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 ?
8501	11^60546-11340	63053	Enzo Doria	12/2012
8502	2^209426+57889	63044	Yves Minet	02/2010
8503	(22699*2^209405+1)/21	63041	Lelio R Paula	06/2014
8504	5^90189+54	63040	Lelio R Paula	04/2013
8505	(22*10^63034-73)/3	63035	Robert Price	09/2017
8506	(314021^11467+1)/314022	63029	Faysal YAtim	05/2008
8507	V(301486)	63007	Henri Lifchitz	05/2003
8508	(31*2^209298+1)/95	63005	Lelio R Paula	08/2012
8509	(27*2^209245+1)/5	62990	Lelio R Paula	08/2012
8510	6^80946-5^(80946-1)	62989	Robert Price	05/2016
8511	467^23596+23596^467	62986	Norbert Schneider	08/2016
8512	(7*2^209212-1)/3	62980	Lelio R Paula	01/2014
8513	(27*2^209206-1)/11	62978	Lelio R Paula	01/2014
8514	1456^19909+19909^1456	62976	Serge Batalov	05/2014
8515	(5^90107-1)/(4*2162569)	62976	Gord Palameta	07/2019
8517	(3^131964-5)/185212396	62955	Lelio R Paula	04/2012
8516	35^40772-1466	62955	Enzo Doria	03/2013
8518	5^90064-13706	62953	Enzo Doria	02/2013
8519	(22*10^62926+257)/9	62927	Robert Price	11/2017
8520	(13*10^62914+401)/9	62915	Robert Price	10/2017
8521	2^208993+107	62914	Lelio R Paula	08/2011
8522	2^208993+77	62914	Lelio R Paula	08/2011
8523	189^27636-2	62913	Lelio R Paula	10/2017
8524	(2^208948-7)/261	62898	Lelio R Paula	03/2012
8525	15804^9545+9545^15804	62897	Hans Havermann	06/2019
8526	(151*10^62879-1)/3	62881	Robert Price	04/2017
8527	15^53464-82	62879	Lelio R Paula	05/2013
8528	2^208843-112921	62869	Enzo Doria	06/2014
8529	2^208779+81	62849	Henri Lifchitz	01/2007
8530	159^28548+158	62846	Norbert Schneider	12/2018
8531	(21181*2^208780+1)/8993838841	62844	Lelio R Paula	06/2014
8532	(73*10^62824+17)/9	62825	Robert Price	10/2015
8533	3^131670-82	62823	Lelio R Paula	04/2013
8534	19^49128-90	62823	Lelio R Paula	05/2013
8535	17687^3562+3562^17687	62819	Hans Havermann	06/2019
8536	11^60314-4410	62811	Enzo Doria	01/2013
8537	(17*2^208614-1)/53	62799	Lelio R Paula	01/2014
8538	2^208594+93	62794	Donovan Johnson	06/2008
8539	(-lucasV(1,2,417184)+2)/(3*104297)	62788	Mike Oakes	02/2017
8540	(2^208534+7)/9059	62772	Lelio R Paula	03/2012
8542	(13^56333+1)/14	62751	Paul Bourdelais	03/2010
8541	10^62750+57	62751	Robert Price	01/2011
8543	10^62750-267429	62750	Patrick De Geest	01/2013
8544	2^208427-69	62743	Lelio R Paula	08/2011
8545	2^208421-111775	62741	Enzo Doria	05/2014
8546	2^208404-112079	62736	Enzo Doria	06/2014
8547	15242^13041+13041^15242	62726	Hans Havermann	06/2019
8548	2^208343-2221	62718	Yves Minet	08/2013
8549	2^208335+513	62716	Lelio R Paula	10/2011
8551	(2^208328+47)/3	62713	Lelio R Paula	03/2012
8550	11^60220-2040	62713	Enzo Doria	12/2012
8552	2^208292+81	62703	Henri Lifchitz	10/2005
8553	15013^15012-15012	62698	Henri Lifchitz	10/2014
8554	2^208271-112747	62696	Enzo Doria	06/2014
8555	11^60202-4380	62694	Enzo Doria	01/2013
8556	(3^131403-4)/157	62693	Lelio R Paula	04/2012
8557	20349^1202+1202^20349	62673	Hans Havermann	06/2019
8558	2^208127-126667	62653	Paul Bourdelais	01/2012
8559	71^33843+2	62653	Lelio R Paula	05/2013
8560	(3^131325+7)/1066850	62652	Lelio R Paula	04/2012
8562	2^208019+119	62620	Lelio R Paula	08/2011
8561	(-lucasV(1,2,416078)+2)/(11*190717)	62620	Mike Oakes	02/2017
8563	11^60126-11370	62615	Enzo Doria	12/2012
8564	2^207976-2489	62608	Yves Minet	07/2014
8565	(22699*2^207945+1)/281709	62597	Lelio R Paula	06/2014
8566	4*21^47335+205	62588	Curtis Bright	05/2015
8567	15^53210+8	62580	Lelio R Paula	05/2013
8568	16529^6106+6106^16529	62575	Hans Havermann	06/2019
8569	2^207865+29	62574	Henri Lifchitz	08/2005
8570	15^53199-38	62567	Lelio R Paula	05/2013
8571	(F(24947)^13-F(24946)^13)/F(24945)	62560	Wayne Halsdorf	03/2012
8572	2^207782+58905	62549	Lelio R Paula	10/2011
8573	(2^207748-3)/8437	62535	Lelio R Paula	03/2012
8574	(2^207711+5)/13	62527	Lelio R Paula	03/2012
8575	(268*10^62523-1)/3	62525	Robert Price	10/2017
8576	10^62523+63	62524	Robert Price	01/2011
8577	10^62523-292373	62523	Patrick De Geest	01/2013
8579	2^207691+1155*207691	62522	Henri Lifchitz	02/2005
8578	(lucasV(1,2,415410)+2)/(17*653)	62522	Mike Oakes	02/2017
8580	2^207626-112157	62502	Enzo Doria	06/2014
8581	3^130987+52	62497	Lelio R Paula	04/2013
8582	8*6^80299-7	62486	Lelio R Paula	09/2014
8583	11^59997-2670	62481	Enzo Doria	12/2012
8584	93^31740+2	62480	Lelio R Paula	05/2013
8585	(10^62451+119)/3	62451	Serge Batalov	12/2014
8586	(2^207443+47)/7645	62443	Lelio R Paula	03/2012
8587	16150^7347+7347^16150	62438	Hans Havermann	06/2019
8588	2^207364+115	62423	Lelio R Paula	08/2011
8589	3^130815-46	62415	Lelio R Paula	04/2013
8590	(F(182)^1657-F(181)^1657)/F(180)	62409	Wayne Halsdorf	03/2012
8591	20^47968-9483	62408	Enzo Doria	03/2013
8592	(10^62402+101)/3	62402	Robert Price	04/2016
8593	(13*2^207264-1)/3	62394	Lelio R Paula	01/2014
8594	(79*10^62387-61)/9	62388	Robert Price	10/2015
8595	5^89244+3*2^89244	62379	Mike Oakes	02/2010
8596	6^80160-13	62377	Lelio R Paula	04/2013
8597	(7*10^62362+53)/3	62363	Robert Price	10/2017
8598	(1000121^10391+1)/1000122	62341	Faysal YAtim	07/2008
8599	(17*10^62328-11)/3	62329	Robert Price	07/2015
8600	2^207023+11715	62321	Lelio R Paula	09/2011
8601	(265*10^62298+11)/3	62300	Robert Price	03/2017
8602	2^206947-69	62298	Lelio R Paula	08/2011
8603	2^206938+29835	62295	Lelio R Paula	02/2013
8604	2^206911-726877	62287	Paul Bourdelais	03/2013
8605	(6883*2^206884-1)/3	62282	Lelio R Paula	04/2015
8606	2^206892-112817	62281	Enzo Doria	06/2014
8607	(7*10^62278+113)/3	62279	Robert Price	10/2017
8608	3^130523+46	62276	Lelio R Paula	04/2013
8609	2^206872-113453	62275	Enzo Doria	07/2014
8610	2^206840-93	62266	Lelio R Paula	08/2011
8611	(1017*2^206815-1)/635	62258	Lelio R Paula	04/2015
8612	96^31406+95	62256	Norbert Schneider	03/2016
8613	(2^206824+7)/646213	62255	Lelio R Paula	03/2012
8614	2^206765-941683	62243	Paul Bourdelais	11/2012
8615	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
8616	2^206755-1579	62240	Yves Minet	03/2013
8617	11^59764-5820	62238	Enzo Doria	01/2013
8618	5*10^62233+3	62234	Dmitry Domanov	11/2010
8619	8*3^130421+7	62228	Lelio R Paula	04/2014
8620	19^48661+10	62226	Lelio R Paula	05/2013
8621	(17*2^206705+1)/5	62225	Lelio R Paula	08/2012
8622	2^206705-112635	62225	Enzo Doria	06/2014
8623	3^130403+8680	62219	Lelio R Paula	04/2013
8624	11^59740-7110	62213	Enzo Doria	01/2013
8625	15113^13068+13068^15113	62209	Hans Havermann	06/2019
8627	2^206596-167	62192	Lelio R Paula	08/2011
8626	2^206597+18915	62192	Lelio R Paula	02/2013
8628	6^79918+137	62189	Lelio R Paula	04/2013
8629	lucasU(2408,1,18390)-lucasU(2408,1,18389)	62186	Mike Oakes	05/2009
8630	2^206574+613	62185	Jason Earls	04/2008
8631	3^130328+80	62183	Lelio R Paula	04/2013
8632	(lucasV(1,2,413270)-2)/(11^2234431871200337571687961)	62181	Mike Oakes	02/2017
8633	2^206550+76819	62178	Enzo Doria	05/2016
8634	11^59703-24	62175	Lelio R Paula	05/2013
8635	2^206524+75781	62170	Enzo Doria	04/2016
8636	2^206506+427	62165	Henri Lifchitz	01/2005
8637	2^206465+7695	62153	Lelio R Paula	02/2013
8638	2^206464-1649	62152	Yves Minet	03/2013
8639	5^88917+56	62151	Lelio R Paula	04/2013
8640	2^206444-111569	62146	Enzo Doria	05/2014
8641	5^88908-42	62145	Lelio R Paula	04/2013
8642	18^49495-29	62130	Lelio R Paula	05/2013
8643	3*6^79842-5	62130	Lelio R Paula	09/2014
8644	7*10^62127-17	62128	Robert Price	01/2017
8645	2^206373+8415	62125	Lelio R Paula	02/2013
8646	20^47745-9583	62118	Enzo Doria	03/2013
8647	41^38516-2	62118	Lelio R Paula	08/2013
8648	2^206332-58695	62113	Lelio R Paula	09/2011
8649	11^59639-1260	62108	Enzo Doria	11/2012
8650	14898^14719+14719^14898	62094	Hans Havermann	06/2019
8651	2^206232-15893	62083	Enzo Doria	04/2013
8652	(115*10^62073-1)/3	62075	Serge Batalov	12/2014
8653	2^206206+75799	62075	Enzo Doria	04/2016
8654	(74*10^62072+43)/9	62073	Robert Price	10/2015
8655	2^206194-185	62071	Lelio R Paula	08/2011
8656	6^79757-103	62064	Lelio R Paula	04/2013
8657	p(13285)#/2-64	62063	Robert Price	04/2017
8658	(29*10^62030-41)/3	62031	Robert Price	07/2016
8659	20^47675-81	62027	Lelio R Paula	06/2013
8660	3^129972+98	62013	Lelio R Paula	04/2013
8661	2^205962+3	62001	Donovan Johnson	02/2006
8662	2^205933-205933^2	61993	Henri Lifchitz	05/2005
8663	(68*10^61991+7)/3	61993	Robert Price	03/2016
8664	20^47641-663	61983	Enzo Doria	03/2013
8665	16737^5036+5036^16737	61962	Hans Havermann	06/2019
8666	3^129861+2660	61960	Lelio R Paula	04/2013
8667	(55459*2^205800+1)/1345	61954	Lelio R Paula	06/2014
8668	18^49354-97	61953	Lelio R Paula	05/2013
8669	(209*10^61947-17)/3	61949	Robert Price	05/2017
8670	14*10^61937+1089	61939	Jens K. Andersen	11/2007
8671	(11*2^205758-1)/53	61939	Lelio R Paula	01/2014
8672	20^47600+63	61930	Lelio R Paula	06/2013
8673	20487^1054+1054^20487	61929	Hans Havermann	06/2019
8674	(16384!+1185)/(3579*10705361)	61926	Makoto Morimoto	09/2017
8675	15267^11374+11374^15267	61922	Hans Havermann	06/2019
8676	44117!3+243	61918	Robert Price	09/2014
8677	(31*2^205677-1)/59	61915	Lelio R Paula	01/2014
8678	(lucasV(1,2,411332)-2)/(139713792940507)	61900	Mike Oakes	02/2017
8679	20^47575-81	61897	Lelio R Paula	06/2013
8680	(58695*2^205593-1)/727	61892	Lelio R Paula	04/2015
8681	87^31909+86	61889	Norbert Schneider	10/2015
8682	2^205568+141	61883	Lelio R Paula	08/2011
8683	10^61868+58927	61869	Patrick De Geest	12/2012
8684	10^61868-39	61868	Robert Price	05/2011
8685	5^88505-88	61863	Lelio R Paula	04/2013
8686	(-lucasV(1,2,411034)-2)/14639	61863	Mike Oakes	02/2017
8688	13^55528-98	61856	Lelio R Paula	05/2013
8687	(55^35543-1)/54	61856	Paul Bourdelais	08/2017
8689	30535!2-8	61844	Robert Price	06/2015
8690	11^59371-1200	61829	Enzo Doria	11/2012
8691	7*2^205370-5	61824	Lelio R Paula	04/2014
8692	(47*10^61821+403)/9	61822	Robert Price	04/2017
8693	2^205275+7695	61794	Lelio R Paula	02/2013
8694	2^205269+12915	61793	Lelio R Paula	02/2013
8695	(47*2^205265+1)/35	61792	Lelio R Paula	04/2015
8696	19^48309+40	61776	Lelio R Paula	05/2013
8697	(424*10^61770-1)/9	61772	Robert Price	11/2017
8698	2^205192-4079	61769	Yves Minet	06/2011
8699	2^205184+16095	61767	Lelio R Paula	09/2011
8700	20^47472-3423	61763	Enzo Doria	03/2013
8701	(17*10^61760-89)/9	61761	Robert Price	11/2017
8702	2^205149-1795	61757	Lelio R Paula	09/2011
8703	2^205110-17	61745	Lelio R Paula	08/2011
8704	(373^24007+1)/374	61737	Eric Chen	10/2017
8705	14734^14811-14811^14734	61737	Norbert Schneider	06/2019
8706	(2^205025-7)/25	61718	Lelio R Paula	03/2012
8707	27^43117-26^43117	61717	Robert Price	08/2012
8708	2^205016+37	61716	Lelio R Paula	08/2011
8709	gcd(V(738275),5F(147655)(F(147655)-1)+1)	61715	Serge Batalov	04/2015
8710	1263^19898+19898^1263	61712	Serge Batalov	05/2014
8711	135^28963-134	61701	Norbert Schneider	04/2015
8712	(33*2^204966+1)/234341	61698	Michael Porter	01/2015
8713	(7*10^61696+167)/3	61696	Robert Kinser	10/2017
8714	(46*10^61693+17)/9	61694	Robert Price	06/2015
8715	((((((((((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
8716	1850^18879+18879^1850	61681	Serge Batalov	05/2014
8718	2^204891-1005	61679	Lelio R Paula	09/2011
8717	151^28306-2	61679	Lelio R Paula	10/2017
8719	(3^129271-5)/41506	61674	Lelio R Paula	03/2012
8720	15937^7408+7408^15937	61672	Hans Havermann	02/2017
8721	5^88216-12	61661	Lelio R Paula	04/2013
8722	18185^2454+2454^18185	61645	Hans Havermann	01/2017
8724	2^204767-15865	61642	Enzo Doria	04/2013
8723	(lucasV(1,2,409560)+2)/3079	61642	Mike Oakes	01/2017
8725	7*2^204751-9	61638	Lelio R Paula	04/2014
8727	4*10^61625+21	61626	Robert Price	08/2016
8726	15369^10226+10226^15369	61626	Hans Havermann	02/2017
8728	2^204702-18125	61622	Enzo Doria	05/2013
8729	5*3^129146+8	61620	Lelio R Paula	04/2014
8730	2^204673+129	61613	Lelio R Paula	08/2011
8731	18^49079+97	61608	Lelio R Paula	05/2013
8732	106^30416+105	61602	Norbert Schneider	12/2016
8733	2^204590-33	61588	Lelio R Paula	08/2011
8734	2^204586-111975	61587	Enzo Doria	06/2014
8735	2^204580-16077	61585	Enzo Doria	04/2013
8736	2^204574-16041	61583	Enzo Doria	04/2013
8737	15^52358+56	61578	Lelio R Paula	05/2013
8738	(28*10^61574+11)/3	61575	Robert Price	11/2015
8739	2^204516-17493	61566	Enzo Doria	05/2013
8740	4*5^88076-3	61564	Lelio R Paula	09/2014
8741	11^59110-2520	61557	Enzo Doria	12/2012
8742	2^204477-58695	61554	Lelio R Paula	09/2011
8743	12^57026-73	61542	Lelio R Paula	05/2013
8744	(257^25537+1)/258	61541	Richard Fischer	04/2018
8745	17^50013+90	61539	Lelio R Paula	05/2013
8746	56^35201-55^35201	61538	Robert Price	10/2013
8747	8*7^72810+5	61533	Lelio R Paula	09/2014
8749	204^26641-203^26641	61531	Jean-Louis Charton	08/2009
8748	43867!3-6561	61531	Robert Price	11/2015
8750	10^61525+62257	61526	Patrick De Geest	12/2016

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Probable Primes Top 10000

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