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	(9179*2^193183-1)/3999267879	58149	Lelio R Paula	04/2015
8502	(19*2^193114-1)/1186755	58129	Lelio R Paula	01/2014
8504	2^193091-1237	58127	Yves Minet	08/2012
8503	9*7^68780-2	58127	Lelio R Paula	09/2014
8505	2^193083-869688105	58124	Lelio R Paula	10/2012
8506	2^193058-45	58117	Lelio R Paula	04/2011
8507	(14016^14016+14017^14017)/(23710319913)	58115	David Broadhurst	09/2009
8508	11^55795-42	58105	Lelio R Paula	03/2013
8509	3^121779-16	58104	Lelio R Paula	10/2012
8510	(13*10^58103+191)/3	58104	Robert Price	08/2017
8511	2^192986+195	58095	Lelio R Paula	04/2011
8512	7^68740+2*3^68740	58093	Mike Oakes	07/2010
8513	(85*10^58091-1)/3	58093	Robert Price	07/2017
8514	(404*10^58087-53)/9	58089	Robert Price	11/2017
8515	12^53821+11	58083	Lelio R Paula	02/2013
8516	119^27979-118	58072	Norbert Schneider	10/2013
8517	(10223*2^192828+1)/243	58049	Lelio R Paula	05/2014
8518	2^192808-1127	58041	Yves Minet	05/2013
8519	(27*2^192803+1)/9827	58037	Lelio R Paula	07/2012
8521	(2^192781+lucasV(1,2,192781)+1)/4	58033	Mike Oakes	11/2016
8520	3*10^58032-23	58033	Robert Price	11/2017
8522	2^192678+72943	58002	Enzo Doria	04/2016
8523	(13*10^57997-37)/3	57998	Robert Price	08/2017
8524	2^192657-3189	57996	Yves Minet	10/2014
8525	6^74525-149	57992	Lelio R Paula	10/2012
8526	42^35723-41	57988	Norbert Schneider	06/2014
8527	(29*2^192625-1)/183	57986	Lelio R Paula	01/2014
8528	(3^121520-8)/3847	57977	Lelio R Paula	03/2012
8529	(2^192596-5)/139	57976	Lelio R Paula	02/2012
8530	10^57975+67833	57976	Patrick De Geest	09/2013
8531	10^57975-47693	57975	Patrick De Geest	09/2013
8532	(F(7707)^37-F(7706)^37)/F(7705)	57972	Wayne Halsdorf	03/2012
8533	(29*10^57967+673)/9	57968	Robert Price	10/2017
8534	(3^121492-5)/4	57966	Lelio R Paula	03/2012
8535	2^192549+35	57964	Lelio R Paula	04/2011
8536	28799!2+2	57962	Robert Price	10/2012
8537	(7*2^192534-1)/1347	57957	Lelio R Paula	01/2014
8538	7001^15069-100	57943	Enzo Doria	07/2012
8539	L(277273)/11090921	57940	Donovan Johnson	11/2005
8540	(2^192469-1017)/35	57938	Lelio R Paula	02/2012
8541	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
8542	2^192443+1385	57932	Lelio R Paula	05/2011
8543	132^27317-131	57928	Norbert Schneider	03/2015
8544	41522!3-59049	57912	Robert Price	12/2015
8545	(3*2^192380-1)/169	57911	Lelio R Paula	01/2014
8546	2^192339-2515	57900	Yves Minet	07/2014
8547	2^192303+7695	57889	Lelio R Paula	10/2012
8548	2^192273-5955	57880	Lelio R Paula	05/2011
8549	2^192257+16095	57876	Lelio R Paula	05/2011
8550	109^28401-2	57865	Lelio R Paula	10/2017
8551	2^192218-111861	57864	Enzo Doria	05/2014
8552	2^192214-3941	57863	Yves Minet	04/2017
8553	(2^192212+3)/259	57860	Lelio R Paula	02/2012
8554	(3^121270+8)/155939753	57853	Lelio R Paula	03/2012
8555	80^30393-79	57841	Norbert Schneider	03/2015
8556	20^44455-3123	57838	Enzo Doria	03/2013
8557	2^192122-195	57835	Lelio R Paula	04/2011
8558	(29*10^57834+91)/3	57835	Robert Price	03/2016
8559	8*6^74306+5	57823	Lelio R Paula	09/2014
8560	(39^36341-1)/38	57820	Robert Price	04/2012
8561	2^192037-111805	57809	Enzo Doria	05/2014
8562	2^192023-192023^2	57805	Henri Lifchitz	05/2005
8563	21^43717+2	57804	Ray Chandler	08/2011
8564	8*5^82687+7	57797	Lelio R Paula	09/2014
8565	5^82680-24	57791	Lelio R Paula	10/2012
8566	(2^191915+47)/95	57771	Lelio R Paula	02/2012
8567	(74*10^57763+133)/9	57764	Robert Price	10/2017
8568	6^74227-95	57760	Lelio R Paula	10/2012
8569	2^191861+29835	57756	Lelio R Paula	10/2012
8570	1908^17605+17605^1908	57755	Serge Batalov	05/2014
8571	5*10^57754+59	57755	Robert Price	09/2016
8572	(5*2^191821-1)/8924067	57738	Lelio R Paula	01/2014
8573	38^63917+5^63917-34^63917+3*2^63917	57724	Mike Oakes	11/2010
8574	41399!3-6561	57723	Robert Price	11/2015
8575	(44*10^57721-233)/9	57722	Robert Price	10/2017
8576	2^191745+17	57721	Lelio R Paula	04/2011
8577	2^191730-761	57717	Yves Minet	01/2012
8578	(2^191733-3)/2251	57715	Lelio R Paula	02/2012
8579	2^191698-111	57707	Lelio R Paula	04/2011
8580	(13*10^57691+23)/9	57692	Robert Price	02/2015
8581	20^44340-5423	57688	Enzo Doria	03/2013
8582	(27*2^191629+1)/125	57686	Lelio R Paula	07/2012
8583	410^57684+37^57684	57685	Mike Oakes	11/2010
8584	2*3^120898+5	57684	Lelio R Paula	04/2014
8585	(6883*2^191610-1)/7347	57681	Lelio R Paula	04/2015
8586	6^74117-49	57675	Lelio R Paula	10/2012
8587	2^191586-113201	57674	Enzo Doria	07/2014
8588	2^191580+193	57672	Lelio R Paula	04/2011
8589	(103*29^39433+10401)/4	57669	Curtis Bright	05/2015
8590	2^191560+255255	57666	Lelio R Paula	05/2011
8591	2^191515-85	57652	Lelio R Paula	04/2011
8592	2^191502-1127	57648	Yves Minet	05/2013
8593	2*5^82473-3^82473	57647	Mike Oakes	08/2010
8594	(13*10^57634-61)/3	57635	Robert Price	08/2017
8595	85^29868-29868^85	57628	Norbert Schneider	11/2017
8596	2^191430+103	57627	Lelio R Paula	04/2011
8597	3*2^191408+5	57621	Lelio R Paula	03/2014
8598	2^191382-1858931	57612	Enzo Doria	04/2016
8599	6*7^68163+5	57606	Lelio R Paula	09/2014
8600	91^29403-2	57602	Lelio R Paula	08/2013
8601	11^55308-7950	57598	Enzo Doria	02/2013
8602	2^191329+65	57596	Lelio R Paula	04/2011
8603	11^55302-240	57592	Enzo Doria	07/2012
8604	2^191299-1031467	57587	Paul Bourdelais	11/2012
8605	2^191295-111991	57586	Enzo Doria	05/2014
8606	2^191279-1297	57581	Yves Minet	08/2012
8607	3*6^73961+5	57554	Lelio R Paula	09/2014
8608	(3^120623+5)/52144	57548	Lelio R Paula	04/2012
8609	(17*10^57543-29)/3	57544	Robert Price	09/2017
8610	42^35445-41	57537	Norbert Schneider	06/2014
8611	(71^31079-1)/70	57534	Paul Bourdelais	08/2017
8612	2^191069-723403	57518	Paul Bourdelais	11/2012
8613	4*10^57506-3	57507	Serge Batalov	11/2010
8614	10^57501+67359	57502	Patrick De Geest	06/2016
8615	10^57501-1000000001	57501	Robert Price	05/2016
8616	10^57501-249861	57501	Patrick De Geest	06/2016
8617	(9^60251+4^60251)/13	57493	Robert Price	02/2013
8618	20^44184-6003	57485	Enzo Doria	03/2013
8619	2^190948+12705	57482	Lelio R Paula	10/2012
8620	2^190945+29	57481	Henri Lifchitz	06/2005
8621	2^190922-401	57474	Yves Minet	01/2012
8622	15^48860+46	57464	Lelio R Paula	02/2013
8623	3^120434+20	57462	Lelio R Paula	10/2012
8624	7^67964-38	57437	Lelio R Paula	10/2012
8625	2^190799-113065	57437	Enzo Doria	07/2014
8626	9*5^82159+2	57428	Lelio R Paula	09/2014
8627	(F(22898)^13-F(22897)^13)/F(22896)	57422	Wayne Halsdorf	03/2012
8630	lucasU(432,25,21787)-5*lucasU(432,25,21786)	57416	Mike Oakes	05/2009
8628	(103*10^57414-1)/3	57416	Serge Batalov	12/2014
8629	(1654*30^38869-1)/29	57416	Karsten Bonath	05/2017
8631	2*10^57410+9^57410	57411	Mike Oakes	04/2011
8632	2^190704-1595	57408	Lelio R Paula	05/2011
8633	11^55121-1740	57403	Enzo Doria	11/2012
8634	2^190644-185	57390	Lelio R Paula	04/2011
8635	41182!3-3^41182	57389	Robert Price	08/2015
8636	2^190629-112255	57386	Enzo Doria	06/2014
8637	(2*10^57384-71)/3	57384	Robert Price	01/2017
8638	2*6^73735+5^73735	57378	Mike Oakes	11/2009
8639	2^190605+59	57378	Lelio R Paula	04/2011
8640	6^73727-7	57371	Lelio R Paula	10/2012
8641	2^190561-112225	57365	Enzo Doria	06/2014
8642	10^57358+170899	57359	Patrick De Geest	06/2016
8643	10^57358-8001	57358	Robert Price	03/2016
8644	18^45687-11	57350	Lelio R Paula	02/2013
8645	11^55069-210	57349	Enzo Doria	07/2012
8646	11^55068-12	57348	Lelio R Paula	02/2013
8647	19^44839+54	57339	Lelio R Paula	02/2013
8648	(7*2^190468-1)/8511	57334	Lelio R Paula	01/2014
8649	(23*10^57333-59)/9	57334	Robert Price	03/2017
8650	2^190455-1155*190455	57333	Henri Lifchitz	02/2005
8651	65^31620+28	57325	Lelio R Paula	01/2016
8652	2^190403+16095	57318	Lelio R Paula	05/2011
8653	(19*10^57316+119)/3	57317	Robert Price	02/2017
8655	(21*2^190393+1)/211	57314	Lelio R Paula	07/2012
8654	2^190392-112025	57314	Enzo Doria	05/2014
8656	(24737*2^190234+1)/9	57270	Lelio R Paula	05/2014
8657	(7*2^190230+1)/23	57265	Lelio R Paula	07/2012
8658	(10223*2^190197+1)/3211	57256	Lelio R Paula	05/2014
8659	18^45590-97	57228	Lelio R Paula	02/2013
8660	(3*2^190105-1)/19205	57224	Lelio R Paula	01/2014
8661	(16*10^57219-31)/3	57220	Robert Price	03/2016
8662	(2^190074+47)/51	57217	Lelio R Paula	02/2012
8663	3^119894-140	57204	Lelio R Paula	10/2012
8665	(37^36473-1)/36	57196	Robert Price	03/2012
8664	2^190000-2163	57196	Yves Minet	08/2013
8666	2^189987-2798107	57192	Enzo Doria	04/2016
8667	2^189935-112117	57177	Enzo Doria	05/2014
8668	2^189909-112231	57169	Enzo Doria	06/2014
8669	132049#+149053	57161	Makoto Morimoto	12/2015
8670	41032!3-27	57158	Robert Price	09/2014
8671	19^44694+22	57153	Lelio R Paula	02/2013
8672	12^52956-17	57150	Lelio R Paula	02/2013
8673	2^189823-967	57143	Yves Minet	01/2012
8674	(25*10^57138-61)/9	57139	Robert Price	02/2015
8675	5^81743-4^(81743+1)	57136	Robert Price	04/2016
8676	7^67593-54	57123	Lelio R Paula	10/2012
8677	7*3^119712+2	57118	Lelio R Paula	03/2014
8678	5^81700+16	57106	Lelio R Paula	10/2012
8679	2^189700+76561	57106	Enzo Doria	05/2016
8681	2^189671+131	57097	Lelio R Paula	04/2011
8680	4*6^73374+5	57097	Lelio R Paula	09/2014
8682	(67607*2^189651+1)/43727	57091	Lelio R Paula	05/2014
8683	(29*2^189619-1)/393	57080	Lelio R Paula	01/2014
8684	3^119587+80	57058	Lelio R Paula	10/2012
8685	2^189502-113453	57046	Enzo Doria	07/2014
8686	2^189455+153	57032	Lelio R Paula	04/2011
8687	24^41317-41317^24	57027	Norbert Schneider	07/2016
8688	2^189414-17	57020	Lelio R Paula	03/2011
8689	24^41311+23	57018	Norbert Schneider	12/2013
8690	norm(Mod(x,x^4+x^3-x+1)^207341-1)/2	56998	Paul Vanderveen	05/2018
8691	(4*10^56989-31)/9	56989	Erik Branger	05/2011
8692	11^54712-1620	56977	Enzo Doria	11/2012
8693	2^189237-112231	56967	Enzo Doria	06/2014
8694	17^46285-48	56952	Lelio R Paula	02/2013
8695	2^189188+75241	56952	Enzo Doria	04/2016
8696	2^189181+94395	56950	Henri Lifchitz	01/2005
8697	7001^14808-108	56940	Enzo Doria	07/2012
8698	2^189147-112639	56939	Enzo Doria	06/2014
8699	(19*10^56933-43)/3	56934	Robert Price	10/2017
8700	2^189110-3	56928	M. Frind & P. Underwood	11/2002
8701	2^189069+12909	56916	Lelio R Paula	04/2011
8702	(13*10^56909+191)/3	56910	Robert Price	08/2017
8703	(35*10^56898-17)/9	56899	Serge Batalov	02/2009
8705	2^189011-5955	56898	Lelio R Paula	04/2011
8704	6^73119-5	56898	Lelio R Paula	10/2012
8706	13^51076-90	56896	Lelio R Paula	02/2013
8707	2^188997+56897	56894	Yves Minet	02/2010
8708	5^81388-13766	56888	Enzo Doria	02/2013
8709	(104^28201+1)/105	56881	Richard Fischer	04/2018
8710	(156^25933+1)/157	56873	Eric Chen	12/2017
8711	20^43713-6403	56872	Enzo Doria	03/2013
8712	(71*10^56858-287)/9	56859	Robert Price	05/2017
8713	2^188857-254233	56852	Gary Barnes	09/2009
8714	15^48338-88	56850	Lelio R Paula	02/2013
8715	10^56849+136437	56850	Patrick De Geest	07/2017
8716	10^56849-701	56849	Robert Price	06/2017
8717	(2^188788+78557)/3	56831	Lelio R Paula	05/2012
8718	2^188771+16095	56826	Lelio R Paula	04/2011
8719	7*2^188742-9	56818	Lelio R Paula	03/2014
8720	12^52646-65	56815	Lelio R Paula	02/2013
8721	5003^15358-158	56813	Enzo Doria	07/2012
8722	2^188713+577294575	56809	Lelio R Paula	03/2013
8723	2^188693-112099	56803	Enzo Doria	05/2014
8724	(7^67211+4^67211)/11	56799	Robert Price	10/2012
8725	2^188678-94395	56798	Lelio R Paula	09/2011
8726	20^43651-8503	56792	Enzo Doria	03/2013
8728	2^188657-2371	56792	Yves Minet	10/2013
8727	152^26029-151^26029	56792	Eric Chen	04/2018
8729	(14^49549+5^49549)/19	56789	Robert Price	05/2013
8730	(45^34351-1)/44	56788	Robert Price	05/2014
8731	7*10^56785-23	56786	Robert Price	04/2016
8732	(10^56781-31)/3	56781	Serge Batalov	12/2014
8733	7*10^56779+3	56780	Erik Branger	11/2009
8734	10^56765+259179	56766	Patrick De Geest	09/2013
8735	10^56765-249497	56765	Patrick De Geest	09/2013
8736	t(188706)	56764	Robert Price	04/2015
8737	2^188551-904327	56760	Paul Bourdelais	11/2012
8739	(64*10^56756+17)/9	56757	Robert Price	09/2015
8738	131101#+146291	56757	Makoto Morimoto	02/2016
8740	2^188539-112519	56756	Enzo Doria	06/2014
8741	6^72927+101	56749	Lelio R Paula	10/2012
8742	20^43617-1603	56748	Enzo Doria	03/2013
8743	(3^118892-8)/91358929	56718	Lelio R Paula	03/2012
8744	(509203*2^188338-1)/3	56701	Lelio R Paula	03/2015
8745	20^43567-5623	56682	Enzo Doria	03/2013
8746	2^188234-113183	56665	Enzo Doria	07/2014
8747	(139^26437+1)/140	56653	Richard Fischer	03/2018
8748	(7*2^188215-1)/1497315125	56651	Lelio R Paula	01/2014
8749	(1017*2^188171-1)/35	56647	Lelio R Paula	03/2015
8750	(34*10^56647-7)/9/37/263	56644	Makoto Morimoto	04/2016

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Probable Primes Top 10000

(218736 PRPs in the top)