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 ?
8501	7*10^58815-83	58816	Robert Price	09/2017
8502	2^195357-4303	58809	Yves Minet	08/2018
8503	(47*2^195254+1)/268821	58774	Lelio R Paula	03/2015
8504	2^195207-18109	58764	Enzo Doria	05/2013
8505	2^195199-1567	58761	Yves Minet	08/2012
8506	2^195190+73759	58759	Enzo Doria	04/2016
8507	9*7^69525-4	58757	Lelio R Paula	09/2014
8508	2^195170-18045	58753	Enzo Doria	05/2013
8509	2^195166-165	58751	Lelio R Paula	04/2011
8510	(754*10^58748-7)/9	58750	Robert Price	11/2017
8511	(22699*2^195140+1)/175	58746	Lelio R Paula	05/2014
8512	7*3^123109-2	58739	Lelio R Paula	04/2014
8513	(8*10^58738-611)/9	58738	Robert Price	11/2017
8514	18^46790+77	58735	Lelio R Paula	03/2013
8515	2^195095-337297	58730	Gary Barnes	09/2009
8516	(14*10^58729+31)/9	58730	Robert Price	02/2015
8517	99^29424+98	58720	Norbert Schneider	07/2013
8518	(15185*2^195039-1)/219	58715	Lelio R Paula	04/2015
8519	2^195001-69	58702	Lelio R Paula	04/2011
8520	2^194978-487811	58695	Gary Barnes	09/2009
8521	163^26530+26530^163	58690	Serge Batalov	05/2014
8522	2^194940-194940+1	58683	Robert Price	10/2014
8523	(76*10^58669+41)/9	58670	Robert Price	10/2015
8524	14^51186+87	58666	Lelio R Paula	03/2013
8525	2^194878-97305	58665	Lelio R Paula	09/2011
8526	5^83927-18136	58663	Enzo Doria	05/2014
8527	(24737*2^194865+1)/1085	58662	Lelio R Paula	06/2014
8528	7^69411+40	58660	Lelio R Paula	10/2012
8529	6^75382-79	58659	Lelio R Paula	10/2012
8530	2^194854+27	58657	Lelio R Paula	04/2011
8531	2^194801+29835	58641	Lelio R Paula	10/2012
8532	2^194752+195	58627	Lelio R Paula	04/2011
8533	7^69371-6^69371	58626	Predrag Minovic	08/2004
8534	2^194747-112519	58625	Enzo Doria	06/2014
8535	(15*2^194737+1)/59	58622	Lelio R Paula	07/2012
8536	(23*2^194700+1)/3	58612	Lelio R Paula	02/2012
8537	10^58608+55273	58609	Patrick De Geest	07/2017
8538	10^58608-800001	58608	Robert Price	06/2017
8539	10^58608-60119	58608	Patrick De Geest	07/2017
8540	5^83836+76	58599	Lelio R Paula	10/2012
8541	18^46664+31	58577	Lelio R Paula	03/2013
8542	(34*10^58577-7)/9/19/463	58574	Makoto Morimoto	04/2016
8543	2^194574+165	58573	Lelio R Paula	04/2011
8546	2^194569-12211	58572	Enzo Doria	06/2014
8544	10^58571+5^58571+2^58571	58572	Robert Price	12/2016
8545	10^58571+202837	58572	Patrick De Geest	02/2017
8547	(10^58571+41)/3	58571	Robert Price	01/2017
8548	10^58571-343629	58571	Patrick De Geest	02/2017
8549	(43*10^58563-403)/9	58564	Robert Price	04/2017
8550	11^56235-7950	58563	Enzo Doria	02/2013
8551	(14*10^58550+211)/9	58551	Robert Price	11/2017
8552	2^194479-113239	58545	Enzo Doria	07/2014
8553	2^194455-112249	58537	Enzo Doria	06/2014
8554	2^194405-111919	58522	Enzo Doria	05/2014
8555	(4*10^58521-19)/3	58522	Robert Price	06/2017
8556	(7^69247-4^69247)/3	58521	Robert Price	06/2012
8557	5*7^69246+8	58521	Lelio R Paula	09/2014
8558	2^194358-1167	58508	Lelio R Paula	05/2011
8559	(2^194366+7)/1373	58507	Lelio R Paula	02/2012
8560	(493*10^58486-7)/9	58488	Robert Price	07/2016
8561	3^122579-340	58486	Lelio R Paula	10/2012
8562	(11*10^58458-149)/3	58459	Robert Price	01/2017
8563	(47*10^58456+133)/9	58457	Robert Price	04/2017
8564	2^194186+85	58456	Lelio R Paula	04/2011
8565	3^122506-2^(122506-1)	58451	Robert Price	01/2016
8566	(74^31267-1)/73	58444	Paul Bourdelais	08/2017
8567	177^25998-2	58443	Lelio R Paula	10/2017
8568	15^49690-26	58440	Lelio R Paula	03/2013
8569	10^58437+110721	58438	Patrick De Geest	12/2012
8570	10^58437-11	58437	Robert Price	05/2011
8571	2^194095+69	58429	Lelio R Paula	04/2011
8572	(29*10^58417-77)/3	58418	Robert Price	01/2017
8573	2^194034+177	58411	Lelio R Paula	04/2011
8574	789^20158+20158^789	58400	Norbert Schneider	06/2016
8575	14^50949+75	58395	Lelio R Paula	03/2013
8576	2^193974-114761	58392	Enzo Doria	05/2015
8577	2^193965+5	58390	Henri Lifchitz	12/2002
8578	(5*10^58384-29)/3	58385	Robert Price	02/2017
8579	3^122360+80	58381	Lelio R Paula	10/2012
8580	10103^14577-114	58373	Enzo Doria	07/2012
8581	(22699*2^193883+1)/21	58368	Lelio R Paula	06/2014
8582	(31*2^193886+1)/140765	58362	Lelio R Paula	07/2012
8583	11^56041-1560	58361	Enzo Doria	11/2012
8584	(2^193881+9)/17699	58360	Lelio R Paula	02/2012
8585	3^122313+58	58359	Lelio R Paula	10/2012
8586	6^74996-119	58359	Lelio R Paula	10/2012
8587	(11*2^193859+1)/13	58358	Lelio R Paula	07/2012
8588	2^193861-112255	58358	Enzo Doria	06/2014
8589	(22699*2^193854+1)/4927	58357	Lelio R Paula	06/2014
8590	18^46487+37	58354	Lelio R Paula	03/2013
8591	17^47419+54	58347	Lelio R Paula	03/2013
8592	(31*2^193791+1)/3	58338	Lelio R Paula	02/2012
8593	(27*2^193805-1)/982249	58337	Lelio R Paula	01/2014
8594	3^122219-2^122219	58314	Mike Oakes	09/2003
8595	(199*10^58306+11)/3	58308	Robert Price	05/2017
8596	2^193674-18825	58302	Lelio R Paula	05/2011
8597	5*10^58275+3	58276	Dmitry Domanov	11/2010
8598	2^193578-112913	58273	Enzo Doria	06/2014
8599	2^193541+1299	58262	Lelio R Paula	05/2011
8600	10^58250+93	58251	Robert Price	01/2011
8601	10^58250-175607	58250	Patrick De Geest	12/2012
8602	(107^28703+1)/108	58248	Richard Fischer	05/2018
8603	2^193492+8415	58247	Lelio R Paula	10/2012
8604	2^193444+157	58233	Lelio R Paula	04/2011
8605	Phi(28754,28754)	58231	Henri Lifchitz	08/2013
8606	2^193430-111881	58229	Enzo Doria	05/2014
8607	10^58225+124579	58226	Patrick De Geest	12/2012
8608	10^58225-93	58225	Robert Price	05/2011
8609	2^193375-295	58212	Yves Minet	05/2013
8610	2^193345+77267	58203	Enzo Doria	05/2016
8611	21^44017-20^44017	58201	Robert Price	05/2012
8612	(17*2^193329-1)/9	58199	Lelio R Paula	01/2014
8613	17^47291+20	58190	Lelio R Paula	03/2013
8614	p(12528)#/2-128	58170	Robert Price	05/2017
8615	2^193214-135	58164	Lelio R Paula	04/2011
8616	19^45483-80	58162	Lelio R Paula	03/2013
8617	(4*10^58155+83)/3	58156	Robert Price	01/2017
8619	14^50739-13	58154	Lelio R Paula	03/2013
8618	(1017*2^193184-1)/4823	58154	Lelio R Paula	04/2015
8620	(2*10^58151+457)/9	58151	Robert Price	01/2017
8621	(9179*2^193183-1)/3999267879	58149	Lelio R Paula	04/2015
8622	(19*2^193114-1)/1186755	58129	Lelio R Paula	01/2014
8624	2^193091-1237	58127	Yves Minet	08/2012
8623	9*7^68780-2	58127	Lelio R Paula	09/2014
8625	2^193083-869688105	58124	Lelio R Paula	10/2012
8626	2^193058-45	58117	Lelio R Paula	04/2011
8627	(14016^14016+14017^14017)/(23710319913)	58115	David Broadhurst	09/2009
8628	11^55795-42	58105	Lelio R Paula	03/2013
8629	3^121779-16	58104	Lelio R Paula	10/2012
8630	(13*10^58103+191)/3	58104	Robert Price	08/2017
8631	2^192986+195	58095	Lelio R Paula	04/2011
8632	7^68740+2*3^68740	58093	Mike Oakes	07/2010
8633	(85*10^58091-1)/3	58093	Robert Price	07/2017
8634	(404*10^58087-53)/9	58089	Robert Price	11/2017
8635	12^53821+11	58083	Lelio R Paula	02/2013
8636	119^27979-118	58072	Norbert Schneider	10/2013
8637	(10223*2^192828+1)/243	58049	Lelio R Paula	05/2014
8638	2^192808-1127	58041	Yves Minet	05/2013
8639	(27*2^192803+1)/9827	58037	Lelio R Paula	07/2012
8641	(2^192781+lucasV(1,2,192781)+1)/4	58033	Mike Oakes	11/2016
8640	3*10^58032-23	58033	Robert Price	11/2017
8642	2^192678+72943	58002	Enzo Doria	04/2016
8643	(13*10^57997-37)/3	57998	Robert Price	08/2017
8644	2^192657-3189	57996	Yves Minet	10/2014
8645	6^74525-149	57992	Lelio R Paula	10/2012
8646	42^35723-41	57988	Norbert Schneider	06/2014
8647	(29*2^192625-1)/183	57986	Lelio R Paula	01/2014
8648	(3^121520-8)/3847	57977	Lelio R Paula	03/2012
8649	(2^192596-5)/139	57976	Lelio R Paula	02/2012
8650	10^57975+67833	57976	Patrick De Geest	09/2013
8651	10^57975-47693	57975	Patrick De Geest	09/2013
8652	(F(7707)^37-F(7706)^37)/F(7705)	57972	Wayne Halsdorf	03/2012
8653	(29*10^57967+673)/9	57968	Robert Price	10/2017
8654	(3^121492-5)/4	57966	Lelio R Paula	03/2012
8655	2^192549+35	57964	Lelio R Paula	04/2011
8656	28799!2+2	57962	Robert Price	10/2012
8657	(7*2^192534-1)/1347	57957	Lelio R Paula	01/2014
8658	7001^15069-100	57943	Enzo Doria	07/2012
8659	L(277273)/11090921	57940	Donovan Johnson	11/2005
8660	(2^192469-1017)/35	57938	Lelio R Paula	02/2012
8661	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
8662	2^192443+1385	57932	Lelio R Paula	05/2011
8663	132^27317-131	57928	Norbert Schneider	03/2015
8664	41522!3-59049	57912	Robert Price	12/2015
8665	(3*2^192380-1)/169	57911	Lelio R Paula	01/2014
8666	2^192339-2515	57900	Yves Minet	07/2014
8667	2^192303+7695	57889	Lelio R Paula	10/2012
8668	2^192273-5955	57880	Lelio R Paula	05/2011
8669	2^192257+16095	57876	Lelio R Paula	05/2011
8670	109^28401-2	57865	Lelio R Paula	10/2017
8671	2^192218-111861	57864	Enzo Doria	05/2014
8672	2^192214-3941	57863	Yves Minet	04/2017
8673	(2^192212+3)/259	57860	Lelio R Paula	02/2012
8674	(3^121270+8)/155939753	57853	Lelio R Paula	03/2012
8675	80^30393-79	57841	Norbert Schneider	03/2015
8676	20^44455-3123	57838	Enzo Doria	03/2013
8677	2^192122-195	57835	Lelio R Paula	04/2011
8678	(29*10^57834+91)/3	57835	Robert Price	03/2016
8679	8*6^74306+5	57823	Lelio R Paula	09/2014
8680	(39^36341-1)/38	57820	Robert Price	04/2012
8681	2^192037-111805	57809	Enzo Doria	05/2014
8682	2^192023-192023^2	57805	Henri Lifchitz	05/2005
8683	21^43717+2	57804	Ray Chandler	08/2011
8684	8*5^82687+7	57797	Lelio R Paula	09/2014
8685	5^82680-24	57791	Lelio R Paula	10/2012
8686	(2^191915+47)/95	57771	Lelio R Paula	02/2012
8687	(74*10^57763+133)/9	57764	Robert Price	10/2017
8688	6^74227-95	57760	Lelio R Paula	10/2012
8689	2^191861+29835	57756	Lelio R Paula	10/2012
8690	1908^17605+17605^1908	57755	Serge Batalov	05/2014
8691	5*10^57754+59	57755	Robert Price	09/2016
8692	(5*2^191821-1)/8924067	57738	Lelio R Paula	01/2014
8693	38^63917+5^63917-34^63917+3*2^63917	57724	Mike Oakes	11/2010
8694	41399!3-6561	57723	Robert Price	11/2015
8695	(44*10^57721-233)/9	57722	Robert Price	10/2017
8696	2^191745+17	57721	Lelio R Paula	04/2011
8697	2^191730-761	57717	Yves Minet	01/2012
8698	(2^191733-3)/2251	57715	Lelio R Paula	02/2012
8699	2^191698-111	57707	Lelio R Paula	04/2011
8700	(13*10^57691+23)/9	57692	Robert Price	02/2015
8701	20^44340-5423	57688	Enzo Doria	03/2013
8702	(27*2^191629+1)/125	57686	Lelio R Paula	07/2012
8703	410^57684+37^57684	57685	Mike Oakes	11/2010
8704	2*3^120898+5	57684	Lelio R Paula	04/2014
8705	(6883*2^191610-1)/7347	57681	Lelio R Paula	04/2015
8706	6^74117-49	57675	Lelio R Paula	10/2012
8707	2^191586-113201	57674	Enzo Doria	07/2014
8708	2^191580+193	57672	Lelio R Paula	04/2011
8709	(103*29^39433+10401)/4	57669	Curtis Bright	05/2015
8710	2^191560+255255	57666	Lelio R Paula	05/2011
8711	2^191515-85	57652	Lelio R Paula	04/2011
8712	2^191502-1127	57648	Yves Minet	05/2013
8713	2*5^82473-3^82473	57647	Mike Oakes	08/2010
8714	(13*10^57634-61)/3	57635	Robert Price	08/2017
8715	85^29868-29868^85	57628	Norbert Schneider	11/2017
8716	2^191430+103	57627	Lelio R Paula	04/2011
8717	3*2^191408+5	57621	Lelio R Paula	03/2014
8718	2^191382-1858931	57612	Enzo Doria	04/2016
8719	6*7^68163+5	57606	Lelio R Paula	09/2014
8720	91^29403-2	57602	Lelio R Paula	08/2013
8721	11^55308-7950	57598	Enzo Doria	02/2013
8722	2^191329+65	57596	Lelio R Paula	04/2011
8723	11^55302-240	57592	Enzo Doria	07/2012
8724	2^191299-1031467	57587	Paul Bourdelais	11/2012
8725	2^191295-111991	57586	Enzo Doria	05/2014
8726	2^191279-1297	57581	Yves Minet	08/2012
8727	3*6^73961+5	57554	Lelio R Paula	09/2014
8728	(3^120623+5)/52144	57548	Lelio R Paula	04/2012
8729	(17*10^57543-29)/3	57544	Robert Price	09/2017
8730	42^35445-41	57537	Norbert Schneider	06/2014
8731	(71^31079-1)/70	57534	Paul Bourdelais	08/2017
8732	2^191069-723403	57518	Paul Bourdelais	11/2012
8733	4*10^57506-3	57507	Serge Batalov	11/2010
8734	10^57501+67359	57502	Patrick De Geest	06/2016
8735	10^57501-1000000001	57501	Robert Price	05/2016
8736	10^57501-249861	57501	Patrick De Geest	06/2016
8737	(9^60251+4^60251)/13	57493	Robert Price	02/2013
8738	20^44184-6003	57485	Enzo Doria	03/2013
8739	2^190948+12705	57482	Lelio R Paula	10/2012
8740	2^190945+29	57481	Henri Lifchitz	06/2005
8741	2^190922-401	57474	Yves Minet	01/2012
8742	15^48860+46	57464	Lelio R Paula	02/2013
8743	3^120434+20	57462	Lelio R Paula	10/2012
8744	7^67964-38	57437	Lelio R Paula	10/2012
8745	2^190799-113065	57437	Enzo Doria	07/2014
8746	9*5^82159+2	57428	Lelio R Paula	09/2014
8747	(F(22898)^13-F(22897)^13)/F(22896)	57422	Wayne Halsdorf	03/2012
8750	lucasU(432,25,21787)-5*lucasU(432,25,21786)	57416	Mike Oakes	05/2009
8749	(103*10^57414-1)/3	57416	Serge Batalov	12/2014
8748	(1654*30^38869-1)/29	57416	Karsten Bonath	05/2017

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Probable Primes Top 10000

(224926 PRPs in the top)