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	11^55302-240	57592	Enzo Doria	07/2012
8502	2^191299-1031467	57587	Paul Bourdelais	11/2012
8503	2^191295-111991	57586	Enzo Doria	05/2014
8504	2^191279-1297	57581	Yves Minet	08/2012
8505	3*6^73961+5	57554	Lelio R Paula	09/2014
8506	(3^120623+5)/52144	57548	Lelio R Paula	04/2012
8507	(17*10^57543-29)/3	57544	Robert Price	09/2017
8508	42^35445-41	57537	Norbert Schneider	06/2014
8509	(71^31079-1)/70	57534	Paul Bourdelais	08/2017
8510	2^191069-723403	57518	Paul Bourdelais	11/2012
8511	4*10^57506-3	57507	Serge Batalov	11/2010
8512	10^57501+67359	57502	Patrick De Geest	06/2016
8513	10^57501-1000000001	57501	Robert Price	05/2016
8514	10^57501-249861	57501	Patrick De Geest	06/2016
8515	(9^60251+4^60251)/13	57493	Robert Price	02/2013
8516	20^44184-6003	57485	Enzo Doria	03/2013
8517	2^190948+12705	57482	Lelio R Paula	10/2012
8518	2^190945+29	57481	Henri Lifchitz	06/2005
8519	2^190922-401	57474	Yves Minet	01/2012
8520	15^48860+46	57464	Lelio R Paula	02/2013
8521	3^120434+20	57462	Lelio R Paula	10/2012
8522	7^67964-38	57437	Lelio R Paula	10/2012
8523	2^190799-113065	57437	Enzo Doria	07/2014
8524	9*5^82159+2	57428	Lelio R Paula	09/2014
8525	(F(22898)^13-F(22897)^13)/F(22896)	57422	Wayne Halsdorf	03/2012
8528	lucasU(432,25,21787)-5*lucasU(432,25,21786)	57416	Mike Oakes	05/2009
8526	(103*10^57414-1)/3	57416	Serge Batalov	12/2014
8527	(1654*30^38869-1)/29	57416	Karsten Bonath	05/2017
8529	2*10^57410+9^57410	57411	Mike Oakes	04/2011
8530	2^190704-1595	57408	Lelio R Paula	05/2011
8531	11^55121-1740	57403	Enzo Doria	11/2012
8532	2^190644-185	57390	Lelio R Paula	04/2011
8533	41182!3-3^41182	57389	Robert Price	08/2015
8534	2^190629-112255	57386	Enzo Doria	06/2014
8535	(2*10^57384-71)/3	57384	Robert Price	01/2017
8536	2*6^73735+5^73735	57378	Mike Oakes	11/2009
8537	2^190605+59	57378	Lelio R Paula	04/2011
8538	6^73727-7	57371	Lelio R Paula	10/2012
8539	2^190561-112225	57365	Enzo Doria	06/2014
8540	10^57358+170899	57359	Patrick De Geest	06/2016
8541	10^57358-8001	57358	Robert Price	03/2016
8542	18^45687-11	57350	Lelio R Paula	02/2013
8543	11^55069-210	57349	Enzo Doria	07/2012
8544	11^55068-12	57348	Lelio R Paula	02/2013
8545	19^44839+54	57339	Lelio R Paula	02/2013
8546	(7*2^190468-1)/8511	57334	Lelio R Paula	01/2014
8547	(23*10^57333-59)/9	57334	Robert Price	03/2017
8548	2^190455-1155*190455	57333	Henri Lifchitz	02/2005
8549	65^31620+28	57325	Lelio R Paula	01/2016
8550	2^190403+16095	57318	Lelio R Paula	05/2011
8551	(19*10^57316+119)/3	57317	Robert Price	02/2017
8553	(21*2^190393+1)/211	57314	Lelio R Paula	07/2012
8552	2^190392-112025	57314	Enzo Doria	05/2014
8554	(24737*2^190234+1)/9	57270	Lelio R Paula	05/2014
8555	(7*2^190230+1)/23	57265	Lelio R Paula	07/2012
8556	(10223*2^190197+1)/3211	57256	Lelio R Paula	05/2014
8557	18^45590-97	57228	Lelio R Paula	02/2013
8558	(3*2^190105-1)/19205	57224	Lelio R Paula	01/2014
8559	(16*10^57219-31)/3	57220	Robert Price	03/2016
8560	(2^190074+47)/51	57217	Lelio R Paula	02/2012
8561	3^119894-140	57204	Lelio R Paula	10/2012
8563	(37^36473-1)/36	57196	Robert Price	03/2012
8562	2^190000-2163	57196	Yves Minet	08/2013
8564	2^189987-2798107	57192	Enzo Doria	04/2016
8565	2^189935-112117	57177	Enzo Doria	05/2014
8566	2^189909-112231	57169	Enzo Doria	06/2014
8567	132049#+149053	57161	Makoto Morimoto	12/2015
8568	41032!3-27	57158	Robert Price	09/2014
8569	19^44694+22	57153	Lelio R Paula	02/2013
8570	12^52956-17	57150	Lelio R Paula	02/2013
8571	2^189823-967	57143	Yves Minet	01/2012
8572	(25*10^57138-61)/9	57139	Robert Price	02/2015
8573	5^81743-4^(81743+1)	57136	Robert Price	04/2016
8574	7^67593-54	57123	Lelio R Paula	10/2012
8575	7*3^119712+2	57118	Lelio R Paula	03/2014
8576	5^81700+16	57106	Lelio R Paula	10/2012
8577	2^189700+76561	57106	Enzo Doria	05/2016
8579	2^189671+131	57097	Lelio R Paula	04/2011
8578	4*6^73374+5	57097	Lelio R Paula	09/2014
8580	(67607*2^189651+1)/43727	57091	Lelio R Paula	05/2014
8581	(29*2^189619-1)/393	57080	Lelio R Paula	01/2014
8582	3^119587+80	57058	Lelio R Paula	10/2012
8583	2^189502-113453	57046	Enzo Doria	07/2014
8584	2^189455+153	57032	Lelio R Paula	04/2011
8585	24^41317-41317^24	57027	Norbert Schneider	07/2016
8586	2^189414-17	57020	Lelio R Paula	03/2011
8587	24^41311+23	57018	Norbert Schneider	12/2013
8588	norm(Mod(x,x^4+x^3-x+1)^207341-1)/2	56998	Paul Vanderveen	05/2018
8589	(4*10^56989-31)/9	56989	Erik Branger	05/2011
8590	11^54712-1620	56977	Enzo Doria	11/2012
8591	2^189237-112231	56967	Enzo Doria	06/2014
8593	17^46285-48	56952	Lelio R Paula	02/2013
8592	2^189188+75241	56952	Enzo Doria	04/2016
8594	2^189181+94395	56950	Henri Lifchitz	01/2005
8595	7001^14808-108	56940	Enzo Doria	07/2012
8596	2^189147-112639	56939	Enzo Doria	06/2014
8597	(19*10^56933-43)/3	56934	Robert Price	10/2017
8598	2^189110-3	56928	M. Frind & P. Underwood	11/2002
8599	2^189069+12909	56916	Lelio R Paula	04/2011
8600	(13*10^56909+191)/3	56910	Robert Price	08/2017
8601	(35*10^56898-17)/9	56899	Serge Batalov	02/2009
8602	2^189011-5955	56898	Lelio R Paula	04/2011
8603	6^73119-5	56898	Lelio R Paula	10/2012
8604	13^51076-90	56896	Lelio R Paula	02/2013
8605	2^188997+56897	56894	Yves Minet	02/2010
8606	5^81388-13766	56888	Enzo Doria	02/2013
8607	(104^28201+1)/105	56881	Richard Fischer	04/2018
8608	(156^25933+1)/157	56873	Eric Chen	12/2017
8609	20^43713-6403	56872	Enzo Doria	03/2013
8610	(71*10^56858-287)/9	56859	Robert Price	05/2017
8611	2^188857-254233	56852	Gary Barnes	09/2009
8612	15^48338-88	56850	Lelio R Paula	02/2013
8613	10^56849+136437	56850	Patrick De Geest	07/2017
8614	10^56849-701	56849	Robert Price	06/2017
8615	(2^188788+78557)/3	56831	Lelio R Paula	05/2012
8616	2^188771+16095	56826	Lelio R Paula	04/2011
8617	7*2^188742-9	56818	Lelio R Paula	03/2014
8618	12^52646-65	56815	Lelio R Paula	02/2013
8619	5003^15358-158	56813	Enzo Doria	07/2012
8620	2^188713+577294575	56809	Lelio R Paula	03/2013
8621	2^188693-112099	56803	Enzo Doria	05/2014
8622	(7^67211+4^67211)/11	56799	Robert Price	10/2012
8623	2^188678-94395	56798	Lelio R Paula	09/2011
8624	20^43651-8503	56792	Enzo Doria	03/2013
8626	2^188657-2371	56792	Yves Minet	10/2013
8625	152^26029-151^26029	56792	Eric Chen	04/2018
8627	(14^49549+5^49549)/19	56789	Robert Price	05/2013
8628	(45^34351-1)/44	56788	Robert Price	05/2014
8629	7*10^56785-23	56786	Robert Price	04/2016
8630	(10^56781-31)/3	56781	Serge Batalov	12/2014
8631	7*10^56779+3	56780	Erik Branger	11/2009
8632	10^56765+259179	56766	Patrick De Geest	09/2013
8633	10^56765-249497	56765	Patrick De Geest	09/2013
8634	t(188706)	56764	Robert Price	04/2015
8635	2^188551-904327	56760	Paul Bourdelais	11/2012
8637	(64*10^56756+17)/9	56757	Robert Price	09/2015
8636	131101#+146291	56757	Makoto Morimoto	02/2016
8638	2^188539-112519	56756	Enzo Doria	06/2014
8639	6^72927+101	56749	Lelio R Paula	10/2012
8640	20^43617-1603	56748	Enzo Doria	03/2013
8641	(3^118892-8)/91358929	56718	Lelio R Paula	03/2012
8642	(509203*2^188338-1)/3	56701	Lelio R Paula	03/2015
8643	20^43567-5623	56682	Enzo Doria	03/2013
8644	2^188234-113183	56665	Enzo Doria	07/2014
8645	(139^26437+1)/140	56653	Richard Fischer	03/2018
8646	(7*2^188215-1)/1497315125	56651	Lelio R Paula	01/2014
8647	(1017*2^188171-1)/35	56647	Lelio R Paula	03/2015
8648	(34*10^56647-7)/9/37/263	56644	Makoto Morimoto	04/2016
8649	(2^188176-1017)/453814543	56638	Lelio R Paula	02/2012
8650	33*10^56634+7	56636	Robert Price	07/2016
8651	(F(31)^9241-F(30)^9241)/F(29)	56634	Wayne Halsdorf	08/2010
8652	14^49413+33	56634	Lelio R Paula	02/2013
8653	3^118680+110	56625	Lelio R Paula	10/2012
8654	(13*10^56624+161)/3	56625	Robert Price	04/2017
8655	(3^118676-2)/7516653263	56613	Lelio R Paula	03/2012
8656	(13*2^188062+1)/17	56613	Lelio R Paula	07/2012
8657	2^188056-1313	56611	Yves Minet	08/2012
8658	20^43510-5583	56608	Enzo Doria	03/2013
8659	2^188032+12285	56604	Lelio R Paula	03/2011
8660	(19*10^56597-43)/3	56598	Robert Price	10/2017
8661	(265*10^56588+17)/3	56590	Robert Price	05/2016
8662	2^187959+5775	56582	Lelio R Paula	03/2011
8663	(5*2^187959+1)/53	56581	Lelio R Paula	07/2012
8664	3*10^56575-13	56576	Robert Price	11/2017
8665	(11*2^187889-1)/351	56559	Lelio R Paula	01/2014
8666	(100049^11311+1)/100050	56553	Faysal YAtim	09/2007
8667	(19*10^56544-1)/9	56545	Serge Batalov	03/2009
8668	20^43447-8923	56526	Enzo Doria	03/2013
8669	2^187743-112177	56517	Enzo Doria	06/2014
8670	(F(5879)^47-F(5878)^47)/F(5877)	56502	Wayne Halsdorf	08/2010
8671	5^80831-22	56499	Lelio R Paula	10/2012
8672	5^80828-13166	56497	Enzo Doria	02/2013
8673	7*2^187590-5	56472	Lelio R Paula	03/2014
8674	2^187555+75473	56460	Enzo Doria	04/2016
8675	2^187541-283	56456	Yves Minet	01/2012
8676	(55*10^56453-1)/9	56454	Serge Batalov	03/2009
8677	2^187506-1451	56445	Yves Minet	08/2012
8678	189^24794-2	56443	Lelio R Paula	10/2017
8679	6^72522+143	56434	Lelio R Paula	10/2012
8680	(15185*2^187452-1)/949	56430	Lelio R Paula	03/2015
8681	2^187390+79	56411	Lelio R Paula	03/2011
8682	2^187386+12909	56409	Lelio R Paula	03/2011
8683	2^187382+613	56408	Jason Earls	04/2008
8684	(34*10^56392-7)/9/37/883/23887	56384	Makoto Morimoto	04/2016
8685	20^43337-9	56383	Lelio R Paula	02/2013
8686	(26*10^56371-173)/3	56372	Robert Price	10/2017
8687	(F(1008)^269-F(1007)^269)/F(1006)	56364	Wayne Halsdorf	08/2010
8689	2^187230+427	56362	Henri Lifchitz	01/2005
8688	11^54121-9480	56362	Enzo Doria	02/2013
8690	(21*2^187202-1)/43	56354	Lelio R Paula	01/2014
8691	2^187173-91	56345	Lelio R Paula	03/2011
8692	(23*2^187174-1)/20719883	56340	Lelio R Paula	01/2014
8693	2^187125-2833	56331	Yves Minet	09/2014
8694	9*7^66655-4	56331	Lelio R Paula	09/2014
8695	18^44874-97	56330	Lelio R Paula	02/2013
8696	60*79^29679+19	56322	Serge Batalov	03/2016
8697	5^80571+56	56317	Lelio R Paula	10/2012
8698	5^80551-22	56303	Lelio R Paula	10/2012
8699	(76*10^56281+41)/9	56282	Robert Price	10/2015
8700	(88*10^56271-43)/9	56272	Robert Price	11/2015
8701	(5*10^56256-119)/3	56257	Robert Price	04/2016
8702	1508^17691+17691^1508	56230	Serge Batalov	05/2014
8703	3^117844-58	56226	Lelio R Paula	10/2012
8704	(19*10^56224+737)/9	56225	Robert Price	10/2017
8705	95^28427+2	56221	Lelio R Paula	05/2013
8706	2^186713+76817	56207	Enzo Doria	05/2016
8707	16534^2505+2505^16534	56196	Hans Havermann	06/2016
8708	14428^7849+7849^14428	56195	Hans Havermann	06/2016
8709	2*10^56194-51	56195	Robert Price	11/2017
8710	14898^5909+5909^14898	56189	Hans Havermann	06/2016
8711	18^44758+95	56184	Lelio R Paula	02/2013
8712	2^186555-741	56159	Lelio R Paula	05/2011
8713	(4*10^56156+173)/3	56157	Robert Price	01/2017
8715	(3^117708+7)/447896	56156	Lelio R Paula	03/2012
8714	15711^3752+3752^15711	56156	Hans Havermann	06/2016
8716	(23*2^186549-1)/2429025	56152	Lelio R Paula	01/2014
8717	387^21694+21694^387	56138	Norbert Schneider	08/2014
8718	2^186422+17239	56119	Yves Minet	01/2010
8719	2^186418+4242429	56118	Jason Earls	10/2008
8720	136^26300+135	56113	Norbert Schneider	04/2015
8721	5*2^186392+9	56111	Lelio R Paula	03/2014
8722	14345^8152+8152^14345	56108	Hans Havermann	07/2016
8723	(5*2^186351-1)/39	56097	Lelio R Paula	01/2014
8724	2^186319-541237	56088	Paul Bourdelais	11/2012
8725	2*10^56083-43	56084	Robert Price	07/2017
8726	(16*10^56082-61)/9	56083	Serge Batalov	05/2009
8727	(14*10^56080-143)/3	56081	Robert Price	01/2017
8728	(265*10^56076+17)/3	56078	Robert Price	05/2016
8729	7^66346-50	56069	Lelio R Paula	10/2012
8730	20^43094-33	56067	Lelio R Paula	02/2013
8731	20^43090-1383	56062	Enzo Doria	03/2013
8732	3^117482+2660	56054	Lelio R Paula	10/2012
8733	(22699*2^186193+1)/111	56052	Lelio R Paula	05/2014
8734	(68*10^56042+13)/9	56043	Ray Chandler	09/2010
8735	3*6^71992+5^71992	56022	Mike Oakes	03/2010
8736	13691^12352+12352^13691	56020	Hans Havermann	07/2016
8737	(2^186095+7)/75	56019	Lelio R Paula	02/2012
8738	247^23412+23412^247	56018	Norbert Schneider	08/2014
8739	1839^17156+17156^1839	56008	Serge Batalov	05/2014
8740	13736^11949+11949^13736	56007	Hans Havermann	04/2016
8741	(5*2^186036-1)/11	56003	Lelio R Paula	01/2014
8742	(299*10^55998-17)/3	56000	Robert Price	01/2017
8743	p(12103)#/2-128	55994	Robert Price	05/2017
8745	2^186003-174337	55993	Gary Barnes	09/2009
8744	(2^186010+78557)/123	55993	Lelio R Paula	05/2012
8746	20^43037-93	55993	Lelio R Paula	02/2013
8747	16375^2626+2626^16375	55991	Hans Havermann	03/2016
8748	15631^3816+3816^15631	55985	Hans Havermann	03/2016
8749	21^42335-2	55977	Lelio R Paula	08/2013
8750	Phi(64736,139)	55959	Enzo Doria	07/2012

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PRP Records

Probable Primes Top 10000

(212140 PRPs in the top)