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 ?
8751	2^208292+81	62703	Henri Lifchitz	10/2005
8752	15013^15012-15012	62698	Henri Lifchitz	10/2014
8753	2^208271-112747	62696	Enzo Doria	06/2014
8754	11^60202-4380	62694	Enzo Doria	01/2013
8755	(3^131403-4)/157	62693	Lelio R Paula	04/2012
8756	20349^1202+1202^20349	62673	Hans Havermann	06/2019
8757	2^208127-126667	62653	Paul Bourdelais	01/2012
8758	71^33843+2	62653	Lelio R Paula	05/2013
8759	(3^131325+7)/1066850	62652	Lelio R Paula	04/2012
8760	2^208019+119	62620	Lelio R Paula	08/2011
8761	(-lucasV(1,2,416078)+2)/(11*190717)	62620	Mike Oakes	02/2017
8762	11^60126-11370	62615	Enzo Doria	12/2012
8763	2^207976-2489	62608	Yves Minet	07/2014
8764	(22699*2^207945+1)/281709	62597	Lelio R Paula	06/2014
8765	4*21^47335+205	62588	Curtis Bright	05/2015
8766	15^53210+8	62580	Lelio R Paula	05/2013
8767	16529^6106+6106^16529	62575	Hans Havermann	06/2019
8768	2^207865+29	62574	Henri Lifchitz	08/2005
8769	15^53199-38	62567	Lelio R Paula	05/2013
8770	(F(24947)^13-F(24946)^13)/F(24945)	62560	Wayne Halsdorf	03/2012
8771	2^207782+58905	62549	Lelio R Paula	10/2011
8772	(2^207748-3)/8437	62535	Lelio R Paula	03/2012
8773	(2^207711+5)/13	62527	Lelio R Paula	03/2012
8774	(268*10^62523-1)/3	62525	Robert Price	10/2017
8775	10^62523+63	62524	Robert Price	01/2011
8776	10^62523-292373	62523	Patrick De Geest	01/2013
8777	2^207691+1155*207691	62522	Henri Lifchitz	02/2005
8778	(lucasV(1,2,415410)+2)/(17*653)	62522	Mike Oakes	02/2017
8779	2^207626-112157	62502	Enzo Doria	06/2014
8780	3^130987+52	62497	Lelio R Paula	04/2013
8781	8*6^80299-7	62486	Lelio R Paula	09/2014
8782	11^59997-2670	62481	Enzo Doria	12/2012
8783	93^31740+2	62480	Lelio R Paula	05/2013
8784	(10^62451+119)/3	62451	Serge Batalov	12/2014
8785	(2^207443+47)/7645	62443	Lelio R Paula	03/2012
8786	16150^7347+7347^16150	62438	Hans Havermann	06/2019
8787	2^207364+115	62423	Lelio R Paula	08/2011
8788	3^130815-46	62415	Lelio R Paula	04/2013
8789	(F(182)^1657-F(181)^1657)/F(180)	62409	Wayne Halsdorf	03/2012
8790	20^47968-9483	62408	Enzo Doria	03/2013
8791	(10^62402+101)/3	62402	Robert Price	04/2016
8792	(13*2^207264-1)/3	62394	Lelio R Paula	01/2014
8793	(79*10^62387-61)/9	62388	Robert Price	10/2015
8794	5^89244+3*2^89244	62379	Mike Oakes	02/2010
8795	6^80160-13	62377	Lelio R Paula	04/2013
8796	(7*10^62362+53)/3	62363	Robert Price	10/2017
8797	(1000121^10391+1)/1000122	62341	Faysal YAtim	07/2008
8798	(17*10^62328-11)/3	62329	Robert Price	07/2015
8799	2^207023+11715	62321	Lelio R Paula	09/2011
8800	(265*10^62298+11)/3	62300	Robert Price	03/2017
8801	2^206947-69	62298	Lelio R Paula	08/2011
8802	2^206938+29835	62295	Lelio R Paula	02/2013
8803	2^206911-726877	62287	Paul Bourdelais	03/2013
8804	(6883*2^206884-1)/3	62282	Lelio R Paula	04/2015
8805	2^206892-112817	62281	Enzo Doria	06/2014
8806	(7*10^62278+113)/3	62279	Robert Price	10/2017
8807	3^130523+46	62276	Lelio R Paula	04/2013
8808	2^206872-113453	62275	Enzo Doria	07/2014
8809	2^206840-93	62266	Lelio R Paula	08/2011
8810	(1017*2^206815-1)/635	62258	Lelio R Paula	04/2015
8811	96^31406+95	62256	Norbert Schneider	03/2016
8812	(2^206824+7)/646213	62255	Lelio R Paula	03/2012
8813	2^206765-941683	62243	Paul Bourdelais	11/2012
8814	(6^79987-1)/5	62242	Paul Bourdelais	11/2007
8815	2^206755-1579	62240	Yves Minet	03/2013
8816	11^59764-5820	62238	Enzo Doria	01/2013
8817	5*10^62233+3	62234	Dmitry Domanov	11/2010
8818	8*3^130421+7	62228	Lelio R Paula	04/2014
8819	19^48661+10	62226	Lelio R Paula	05/2013
8820	(17*2^206705+1)/5	62225	Lelio R Paula	08/2012
8821	2^206705-112635	62225	Enzo Doria	06/2014
8822	3^130403+8680	62219	Lelio R Paula	04/2013
8823	11^59740-7110	62213	Enzo Doria	01/2013
8824	15113^13068+13068^15113	62209	Hans Havermann	06/2019
8826	2^206596-167	62192	Lelio R Paula	08/2011
8825	2^206597+18915	62192	Lelio R Paula	02/2013
8827	6^79918+137	62189	Lelio R Paula	04/2013
8828	lucasU(2408,1,18390)-lucasU(2408,1,18389)	62186	Mike Oakes	05/2009
8829	2^206574+613	62185	Jason Earls	04/2008
8830	3^130328+80	62183	Lelio R Paula	04/2013
8831	(lucasV(1,2,413270)-2)/(11^2234431871200337571687961)	62181	Mike Oakes	02/2017
8832	2^206550+76819	62178	Enzo Doria	05/2016
8833	11^59703-24	62175	Lelio R Paula	05/2013
8834	2^206524+75781	62170	Enzo Doria	04/2016
8835	2^206506+427	62165	Henri Lifchitz	01/2005
8836	2^206465+7695	62153	Lelio R Paula	02/2013
8837	2^206464-1649	62152	Yves Minet	03/2013
8838	5^88917+56	62151	Lelio R Paula	04/2013
8839	2^206444-111569	62146	Enzo Doria	05/2014
8840	5^88908-42	62145	Lelio R Paula	04/2013
8841	18^49495-29	62130	Lelio R Paula	05/2013
8842	3*6^79842-5	62130	Lelio R Paula	09/2014
8843	7*10^62127-17	62128	Robert Price	01/2017
8844	2^206373+8415	62125	Lelio R Paula	02/2013
8845	20^47745-9583	62118	Enzo Doria	03/2013
8846	41^38516-2	62118	Lelio R Paula	08/2013
8847	2^206332-58695	62113	Lelio R Paula	09/2011
8848	11^59639-1260	62108	Enzo Doria	11/2012
8849	14898^14719+14719^14898	62094	Hans Havermann	06/2019
8850	2^206232-15893	62083	Enzo Doria	04/2013
8851	(115*10^62073-1)/3	62075	Serge Batalov	12/2014
8852	2^206206+75799	62075	Enzo Doria	04/2016
8853	(74*10^62072+43)/9	62073	Robert Price	10/2015
8854	2^206194-185	62071	Lelio R Paula	08/2011
8855	6^79757-103	62064	Lelio R Paula	04/2013
8856	p(13285)#/2-64	62063	Robert Price	04/2017
8857	(29*10^62030-41)/3	62031	Robert Price	07/2016
8858	20^47675-81	62027	Lelio R Paula	06/2013
8859	3^129972+98	62013	Lelio R Paula	04/2013
8860	2^205962+3	62001	Donovan Johnson	02/2006
8861	2^205933-205933^2	61993	Henri Lifchitz	05/2005
8862	(68*10^61991+7)/3	61993	Robert Price	03/2016
8863	20^47641-663	61983	Enzo Doria	03/2013
8864	16737^5036+5036^16737	61962	Hans Havermann	06/2019
8865	3^129861+2660	61960	Lelio R Paula	04/2013
8866	(55459*2^205800+1)/1345	61954	Lelio R Paula	06/2014
8867	18^49354-97	61953	Lelio R Paula	05/2013
8868	(209*10^61947-17)/3	61949	Robert Price	05/2017
8870	14*10^61937+1089	61939	Jens K. Andersen	11/2007
8869	(11*2^205758-1)/53	61939	Lelio R Paula	01/2014
8871	20^47600+63	61930	Lelio R Paula	06/2013
8872	20487^1054+1054^20487	61929	Hans Havermann	06/2019
8873	(16384!+1185)/(3579*10705361)	61926	Makoto Morimoto	09/2017
8874	15267^11374+11374^15267	61922	Hans Havermann	06/2019
8875	44117!3+243	61918	Robert Price	09/2014
8876	(31*2^205677-1)/59	61915	Lelio R Paula	01/2014
8877	57269!4-512	61905	Robert Price	11/2019
8878	(lucasV(1,2,411332)-2)/(139713792940507)	61900	Mike Oakes	02/2017
8879	20^47575-81	61897	Lelio R Paula	06/2013
8880	(58695*2^205593-1)/727	61892	Lelio R Paula	04/2015
8881	87^31909+86	61889	Norbert Schneider	10/2015
8882	2^205568+141	61883	Lelio R Paula	08/2011
8883	10^61868+58927	61869	Patrick De Geest	12/2012
8884	10^61868-39	61868	Robert Price	05/2011
8885	5^88505-88	61863	Lelio R Paula	04/2013
8886	(-lucasV(1,2,411034)-2)/14639	61863	Mike Oakes	02/2017
8888	13^55528-98	61856	Lelio R Paula	05/2013
8887	(55^35543-1)/54	61856	Paul Bourdelais	08/2017
8889	30535!2-8	61844	Robert Price	06/2015
8890	11^59371-1200	61829	Enzo Doria	11/2012
8891	7*2^205370-5	61824	Lelio R Paula	04/2014
8892	(47*10^61821+403)/9	61822	Robert Price	04/2017
8893	2^205275+7695	61794	Lelio R Paula	02/2013
8894	2^205269+12915	61793	Lelio R Paula	02/2013
8895	(47*2^205265+1)/35	61792	Lelio R Paula	04/2015
8896	19^48309+40	61776	Lelio R Paula	05/2013
8897	(424*10^61770-1)/9	61772	Robert Price	11/2017
8898	2^205192-4079	61769	Yves Minet	06/2011
8899	2^205184+16095	61767	Lelio R Paula	09/2011
8900	20^47472-3423	61763	Enzo Doria	03/2013
8901	(17*10^61760-89)/9	61761	Robert Price	11/2017
8902	2^205149-1795	61757	Lelio R Paula	09/2011
8903	2^205110-17	61745	Lelio R Paula	08/2011
8904	(373^24007+1)/374	61737	Eric Chen	10/2017
8905	14734^14811-14811^14734	61737	Norbert Schneider	06/2019
8906	(2^205025-7)/25	61718	Lelio R Paula	03/2012
8907	27^43117-26^43117	61717	Robert Price	08/2012
8908	2^205016+37	61716	Lelio R Paula	08/2011
8909	gcd(V(738275),5F(147655)(F(147655)-1)+1)	61715	Serge Batalov	04/2015
8910	1263^19898+19898^1263	61712	Serge Batalov	05/2014
8911	135^28963-134	61701	Norbert Schneider	04/2015
8912	(33*2^204966+1)/234341	61698	Michael Porter	01/2015
8913	(7*10^61696+167)/3	61696	Robert Kinser	10/2017
8914	(46*10^61693+17)/9	61694	Robert Price	06/2015
8915	((((((((((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
8916	1850^18879+18879^1850	61681	Serge Batalov	05/2014
8918	2^204891-1005	61679	Lelio R Paula	09/2011
8917	151^28306-2	61679	Lelio R Paula	10/2017
8919	(3^129271-5)/41506	61674	Lelio R Paula	03/2012
8920	15937^7408+7408^15937	61672	Hans Havermann	02/2017
8921	5^88216-12	61661	Lelio R Paula	04/2013
8922	18185^2454+2454^18185	61645	Hans Havermann	01/2017
8924	2^204767-15865	61642	Enzo Doria	04/2013
8923	(lucasV(1,2,409560)+2)/3079	61642	Mike Oakes	01/2017
8925	7*2^204751-9	61638	Lelio R Paula	04/2014
8926	4*10^61625+21	61626	Robert Price	08/2016
8927	15369^10226+10226^15369	61626	Hans Havermann	02/2017
8928	2^204702-18125	61622	Enzo Doria	05/2013
8929	5*3^129146+8	61620	Lelio R Paula	04/2014
8930	2^204673+129	61613	Lelio R Paula	08/2011
8931	18^49079+97	61608	Lelio R Paula	05/2013
8932	106^30416+105	61602	Norbert Schneider	12/2016
8933	2^204590-33	61588	Lelio R Paula	08/2011
8934	2^204586-111975	61587	Enzo Doria	06/2014
8935	2^204580-16077	61585	Enzo Doria	04/2013
8936	2^204574-16041	61583	Enzo Doria	04/2013
8937	15^52358+56	61578	Lelio R Paula	05/2013
8938	(28*10^61574+11)/3	61575	Robert Price	11/2015
8939	2^204516-17493	61566	Enzo Doria	05/2013
8940	4*5^88076-3	61564	Lelio R Paula	09/2014
8941	11^59110-2520	61557	Enzo Doria	12/2012
8942	2^204477-58695	61554	Lelio R Paula	09/2011
8943	12^57026-73	61542	Lelio R Paula	05/2013
8944	(257^25537+1)/258	61541	Richard Fischer	04/2018
8945	17^50013+90	61539	Lelio R Paula	05/2013
8946	56^35201-55^35201	61538	Robert Price	10/2013
8947	8*7^72810+5	61533	Lelio R Paula	09/2014
8949	204^26641-203^26641	61531	Jean-Louis Charton	08/2009
8948	43867!3-6561	61531	Robert Price	11/2015
8950	10^61525+9^(61525-1)	61526	Robert Price	03/2016
8951	10^61525+62257	61526	Patrick De Geest	12/2016
8952	14821^14166+14166^14821	61526	Hans Havermann	01/2017
8954	12^57010-85	61525	Lelio R Paula	05/2013
8953	10^61525-213579	61525	Patrick De Geest	12/2016
8955	2^204332-99	61511	Lelio R Paula	08/2011
8956	2^204323-2221	61508	Yves Minet	08/2013
8958	2^204317-195	61506	Lelio R Paula	08/2011
8957	3^128910-86	61506	Lelio R Paula	04/2013
8959	2^204318+74539	61506	Enzo Doria	04/2016
8960	(2^204334-3)/1141333	61505	Lelio R Paula	03/2012
8961	2^204297-1036093	61500	Paul Bourdelais	11/2012
8962	3^128880+58	61492	Lelio R Paula	04/2013
8963	2^204216-111677	61476	Enzo Doria	05/2014
8964	13262^14909-14909^13262	61464	Norbert Schneider	08/2019
8965	(F(73524)^5-F(73523)^5)/F(73522)	61462	Wayne Halsdorf	03/2012
8966	14677^14750-14750^14677	61458	Norbert Schneider	05/2019
8967	2^204129+204129	61449	Henri Lifchitz	04/2002
8968	3^128787+2^(128787-1)	61448	Robert Price	05/2016
8969	11^58999-78	61442	Lelio R Paula	05/2013
8970	2^204083-111967	61436	Enzo Doria	05/2014
8971	(45^37159+1)/46	61431	Robert Price	11/2013
8972	677^21702+21702^677	61430	Norbert Schneider	06/2016
8973	14837^13810+13810^14837	61429	Hans Havermann	02/2017
8974	(7*2^204043+1)/39	61423	Lelio R Paula	03/2012
8975	11^58976-1740	61418	Enzo Doria	11/2012
8976	2^204016-16085	61415	Enzo Doria	04/2013
8977	V(379967)	61393	Serge Batalov	03/2015
8978	43777!3-3^43777	61392	Robert Price	08/2015
8979	7^72642+88	61390	Lelio R Paula	04/2013
8980	3^128656+32	61385	Lelio R Paula	04/2013
8981	2^203916-17493	61385	Enzo Doria	05/2013
8982	6^78880+23	61381	Lelio R Paula	04/2013
8983	(388*10^61374-1)/9	61376	Robert Price	11/2017
8984	2^203877-111799	61374	Enzo Doria	05/2014
8985	2^203867-1615	61371	Lelio R Paula	10/2011
8986	4*10^61367+19	61368	Robert Price	04/2016
8987	(19*2^203854+1)/42319	61363	Lelio R Paula	08/2012
8988	12543^14972-14972^12543	61362	Norbert Schneider	10/2019
8989	L(293659)/76528122719	61361	Serge Batalov	07/2017
8990	2^203825-15805	61358	Enzo Doria	04/2013
8991	2^203816-15825	61355	Enzo Doria	04/2013
8992	5*10^61348+59	61349	Robert Price	09/2016
8993	21^46395-2	61345	Lelio R Paula	08/2013
8994	(809*29^41946-165)/28	61344	Curtis Bright	05/2015
8995	7*6^78826+5	61340	Lelio R Paula	09/2014
8996	(3^128558+7)/83773166429696	61324	Lelio R Paula	04/2012
8997	2^203706-111	61322	Lelio R Paula	08/2011
8998	17567^3094+3094^17567	61318	Hans Havermann	02/2017
8999	2^203689-31	61317	Thomas Masser	10/2005
9000	(11*2^203678-1)/53689	61310	Lelio R Paula	01/2014

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PRP Records

Probable Primes Top 10000

(255244 PRPs in the top)