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 ?
9751	16726^2645+2645^16726	57244	Hans Havermann	04/2019
9752	18^45590-97	57228	Lelio R Paula	02/2013
9753	(3*2^190105-1)/19205	57224	Lelio R Paula	01/2014
9754	(16*10^57219-31)/3	57220	Robert Price	03/2016
9755	(2^190074+47)/51	57217	Lelio R Paula	02/2012
9756	14899^6912+6912^14899	57207	Hans Havermann	04/2019
9757	3^119894-140	57204	Lelio R Paula	10/2012
9759	(37^36473-1)/36	57196	Robert Price	03/2012
9758	2^190000-2163	57196	Yves Minet	08/2013
9760	2^189987-2798107	57192	Enzo Doria	04/2016
9761	2^189935-112117	57177	Enzo Doria	05/2014
9762	2^189909-112231	57169	Enzo Doria	06/2014
9763	132049#+149053	57161	Makoto Morimoto	12/2015
9764	41032!3-27	57158	Robert Price	09/2014
9765	19^44694+22	57153	Lelio R Paula	02/2013
9766	16046^3645+3645^16046	57151	Hans Havermann	04/2019
9767	12^52956-17	57150	Lelio R Paula	02/2013
9768	2^189823-967	57143	Yves Minet	01/2012
9769	(25*10^57138-61)/9	57139	Robert Price	02/2015
9770	5^81743-4^(81743+1)	57136	Robert Price	04/2016
9771	14476^8843+8843^14476	57131	Hans Havermann	04/2019
9772	15327^5338+5338^15327	57130	Hans Havermann	04/2019
9773	7^67593-54	57123	Lelio R Paula	10/2012
9774	7*3^119712+2	57118	Lelio R Paula	03/2014
9775	5^81700+16	57106	Lelio R Paula	10/2012
9776	2^189700+76561	57106	Enzo Doria	05/2016
9778	2^189671+131	57097	Lelio R Paula	04/2011
9777	4*6^73374+5	57097	Lelio R Paula	09/2014
9779	(67607*2^189651+1)/43727	57091	Lelio R Paula	05/2014
9780	(29*2^189619-1)/393	57080	Lelio R Paula	01/2014
9781	3^119587+80	57058	Lelio R Paula	10/2012
9782	2^189502-113453	57046	Enzo Doria	07/2014
9783	2^189455+153	57032	Lelio R Paula	04/2011
9784	24^41317-41317^24	57027	Norbert Schneider	07/2016
9785	2^189414-17	57020	Lelio R Paula	03/2011
9786	24^41311+23	57018	Norbert Schneider	12/2013
9787	norm(Mod(x,x^4+x^3-x+1)^207341-1)/2	56998	Paul Vanderveen	05/2018
9788	14276^9819+9819^14276	56991	Hans Havermann	04/2019
9789	(4*10^56989-31)/9	56989	Erik Branger	05/2011
9790	11^54712-1620	56977	Enzo Doria	11/2012
9791	8102^14577-14577^8102	56976	Norbert Schneider	01/2019
9792	2^189237-112231	56967	Enzo Doria	06/2014
9794	17^46285-48	56952	Lelio R Paula	02/2013
9793	2^189188+75241	56952	Enzo Doria	04/2016
9795	2^189181+94395	56950	Henri Lifchitz	01/2005
9796	7001^14808-108	56940	Enzo Doria	07/2012
9797	2^189147-112639	56939	Enzo Doria	06/2014
9798	(19*10^56933-43)/3	56934	Robert Price	10/2017
9799	2^189110-3	56928	M. Frind & P. Underwood	11/2002
9800	2^189069+12909	56916	Lelio R Paula	04/2011
9801	(13*10^56909+191)/3	56910	Robert Price	08/2017
9802	(35*10^56898-17)/9	56899	Serge Batalov	02/2009
9803	2^189011-5955	56898	Lelio R Paula	04/2011
9804	6^73119-5	56898	Lelio R Paula	10/2012
9805	13^51076-90	56896	Lelio R Paula	02/2013
9806	2^188997+56897	56894	Yves Minet	02/2010
9807	5^81388-13766	56888	Enzo Doria	02/2013
9808	(104^28201+1)/105	56881	Richard Fischer	04/2018
9809	(156^25933+1)/157	56873	Eric Chen	12/2017
9810	20^43713-6403	56872	Enzo Doria	03/2013
9811	(71*10^56858-287)/9	56859	Robert Price	05/2017
9812	2^188857-254233	56852	Gary Barnes	09/2009
9814	15^48338-88	56850	Lelio R Paula	02/2013
9813	10^56849+136437	56850	Patrick De Geest	07/2017
9815	10^56849-701	56849	Robert Price	06/2017
9816	(2^188788+78557)/3	56831	Lelio R Paula	05/2012
9817	2^188771+16095	56826	Lelio R Paula	04/2011
9818	7*2^188742-9	56818	Lelio R Paula	03/2014
9819	12^52646-65	56815	Lelio R Paula	02/2013
9820	5003^15358-158	56813	Enzo Doria	07/2012
9821	2^188713+577294575	56809	Lelio R Paula	03/2013
9822	10060^14193-14193^10060	56809	Norbert Schneider	02/2019
9823	2^188693-112099	56803	Enzo Doria	05/2014
9824	(7^67211+4^67211)/11	56799	Robert Price	10/2012
9825	2^188678-94395	56798	Lelio R Paula	09/2011
9826	20^43651-8503	56792	Enzo Doria	03/2013
9828	2^188657-2371	56792	Yves Minet	10/2013
9827	152^26029-151^26029	56792	Eric Chen	04/2018
9829	(14^49549+5^49549)/19	56789	Robert Price	05/2013
9830	(45^34351-1)/44	56788	Robert Price	05/2014
9831	7*10^56785-23	56786	Robert Price	04/2016
9832	(10^56781-31)/3	56781	Serge Batalov	12/2014
9833	7*10^56779+3	56780	Erik Branger	11/2009
9834	((10^14197+1)((10^28394+10^14197)(10^14197-10^7099+3)-10^7099+2)-1)/3541/3407281	56778	Makoto Kamada	03/2019
9835	12858^13817-13817^12858	56777	Norbert Schneider	11/2018
9836	10^56765+259179	56766	Patrick De Geest	09/2013
9837	10^56765-249497	56765	Patrick De Geest	09/2013
9838	t(188706)	56764	Robert Price	04/2015
9839	2^188551-904327	56760	Paul Bourdelais	11/2012
9840	(64*10^56756+17)/9	56757	Robert Price	09/2015
9841	131101#+146291	56757	Makoto Morimoto	02/2016
9842	2^188539-112519	56756	Enzo Doria	06/2014
9843	6^72927+101	56749	Lelio R Paula	10/2012
9844	20^43617-1603	56748	Enzo Doria	03/2013
9845	(3^118892-8)/91358929	56718	Lelio R Paula	03/2012
9846	13339^13748-13748^13339	56713	Norbert Schneider	09/2018
9847	6693^14824-14824^6693	56712	Norbert Schneider	06/2019
9848	(509203*2^188338-1)/3	56701	Lelio R Paula	03/2015
9849	20^43567-5623	56682	Enzo Doria	03/2013
9850	2^188234-113183	56665	Enzo Doria	07/2014
9851	(139^26437+1)/140	56653	Richard Fischer	03/2018
9852	(7*2^188215-1)/1497315125	56651	Lelio R Paula	01/2014
9853	(1017*2^188171-1)/35	56647	Lelio R Paula	03/2015
9854	(34*10^56647-7)/9/37/263	56644	Makoto Morimoto	04/2016
9855	(2^188176-1017)/453814543	56638	Lelio R Paula	02/2012
9856	33*10^56634+7	56636	Robert Price	07/2016
9858	(F(31)^9241-F(30)^9241)/F(29)	56634	Wayne Halsdorf	08/2010
9857	14^49413+33	56634	Lelio R Paula	02/2013
9859	14240^9483+9483^14240	56632	Hans Havermann	04/2019
9860	15991^3478+3478^15991	56630	Hans Havermann	04/2019
9861	3^118680+110	56625	Lelio R Paula	10/2012
9862	(13*10^56624+161)/3	56625	Robert Price	04/2017
9863	(3^118676-2)/7516653263	56613	Lelio R Paula	03/2012
9864	(13*2^188062+1)/17	56613	Lelio R Paula	07/2012
9865	2^188056-1313	56611	Yves Minet	08/2012
9866	20^43510-5583	56608	Enzo Doria	03/2013
9867	2^188032+12285	56604	Lelio R Paula	03/2011
9868	(19*10^56597-43)/3	56598	Robert Price	10/2017
9869	(265*10^56588+17)/3	56590	Robert Price	05/2016
9870	2^187959+5775	56582	Lelio R Paula	03/2011
9871	(5*2^187959+1)/53	56581	Lelio R Paula	07/2012
9872	3*10^56575-13	56576	Robert Price	11/2017
9873	(11*2^187889-1)/351	56559	Lelio R Paula	01/2014
9874	(100049^11311+1)/100050	56553	Faysal YAtim	09/2007
9875	(19*10^56544-1)/9	56545	Serge Batalov	03/2009
9876	20^43447-8923	56526	Enzo Doria	03/2013
9877	10423^14066-14066^10423	56518	Norbert Schneider	11/2018
9878	2^187743-112177	56517	Enzo Doria	06/2014
9879	(F(5879)^47-F(5878)^47)/F(5877)	56502	Wayne Halsdorf	08/2010
9880	5^80831-22	56499	Lelio R Paula	10/2012
9881	5^80828-13166	56497	Enzo Doria	02/2013
9882	7*2^187590-5	56472	Lelio R Paula	03/2014
9883	16361^2826+2826^16361	56465	Hans Havermann	04/2019
9884	2^187555+75473	56460	Enzo Doria	04/2016
9885	2^187541-283	56456	Yves Minet	01/2012
9886	(55*10^56453-1)/9	56454	Serge Batalov	03/2009
9887	12933^13730-13730^12933	56454	Norbert Schneider	09/2018
9888	2^187506-1451	56445	Yves Minet	08/2012
9889	189^24794-2	56443	Lelio R Paula	10/2017
9890	13600^13653-13653^13600	56436	Norbert Schneider	08/2018
9891	6^72522+143	56434	Lelio R Paula	10/2012
9892	(15185*2^187452-1)/949	56430	Lelio R Paula	03/2015
9893	15992^3369+3369^15992	56412	Hans Havermann	03/2019
9894	2^187390+79	56411	Lelio R Paula	03/2011
9895	2^187386+12909	56409	Lelio R Paula	03/2011
9896	2^187382+613	56408	Jason Earls	04/2008
9897	13931^11188+11188^13931	56404	Hans Havermann	04/2019
9898	(34*10^56392-7)/9/37/883/23887	56384	Makoto Morimoto	04/2016
9899	20^43337-9	56383	Lelio R Paula	02/2013
9900	(26*10^56371-173)/3	56372	Robert Price	10/2017
9901	(F(1008)^269-F(1007)^269)/F(1006)	56364	Wayne Halsdorf	08/2010
9902	2^187230+427	56362	Henri Lifchitz	01/2005
9903	11^54121-9480	56362	Enzo Doria	02/2013
9904	10758^13979-13979^10758	56360	Norbert Schneider	09/2018
9905	10635^13996-13996^10635	56359	Norbert Schneider	09/2018
9906	(21*2^187202-1)/43	56354	Lelio R Paula	01/2014
9907	2^187173-91	56345	Lelio R Paula	03/2011
9908	(23*2^187174-1)/20719883	56340	Lelio R Paula	01/2014
9909	2^187125-2833	56331	Yves Minet	09/2014
9910	9*7^66655-4	56331	Lelio R Paula	09/2014
9911	18^44874-97	56330	Lelio R Paula	02/2013
9912	13304^13659-13659^13304	56330	Norbert Schneider	08/2018
9913	60*79^29679+19	56322	Serge Batalov	03/2016
9914	5^80571+56	56317	Lelio R Paula	10/2012
9915	5^80551-22	56303	Lelio R Paula	10/2012
9916	(76*10^56281+41)/9	56282	Robert Price	10/2015
9917	(88*10^56271-43)/9	56272	Robert Price	11/2015
9918	9191^14198-14198^9191	56272	Norbert Schneider	02/2019
9919	(5*10^56256-119)/3	56257	Robert Price	04/2016
9920	2^186840-4475	56245	Yves Minet	03/2019
9921	1508^17691+17691^1508	56230	Serge Batalov	05/2014
9922	3^117844-58	56226	Lelio R Paula	10/2012
9923	(19*10^56224+737)/9	56225	Robert Price	10/2017
9924	95^28427+2	56221	Lelio R Paula	05/2013
9925	2^186713+76817	56207	Enzo Doria	05/2016
9926	16534^2505+2505^16534	56196	Hans Havermann	06/2016
9927	14428^7849+7849^14428	56195	Hans Havermann	06/2016
9928	2*10^56194-51	56195	Robert Price	11/2017
9929	14898^5909+5909^14898	56189	Hans Havermann	06/2016
9930	18^44758+95	56184	Lelio R Paula	02/2013
9931	7478^14503-14503^7478	56182	Norbert Schneider	11/2018
9932	2^186555-741	56159	Lelio R Paula	05/2011
9933	(4*10^56156+173)/3	56157	Robert Price	01/2017
9935	(3^117708+7)/447896	56156	Lelio R Paula	03/2012
9934	15711^3752+3752^15711	56156	Hans Havermann	06/2016
9936	(23*2^186549-1)/2429025	56152	Lelio R Paula	01/2014
9937	387^21694+21694^387	56138	Norbert Schneider	08/2014
9938	6093^14828-14828^6093	56122	Norbert Schneider	06/2019
9939	2^186422+17239	56119	Yves Minet	01/2010
9940	2^186418+4242429	56118	Jason Earls	10/2008
9941	136^26300+135	56113	Norbert Schneider	04/2015
9942	5*2^186392+9	56111	Lelio R Paula	03/2014
9943	14345^8152+8152^14345	56108	Hans Havermann	07/2016
9944	(5*2^186351-1)/39	56097	Lelio R Paula	01/2014
9945	2^186319-541237	56088	Paul Bourdelais	11/2012
9946	2*10^56083-43	56084	Robert Price	07/2017
9947	(16*10^56082-61)/9	56083	Serge Batalov	05/2009
9948	(14*10^56080-143)/3	56081	Robert Price	01/2017
9949	(265*10^56076+17)/3	56078	Robert Price	05/2016
9950	7^66346-50	56069	Lelio R Paula	10/2012
9951	20^43094-33	56067	Lelio R Paula	02/2013
9952	20^43090-1383	56062	Enzo Doria	03/2013
9953	3^117482+2660	56054	Lelio R Paula	10/2012
9954	(22699*2^186193+1)/111	56052	Lelio R Paula	05/2014
9955	(68*10^56042+13)/9	56043	Ray Chandler	09/2010
9956	3*6^71992+5^71992	56022	Mike Oakes	03/2010
9957	13691^12352+12352^13691	56020	Hans Havermann	07/2016
9958	(2^186095+7)/75	56019	Lelio R Paula	02/2012
9959	247^23412+23412^247	56018	Norbert Schneider	08/2014
9960	1839^17156+17156^1839	56008	Serge Batalov	05/2014
9961	13736^11949+11949^13736	56007	Hans Havermann	04/2016
9962	(5*2^186036-1)/11	56003	Lelio R Paula	01/2014
9963	(299*10^55998-17)/3	56000	Robert Price	01/2017
9964	p(12103)#/2-128	55994	Robert Price	05/2017
9965	2^186003-174337	55993	Gary Barnes	09/2009
9966	(2^186010+78557)/123	55993	Lelio R Paula	05/2012
9967	20^43037-93	55993	Lelio R Paula	02/2013
9968	16375^2626+2626^16375	55991	Hans Havermann	03/2016
9969	11083^13842-13842^11083	55987	Norbert Schneider	11/2018
9970	15631^3816+3816^15631	55985	Hans Havermann	03/2016
9971	21^42335-2	55977	Lelio R Paula	08/2013
9972	Phi(64736,139)	55959	Enzo Doria	07/2012
9973	15215^4762+4762^15215	55958	Hans Havermann	03/2016
9974	19317^788+788^19317	55953	Anatoly F. Selevich	12/2006
9975	13582^13165+13165^13582	55950	Hans Havermann	08/2016
9976	(78557*2^185842+1)/189	55947	Lelio R Paula	06/2014
9977	11867^13730-13730^11867	55941	Norbert Schneider	09/2018
9978	15^47562-86	55938	Lelio R Paula	02/2013
9979	4*10^55932+91	55933	Robert Price	11/2017
9980	3^117222+4	55930	Lelio R Paula	03/2012
9981	24^40519-23^40519	55925	Robert Price	07/2012
9982	13636^12623+12623^13636	55924	Hans Havermann	07/2016
9983	2^185767-99	55922	Lelio R Paula	03/2011
9984	(19*2^185750-1)/15	55917	Lelio R Paula	01/2014
9986	15^47542-58	55914	Lelio R Paula	02/2013
9985	52211!4+2	55914	Robert Price	08/2017
9987	20^42973-5583	55910	Enzo Doria	03/2013
9988	4*10^55906+21	55907	Robert Price	08/2016
9989	2^185713-111	55906	Lelio R Paula	03/2011
9990	13^50174+88	55891	Lelio R Paula	01/2013
9991	14569^6846+6846^14569	55879	Hans Havermann	08/2016
9992	Pell-LucasQ(145969)/2	55874	Eric W. Weisstein	08/2006
9993	3^117087-80	55865	Lelio R Paula	10/2012
9994	8384^14237-14237^8384	55859	Norbert Schneider	03/2019
9995	(7*10^55851-43)/9	55851	Robert Price	10/2014
9996	2^185519-169	55847	Lelio R Paula	03/2011
9997	7^66074+10	55840	Lelio R Paula	10/2012
9998	(19*10^55833-49)/3	55834	Robert Price	02/2017
9999	(2*10^55834-59)/3	55834	Robert Price	05/2017
10000	2^185463-4237	55830	Yves Minet	08/2018

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PRP Records

Probable Primes Top 10000

(253466 PRPs in the top)