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 ?
8751	2*10^57410+9^57410	57411	Mike Oakes	04/2011
8752	2^190704-1595	57408	Lelio R Paula	05/2011
8753	11^55121-1740	57403	Enzo Doria	11/2012
8754	2^190644-185	57390	Lelio R Paula	04/2011
8755	41182!3-3^41182	57389	Robert Price	08/2015
8756	2^190629-112255	57386	Enzo Doria	06/2014
8757	(2*10^57384-71)/3	57384	Robert Price	01/2017
8758	2*6^73735+5^73735	57378	Mike Oakes	11/2009
8759	2^190605+59	57378	Lelio R Paula	04/2011
8760	6^73727-7	57371	Lelio R Paula	10/2012
8761	2^190561-112225	57365	Enzo Doria	06/2014
8762	10^57358+170899	57359	Patrick De Geest	06/2016
8763	10^57358-8001	57358	Robert Price	03/2016
8764	18^45687-11	57350	Lelio R Paula	02/2013
8765	11^55069-210	57349	Enzo Doria	07/2012
8766	11^55068-12	57348	Lelio R Paula	02/2013
8767	19^44839+54	57339	Lelio R Paula	02/2013
8769	(7*2^190468-1)/8511	57334	Lelio R Paula	01/2014
8768	(23*10^57333-59)/9	57334	Robert Price	03/2017
8770	2^190455-1155*190455	57333	Henri Lifchitz	02/2005
8771	65^31620+28	57325	Lelio R Paula	01/2016
8772	2^190403+16095	57318	Lelio R Paula	05/2011
8773	(19*10^57316+119)/3	57317	Robert Price	02/2017
8774	(21*2^190393+1)/211	57314	Lelio R Paula	07/2012
8776	2^190392-112025	57314	Enzo Doria	05/2014
8775	13173^13912-13912^13173	57314	Norbert Schneider	08/2018
8777	(24737*2^190234+1)/9	57270	Lelio R Paula	05/2014
8778	(7*2^190230+1)/23	57265	Lelio R Paula	07/2012
8779	(10223*2^190197+1)/3211	57256	Lelio R Paula	05/2014
8780	18^45590-97	57228	Lelio R Paula	02/2013
8781	(3*2^190105-1)/19205	57224	Lelio R Paula	01/2014
8782	(16*10^57219-31)/3	57220	Robert Price	03/2016
8783	(2^190074+47)/51	57217	Lelio R Paula	02/2012
8784	3^119894-140	57204	Lelio R Paula	10/2012
8786	(37^36473-1)/36	57196	Robert Price	03/2012
8785	2^190000-2163	57196	Yves Minet	08/2013
8787	2^189987-2798107	57192	Enzo Doria	04/2016
8788	2^189935-112117	57177	Enzo Doria	05/2014
8789	2^189909-112231	57169	Enzo Doria	06/2014
8790	132049#+149053	57161	Makoto Morimoto	12/2015
8791	41032!3-27	57158	Robert Price	09/2014
8792	19^44694+22	57153	Lelio R Paula	02/2013
8793	12^52956-17	57150	Lelio R Paula	02/2013
8794	2^189823-967	57143	Yves Minet	01/2012
8795	(25*10^57138-61)/9	57139	Robert Price	02/2015
8796	5^81743-4^(81743+1)	57136	Robert Price	04/2016
8797	7^67593-54	57123	Lelio R Paula	10/2012
8798	7*3^119712+2	57118	Lelio R Paula	03/2014
8800	5^81700+16	57106	Lelio R Paula	10/2012
8799	2^189700+76561	57106	Enzo Doria	05/2016
8802	2^189671+131	57097	Lelio R Paula	04/2011
8801	4*6^73374+5	57097	Lelio R Paula	09/2014
8803	(67607*2^189651+1)/43727	57091	Lelio R Paula	05/2014
8804	(29*2^189619-1)/393	57080	Lelio R Paula	01/2014
8805	3^119587+80	57058	Lelio R Paula	10/2012
8806	2^189502-113453	57046	Enzo Doria	07/2014
8807	2^189455+153	57032	Lelio R Paula	04/2011
8808	24^41317-41317^24	57027	Norbert Schneider	07/2016
8809	2^189414-17	57020	Lelio R Paula	03/2011
8810	24^41311+23	57018	Norbert Schneider	12/2013
8811	norm(Mod(x,x^4+x^3-x+1)^207341-1)/2	56998	Paul Vanderveen	05/2018
8812	(4*10^56989-31)/9	56989	Erik Branger	05/2011
8813	11^54712-1620	56977	Enzo Doria	11/2012
8814	2^189237-112231	56967	Enzo Doria	06/2014
8815	17^46285-48	56952	Lelio R Paula	02/2013
8816	2^189188+75241	56952	Enzo Doria	04/2016
8817	2^189181+94395	56950	Henri Lifchitz	01/2005
8818	7001^14808-108	56940	Enzo Doria	07/2012
8819	2^189147-112639	56939	Enzo Doria	06/2014
8820	(19*10^56933-43)/3	56934	Robert Price	10/2017
8821	2^189110-3	56928	M. Frind & P. Underwood	11/2002
8822	2^189069+12909	56916	Lelio R Paula	04/2011
8823	(13*10^56909+191)/3	56910	Robert Price	08/2017
8824	(35*10^56898-17)/9	56899	Serge Batalov	02/2009
8825	2^189011-5955	56898	Lelio R Paula	04/2011
8826	6^73119-5	56898	Lelio R Paula	10/2012
8827	13^51076-90	56896	Lelio R Paula	02/2013
8828	2^188997+56897	56894	Yves Minet	02/2010
8829	5^81388-13766	56888	Enzo Doria	02/2013
8830	(104^28201+1)/105	56881	Richard Fischer	04/2018
8831	(156^25933+1)/157	56873	Eric Chen	12/2017
8832	20^43713-6403	56872	Enzo Doria	03/2013
8833	(71*10^56858-287)/9	56859	Robert Price	05/2017
8834	2^188857-254233	56852	Gary Barnes	09/2009
8835	15^48338-88	56850	Lelio R Paula	02/2013
8836	10^56849+136437	56850	Patrick De Geest	07/2017
8837	10^56849-701	56849	Robert Price	06/2017
8838	(2^188788+78557)/3	56831	Lelio R Paula	05/2012
8839	2^188771+16095	56826	Lelio R Paula	04/2011
8840	7*2^188742-9	56818	Lelio R Paula	03/2014
8841	12^52646-65	56815	Lelio R Paula	02/2013
8842	5003^15358-158	56813	Enzo Doria	07/2012
8843	2^188713+577294575	56809	Lelio R Paula	03/2013
8844	2^188693-112099	56803	Enzo Doria	05/2014
8845	(7^67211+4^67211)/11	56799	Robert Price	10/2012
8846	2^188678-94395	56798	Lelio R Paula	09/2011
8847	20^43651-8503	56792	Enzo Doria	03/2013
8849	2^188657-2371	56792	Yves Minet	10/2013
8848	152^26029-151^26029	56792	Eric Chen	04/2018
8850	(14^49549+5^49549)/19	56789	Robert Price	05/2013
8851	(45^34351-1)/44	56788	Robert Price	05/2014
8852	7*10^56785-23	56786	Robert Price	04/2016
8853	(10^56781-31)/3	56781	Serge Batalov	12/2014
8854	7*10^56779+3	56780	Erik Branger	11/2009
8855	10^56765+259179	56766	Patrick De Geest	09/2013
8856	10^56765-249497	56765	Patrick De Geest	09/2013
8857	t(188706)	56764	Robert Price	04/2015
8858	2^188551-904327	56760	Paul Bourdelais	11/2012
8860	(64*10^56756+17)/9	56757	Robert Price	09/2015
8859	131101#+146291	56757	Makoto Morimoto	02/2016
8861	2^188539-112519	56756	Enzo Doria	06/2014
8862	6^72927+101	56749	Lelio R Paula	10/2012
8863	20^43617-1603	56748	Enzo Doria	03/2013
8864	(3^118892-8)/91358929	56718	Lelio R Paula	03/2012
8865	13339^13748-13748^13339	56713	Norbert Schneider	09/2018
8866	(509203*2^188338-1)/3	56701	Lelio R Paula	03/2015
8867	20^43567-5623	56682	Enzo Doria	03/2013
8868	2^188234-113183	56665	Enzo Doria	07/2014
8869	(139^26437+1)/140	56653	Richard Fischer	03/2018
8870	(7*2^188215-1)/1497315125	56651	Lelio R Paula	01/2014
8871	(1017*2^188171-1)/35	56647	Lelio R Paula	03/2015
8872	(34*10^56647-7)/9/37/263	56644	Makoto Morimoto	04/2016
8873	(2^188176-1017)/453814543	56638	Lelio R Paula	02/2012
8874	33*10^56634+7	56636	Robert Price	07/2016
8875	(F(31)^9241-F(30)^9241)/F(29)	56634	Wayne Halsdorf	08/2010
8876	14^49413+33	56634	Lelio R Paula	02/2013
8877	3^118680+110	56625	Lelio R Paula	10/2012
8878	(13*10^56624+161)/3	56625	Robert Price	04/2017
8879	(3^118676-2)/7516653263	56613	Lelio R Paula	03/2012
8880	(13*2^188062+1)/17	56613	Lelio R Paula	07/2012
8881	2^188056-1313	56611	Yves Minet	08/2012
8882	20^43510-5583	56608	Enzo Doria	03/2013
8883	2^188032+12285	56604	Lelio R Paula	03/2011
8884	(19*10^56597-43)/3	56598	Robert Price	10/2017
8885	(265*10^56588+17)/3	56590	Robert Price	05/2016
8886	2^187959+5775	56582	Lelio R Paula	03/2011
8887	(5*2^187959+1)/53	56581	Lelio R Paula	07/2012
8888	3*10^56575-13	56576	Robert Price	11/2017
8889	(11*2^187889-1)/351	56559	Lelio R Paula	01/2014
8890	(100049^11311+1)/100050	56553	Faysal YAtim	09/2007
8891	(19*10^56544-1)/9	56545	Serge Batalov	03/2009
8892	20^43447-8923	56526	Enzo Doria	03/2013
8893	2^187743-112177	56517	Enzo Doria	06/2014
8894	(F(5879)^47-F(5878)^47)/F(5877)	56502	Wayne Halsdorf	08/2010
8895	5^80831-22	56499	Lelio R Paula	10/2012
8896	5^80828-13166	56497	Enzo Doria	02/2013
8897	7*2^187590-5	56472	Lelio R Paula	03/2014
8898	2^187555+75473	56460	Enzo Doria	04/2016
8899	2^187541-283	56456	Yves Minet	01/2012
8901	(55*10^56453-1)/9	56454	Serge Batalov	03/2009
8900	12933^13730-13730^12933	56454	Norbert Schneider	09/2018
8902	2^187506-1451	56445	Yves Minet	08/2012
8903	189^24794-2	56443	Lelio R Paula	10/2017
8904	13600^13653-13653^13600	56436	Norbert Schneider	08/2018
8905	6^72522+143	56434	Lelio R Paula	10/2012
8906	(15185*2^187452-1)/949	56430	Lelio R Paula	03/2015
8907	2^187390+79	56411	Lelio R Paula	03/2011
8908	2^187386+12909	56409	Lelio R Paula	03/2011
8909	2^187382+613	56408	Jason Earls	04/2008
8910	(34*10^56392-7)/9/37/883/23887	56384	Makoto Morimoto	04/2016
8911	20^43337-9	56383	Lelio R Paula	02/2013
8912	(26*10^56371-173)/3	56372	Robert Price	10/2017
8913	(F(1008)^269-F(1007)^269)/F(1006)	56364	Wayne Halsdorf	08/2010
8914	2^187230+427	56362	Henri Lifchitz	01/2005
8915	11^54121-9480	56362	Enzo Doria	02/2013
8916	10758^13979-13979^10758	56360	Norbert Schneider	09/2018
8917	10635^13996-13996^10635	56359	Norbert Schneider	09/2018
8918	(21*2^187202-1)/43	56354	Lelio R Paula	01/2014
8919	2^187173-91	56345	Lelio R Paula	03/2011
8920	(23*2^187174-1)/20719883	56340	Lelio R Paula	01/2014
8921	2^187125-2833	56331	Yves Minet	09/2014
8922	9*7^66655-4	56331	Lelio R Paula	09/2014
8924	18^44874-97	56330	Lelio R Paula	02/2013
8923	13304^13659-13659^13304	56330	Norbert Schneider	08/2018
8925	60*79^29679+19	56322	Serge Batalov	03/2016
8926	5^80571+56	56317	Lelio R Paula	10/2012
8927	5^80551-22	56303	Lelio R Paula	10/2012
8928	(76*10^56281+41)/9	56282	Robert Price	10/2015
8929	(88*10^56271-43)/9	56272	Robert Price	11/2015
8930	(5*10^56256-119)/3	56257	Robert Price	04/2016
8931	1508^17691+17691^1508	56230	Serge Batalov	05/2014
8932	3^117844-58	56226	Lelio R Paula	10/2012
8933	(19*10^56224+737)/9	56225	Robert Price	10/2017
8934	95^28427+2	56221	Lelio R Paula	05/2013
8935	2^186713+76817	56207	Enzo Doria	05/2016
8936	16534^2505+2505^16534	56196	Hans Havermann	06/2016
8937	14428^7849+7849^14428	56195	Hans Havermann	06/2016
8938	2*10^56194-51	56195	Robert Price	11/2017
8939	14898^5909+5909^14898	56189	Hans Havermann	06/2016
8940	18^44758+95	56184	Lelio R Paula	02/2013
8941	2^186555-741	56159	Lelio R Paula	05/2011
8942	(4*10^56156+173)/3	56157	Robert Price	01/2017
8943	(3^117708+7)/447896	56156	Lelio R Paula	03/2012
8944	15711^3752+3752^15711	56156	Hans Havermann	06/2016
8945	(23*2^186549-1)/2429025	56152	Lelio R Paula	01/2014
8946	387^21694+21694^387	56138	Norbert Schneider	08/2014
8947	2^186422+17239	56119	Yves Minet	01/2010
8948	2^186418+4242429	56118	Jason Earls	10/2008
8949	136^26300+135	56113	Norbert Schneider	04/2015
8950	5*2^186392+9	56111	Lelio R Paula	03/2014
8951	14345^8152+8152^14345	56108	Hans Havermann	07/2016
8952	(5*2^186351-1)/39	56097	Lelio R Paula	01/2014
8953	2^186319-541237	56088	Paul Bourdelais	11/2012
8954	2*10^56083-43	56084	Robert Price	07/2017
8955	(16*10^56082-61)/9	56083	Serge Batalov	05/2009
8956	(14*10^56080-143)/3	56081	Robert Price	01/2017
8957	(265*10^56076+17)/3	56078	Robert Price	05/2016
8958	7^66346-50	56069	Lelio R Paula	10/2012
8959	20^43094-33	56067	Lelio R Paula	02/2013
8960	20^43090-1383	56062	Enzo Doria	03/2013
8961	3^117482+2660	56054	Lelio R Paula	10/2012
8962	(22699*2^186193+1)/111	56052	Lelio R Paula	05/2014
8963	(68*10^56042+13)/9	56043	Ray Chandler	09/2010
8964	3*6^71992+5^71992	56022	Mike Oakes	03/2010
8965	13691^12352+12352^13691	56020	Hans Havermann	07/2016
8966	(2^186095+7)/75	56019	Lelio R Paula	02/2012
8967	247^23412+23412^247	56018	Norbert Schneider	08/2014
8968	1839^17156+17156^1839	56008	Serge Batalov	05/2014
8969	13736^11949+11949^13736	56007	Hans Havermann	04/2016
8970	(5*2^186036-1)/11	56003	Lelio R Paula	01/2014
8971	(299*10^55998-17)/3	56000	Robert Price	01/2017
8972	p(12103)#/2-128	55994	Robert Price	05/2017
8974	2^186003-174337	55993	Gary Barnes	09/2009
8975	(2^186010+78557)/123	55993	Lelio R Paula	05/2012
8973	20^43037-93	55993	Lelio R Paula	02/2013
8976	16375^2626+2626^16375	55991	Hans Havermann	03/2016
8977	15631^3816+3816^15631	55985	Hans Havermann	03/2016
8978	21^42335-2	55977	Lelio R Paula	08/2013
8979	Phi(64736,139)	55959	Enzo Doria	07/2012
8980	15215^4762+4762^15215	55958	Hans Havermann	03/2016
8981	19317^788+788^19317	55953	Anatoly F. Selevich	12/2006
8982	13582^13165+13165^13582	55950	Hans Havermann	08/2016
8983	(78557*2^185842+1)/189	55947	Lelio R Paula	06/2014
8984	11867^13730-13730^11867	55941	Norbert Schneider	09/2018
8985	15^47562-86	55938	Lelio R Paula	02/2013
8986	4*10^55932+91	55933	Robert Price	11/2017
8987	3^117222+4	55930	Lelio R Paula	03/2012
8988	24^40519-23^40519	55925	Robert Price	07/2012
8989	13636^12623+12623^13636	55924	Hans Havermann	07/2016
8990	2^185767-99	55922	Lelio R Paula	03/2011
8991	(19*2^185750-1)/15	55917	Lelio R Paula	01/2014
8993	15^47542-58	55914	Lelio R Paula	02/2013
8992	52211!4+2	55914	Robert Price	08/2017
8994	20^42973-5583	55910	Enzo Doria	03/2013
8995	4*10^55906+21	55907	Robert Price	08/2016
8996	2^185713-111	55906	Lelio R Paula	03/2011
8997	13^50174+88	55891	Lelio R Paula	01/2013
8998	14569^6846+6846^14569	55879	Hans Havermann	08/2016
8999	Pell-LucasQ(145969)/2	55874	Eric W. Weisstein	08/2006
9000	3^117087-80	55865	Lelio R Paula	10/2012

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PRP Records

Probable Primes Top 10000

(224660 PRPs in the top)