/2011
7522	(-lucasV(1,2,416078)+2)/(11*190717)	62620	Mike Oakes	02/2017
7523	11^60126-11370	62615	Enzo Doria	12/2012
7524	2^207976-2489	62608	Yves Minet	07/2014
7525	(22699*2^207945+1)/281709	62597	Lelio R Paula	06/2014
7526	4*21^47335+205	62588	Curtis Bright	05/2015
7527	15^53210+8	62580	Lelio R Paula	05/2013
7528	2^207865+29	62574	Henri Lifchitz	08/2005
7529	15^53199-38	62567	Lelio R Paula	05/2013
7530	(F(24947)^13-F(24946)^13)/F(24945)	62560	Wayne Halsdorf	03/2012
7531	2^207782+58905	62549	Lelio R Paula	10/2011
7532	(2^207748-3)/8437	62535	Lelio R Paula	03/2012
7533	(2^207711+5)/13	62527	Lelio R Paula	03/2012
7534	(268*10^62523-1)/3	62525	Robert Price	10/2017
7535	10^62523+63	62524	Robert Price	01/2011
7536	10^62523-292373	62523	Patrick De Geest	01/2013
7537	2^207691+1155*207691	62522	Henri Lifchitz	02/2005
7538	(lucasV(1,2,415410)+2)/(17*653)	62522	Mike Oakes	02/2017
7539	2^207626-112157	62502	Enzo Doria	06/2014
7540	3^130987+52	62497	Lelio R Paula	04/2013
7541	8*6^80299-7	62486	Lelio R Paula	09/2014
7542	11^59997-2670	62481	Enzo Doria	12/2012
7543	93^31740+2	62480	Lelio R Paula	05/2013
7544	(10^62451+119)/3	62451	Serge Batalov	12/2014
7545	(2^207443+47)/7645	62443	Lelio R Paula	03/2012
7546	2^207364+115	62423	Lelio R Paula	08/2011
7547	3^130815-46	62415	Lelio R Paula	04/2013
7548	(F(182)^1657-F(181)^1657)/F(180)	62409	Wayne Halsdorf	03/2012
7549	20^47968-9483	62408	Enzo Doria	03/2013
7550	(10^62402+101)/3	62402	Robert Price	04/2016
7551	(13*2^207264-1)/3	62394	Lelio R Paula	01/2014
7552	(79*10^62387-61)/9	62388	Robert Price	10/2015
7553	5^89244+3*2^89244	62379	Mike Oakes	02/2010
7554	6^80160-13	62377	Lelio R Paula	04/2013
7555	(7*10^62362+53)/3	62363	Robert Price	10/2017
7556	(1000121^10391+1)/1000122	62341	Faysal YAtim	07/2008
7557	(17*10^62328-11)/3	62329	Robert Price	07/2015
7558	2^207023+11715	62321	Lelio R Paula	09/2011
7559	(265*10^62298+11)/3	62300	Robert Price	03/2017
7560	2^206947-69	62298	Lelio R Paula	08/2011
7561	2^206938+29835	62295	Lelio R Paula	02/2013
7562	2^206911-726877	62287	Paul Bourdelais	03/2013
7563	(6883*2^206884-1)/3	62282	Lelio R Paula	04/2015
7564	2^206892-112817	62281	Enzo Doria	06/2014
7565	(7*10^62278+113)/3	62279	Robert Price	10/2017
7566	3^130523+46	62276	Lelio R Paula	04/2013
7567	2^206872-113453	62275	Enzo Doria	07/2014
7568	2^206840-93	62266	Lelio R Paula	08/2011
7569	(1017*2^206815-1)/635	62258	Lelio R Paula	04/2015
7570	96^31406+95	62256	Norbert Schneider	03/2016
7571	(2^206824+7)/646213	62255	Lelio R Paula	03/2012
7572	2^206765-941683	62243	Paul Bourdelais	11/2012
7573	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
7574	2^206755-1579	62240	Yves Minet	03/2013
7575	11^59764-5820	62238	Enzo Doria	01/2013
7576	5*10^62233+3	62234	Dmitry Domanov	11/2010
7577	8*3^130421+7	62228	Lelio R Paula	04/2014
7578	19^48661+10	62226	Lelio R Paula	05/2013
7580	(17*2^206705+1)/5	62225	Lelio R Paula	08/2012
7579	2^206705-112635	62225	Enzo Doria	06/2014
7581	3^130403+8680	62219	Lelio R Paula	04/2013
7582	11^59740-7110	62213	Enzo Doria	01/2013
7584	2^206596-167	62192	Lelio R Paula	08/2011
7583	2^206597+18915	62192	Lelio R Paula	02/2013
7585	6^79918+137	62189	Lelio R Paula	04/2013
7586	lucasU(2408,1,18390)-lucasU(2408,1,18389)	62186	Mike Oakes	05/2009
7587	2^206574+613	62185	Jason Earls	04/2008
7588	3^130328+80	62183	Lelio R Paula	04/2013
7589	(lucasV(1,2,413270)-2)/(11^2234431871200337571687961)	62181	Mike Oakes	02/2017
7590	2^206550+76819	62178	Enzo Doria	05/2016
7591	11^59703-24	62175	Lelio R Paula	05/2013
7592	2^206524+75781	62170	Enzo Doria	04/2016
7593	2^206506+427	62165	Henri Lifchitz	01/2005
7594	2^206465+7695	62153	Lelio R Paula	02/2013
7595	2^206464-1649	62152	Yves Minet	03/2013
7596	5^88917+56	62151	Lelio R Paula	04/2013
7597	2^206444-111569	62146	Enzo Doria	05/2014
7598	5^88908-42	62145	Lelio R Paula	04/2013
7599	18^49495-29	62130	Lelio R Paula	05/2013
7600	3*6^79842-5	62130	Lelio R Paula	09/2014
7601	7*10^62127-17	62128	Robert Price	01/2017
7602	2^206373+8415	62125	Lelio R Paula	02/2013
7603	20^47745-9583	62118	Enzo Doria	03/2013
7604	41^38516-2	62118	Lelio R Paula	08/2013
7605	2^206332-58695	62113	Lelio R Paula	09/2011
7606	11^59639-1260	62108	Enzo Doria	11/2012
7607	2^206232-15893	62083	Enzo Doria	04/2013
7608	(115*10^62073-1)/3	62075	Serge Batalov	12/2014
7609	2^206206+75799	62075	Enzo Doria	04/2016
7610	(74*10^62072+43)/9	62073	Robert Price	10/2015
7611	2^206194-185	62071	Lelio R Paula	08/2011
7612	6^79757-103	62064	Lelio R Paula	04/2013
7613	p(13285)#/2-64	62063	Robert Price	04/2017
7614	(29*10^62030-41)/3	62031	Robert Price	07/2016
7615	20^47675-81	62027	Lelio R Paula	06/2013
7616	3^129972+98	62013	Lelio R Paula	04/2013
7617	2^205962+3	62001	Donovan Johnson	02/2006
7618	2^205933-205933^2	61993	Henri Lifchitz	05/2005
7619	(68*10^61991+7)/3	61993	Robert Price	03/2016
7620	20^47641-663	61983	Enzo Doria	03/2013
7621	3^129861+2660	61960	Lelio R Paula	04/2013
7622	(55459*2^205800+1)/1345	61954	Lelio R Paula	06/2014
7623	18^49354-97	61953	Lelio R Paula	05/2013
7624	(209*10^61947-17)/3	61949	Robert Price	05/2017
7626	14*10^61937+1089	61939	Jens K. Andersen	11/2007
7625	(11*2^205758-1)/53	61939	Lelio R Paula	01/2014
7627	20^47600+63	61930	Lelio R Paula	06/2013
7628	(16384!+1185)/(3579*10705361)	61926	Makoto Morimoto	09/2017
7629	44117!3+243	61918	Robert Price	09/2014
7630	(31*2^205677-1)/59	61915	Lelio R Paula	01/2014
7631	(lucasV(1,2,411332)-2)/(139713792940507)	61900	Mike Oakes	02/2017
7632	20^47575-81	61897	Lelio R Paula	06/2013
7633	(58695*2^205593-1)/727	61892	Lelio R Paula	04/2015
7634	87^31909+86	61889	Norbert Schneider	10/2015
7635	2^205568+141	61883	Lelio R Paula	08/2011
7636	10^61868+58927	61869	Patrick De Geest	12/2012
7637	10^61868-39	61868	Robert Price	05/2011
7639	5^88505-88	61863	Lelio R Paula	04/2013
7638	(-lucasV(1,2,411034)-2)/14639	61863	Mike Oakes	02/2017
7640	13^55528-98	61856	Lelio R Paula	05/2013
7641	(55^35543-1)/54	61856	Paul Bourdelais	08/2017
7642	30535!2-8	61844	Robert Price	06/2015
7643	11^59371-1200	61829	Enzo Doria	11/2012
7644	7*2^205370-5	61824	Lelio R Paula	04/2014
7645	(47*10^61821+403)/9	61822	Robert Price	04/2017
7646	2^205275+7695	61794	Lelio R Paula	02/2013
7647	2^205269+12915	61793	Lelio R Paula	02/2013
7648	(47*2^205265+1)/35	61792	Lelio R Paula	04/2015
7649	19^48309+40	61776	Lelio R Paula	05/2013
7650	(424*10^61770-1)/9	61772	Robert Price	11/2017
7651	2^205192-4079	61769	Yves Minet	06/2011
7652	2^205184+16095	61767	Lelio R Paula	09/2011
7653	20^47472-3423	61763	Enzo Doria	03/2013
7654	(17*10^61760-89)/9	61761	Robert Price	11/2017
7655	2^205149-1795	61757	Lelio R Paula	09/2011
7656	2^205110-17	61745	Lelio R Paula	08/2011
7657	(373^24007+1)/374	61737	Eric Chen	10/2017
7658	(2^205025-7)/25	61718	Lelio R Paula	03/2012
7659	27^43117-26^43117	61717	Robert Price	08/2012
7660	2^205016+37	61716	Lelio R Paula	08/2011
7661	gcd(V(738275),5F(147655)(F(147655)-1)+1)	61715	Serge Batalov	04/2015
7662	1263^19898+19898^1263	61712	Serge Batalov	05/2014
7663	135^28963-134	61701	Norbert Schneider	04/2015
7664	(33*2^204966+1)/234341	61698	Michael Porter	01/2015
7665	(7*10^61696+167)/3	61696	Robert Kinser	10/2017
7666	(46*10^61693+17)/9	61694	Robert Price	06/2015
7667	((((((((((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
7668	1850^18879+18879^1850	61681	Serge Batalov	05/2014
7670	2^204891-1005	61679	Lelio R Paula	09/2011
7669	151^28306-2	61679	Lelio R Paula	10/2017
7671	(3^129271-5)/41506	61674	Lelio R Paula	03/2012
7672	15937^7408+7408^15937	61672	Hans Havermann	02/2017
7673	5^88216-12	61661	Lelio R Paula	04/2013
7674	18185^2454+2454^18185	61645	Hans Havermann	01/2017
7676	2^204767-15865	61642	Enzo Doria	04/2013
7675	(lucasV(1,2,409560)+2)/3079	61642	Mike Oakes	01/2017
7677	7*2^204751-9	61638	Lelio R Paula	04/2014
7678	4*10^61625+21	61626	Robert Price	08/2016
7679	15369^10226+10226^15369	61626	Hans Havermann	02/2017
7680	2^204702-18125	61622	Enzo Doria	05/2013
7681	5*3^129146+8	61620	Lelio R Paula	04/2014
7682	2^204673+129	61613	Lelio R Paula	08/2011
7683	18^49079+97	61608	Lelio R Paula	05/2013
7684	106^30416+105	61602	Norbert Schneider	12/2016
7685	2^204590-33	61588	Lelio R Paula	08/2011
7686	2^204586-111975	61587	Enzo Doria	06/2014
7687	2^204580-16077	61585	Enzo Doria	04/2013
7688	2^204574-16041	61583	Enzo Doria	04/2013
7689	15^52358+56	61578	Lelio R Paula	05/2013
7690	(28*10^61574+11)/3	61575	Robert Price	11/2015
7691	2^204516-17493	61566	Enzo Doria	05/2013
7692	4*5^88076-3	61564	Lelio R Paula	09/2014
7693	11^59110-2520	61557	Enzo Doria	12/2012
7694	2^204477-58695	61554	Lelio R Paula	09/2011
7695	12^57026-73	61542	Lelio R Paula	05/2013
7696	17^50013+90	61539	Lelio R Paula	05/2013
7697	56^35201-55^35201	61538	Robert Price	10/2013
7698	8*7^72810+5	61533	Lelio R Paula	09/2014
7700	204^26641-203^26641	61531	Jean-Louis Charton	08/2009
7699	43867!3-6561	61531	Robert Price	11/2015
7701	10^61525+9^(61525-1)	61526	Robert Price	03/2016
7702	10^61525+62257	61526	Patrick De Geest	12/2016
7703	14821^14166+14166^14821	61526	Hans Havermann	01/2017
7705	12^57010-85	61525	Lelio R Paula	05/2013
7704	10^61525-213579	61525	Patrick De Geest	12/2016
7706	2^204332-99	61511	Lelio R Paula	08/2011
7707	2^204323-2221	61508	Yves Minet	08/2013
7709	2^204317-195	61506	Lelio R Paula	08/2011
7708	3^128910-86	61506	Lelio R Paula	04/2013
7710	2^204318+74539	61506	Enzo Doria	04/2016
7711	(2^204334-3)/1141333	61505	Lelio R Paula	03/2012
7712	2^204297-1036093	61500	Paul Bourdelais	11/2012
7713	3^128880+58	61492	Lelio R Paula	04/2013
7714	2^204216-111677	61476	Enzo Doria	05/2014
7715	(F(73524)^5-F(73523)^5)/F(73522)	61462	Wayne Halsdorf	03/2012
7716	2^204129+204129	61449	Henri Lifchitz	04/2002
7717	3^128787+2^(128787-1)	61448	Robert Price	05/2016
7718	11^58999-78	61442	Lelio R Paula	05/2013
7719	2^204083-111967	61436	Enzo Doria	05/2014
7720	(45^37159+1)/46	61431	Robert Price	11/2013
7721	677^21702+21702^677	61430	Norbert Schneider	06/2016
7722	14837^13810+13810^14837	61429	Hans Havermann	02/2017
7723	(7*2^204043+1)/39	61423	Lelio R Paula	03/2012
7724	11^58976-1740	61418	Enzo Doria	11/2012
7725	2^204016-16085	61415	Enzo Doria	04/2013
7726	V(379967)	61393	Serge Batalov	03/2015
7727	43777!3-3^43777	61392	Robert Price	08/2015
7728	7^72642+88	61390	Lelio R Paula	04/2013
7729	3^128656+32	61385	Lelio R Paula	04/2013
7730	2^203916-17493	61385	Enzo Doria	05/2013
7731	6^78880+23	61381	Lelio R Paula	04/2013
7732	(388*10^61374-1)/9	61376	Robert Price	11/2017
7733	2^203877-111799	61374	Enzo Doria	05/2014
7734	2^203867-1615	61371	Lelio R Paula	10/2011
7735	4*10^61367+19	61368	Robert Price	04/2016
7736	(19*2^203854+1)/42319	61363	Lelio R Paula	08/2012
7737	L(293659)/76528122719	61361	Serge Batalov	07/2017
7738	2^203825-15805	61358	Enzo Doria	04/2013
7739	2^203816-15825	61355	Enzo Doria	04/2013
7740	5*10^61348+59	61349	Robert Price	09/2016
7741	21^46395-2	61345	Lelio R Paula	08/2013
7742	(809*29^41946-165)/28	61344	Curtis Bright	05/2015
7743	7*6^78826+5	61340	Lelio R Paula	09/2014
7744	(3^128558+7)/83773166429696	61324	Lelio R Paula	04/2012
7745	2^203706-111	61322	Lelio R Paula	08/2011
7746	17567^3094+3094^17567	61318	Hans Havermann	02/2017
7747	2^203689-31	61317	Thomas Masser	10/2005
7748	(11*2^203678-1)/53689	61310	Lelio R Paula	01/2014
7750	2^203642+39	61303	Lelio R Paula	08/2011
7749	floor(Pi*10^61382)%(10^61303)	61303	Serge Batalov	07/2012

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Probable Primes Top 10000

(205869 PRPs in the top)