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	(24728^21751-1)/24727	95552	Serge Batalov	06/2022
9752	(49764^20341-1)/49763	95536	Serge Batalov	06/2022
9753	(36155^20959-1)/36154	95531	Serge Batalov	06/2022
9754	(7725^24571-1)/7724	95526	Serge Batalov	06/2022
9755	(20546^22147-1)/20545	95510	Serge Batalov	06/2022
9756	2^317251+465	95503	Lelio R Paula	03/2016
9757	19^74684+58	95503	Lelio R Paula	06/2016
9758	(2^317250-7)/339	95500	Lelio R Paula	07/2013
9759	5*10^95498-21	95499	Robert Price	12/2021
9760	(21615^22031-1)/21614	95495	Serge Batalov	06/2022
9761	6^122718-79	95494	Lelio R Paula	05/2016
9762	22168^20291+20291^22168	95485	Hans Havermann	10/2019
9763	(77427^19531-1)/77426	95481	Serge Batalov	06/2022
9764	(13026^23203-1)/13025	95472	Serge Batalov	06/2022
9765	2^317141-110491	95469	Enzo Doria	05/2014
9766	(2^317097+3014)/2	95456	Stefano Morozzi	09/2020
9767	2^317094+76309	95455	Enzo Doria	05/2016
9768	2^317085+95	95453	Lelio R Paula	11/2012
9769	(17*10^95451-377)/9	95452	Robert Price	11/2017
9770	2^317057-109551	95444	Enzo Doria	04/2014
9771	3^200026+28	95437	Lelio R Paula	05/2016
9772	2^317024+93	95434	Donovan Johnson	06/2008
9773	(86*10^95428-437)/9	95429	Robert Price	03/2021
9774	10^95427+192591	95428	Patrick De Geest	05/2021
9777	2^316999+1605	95427	Lelio R Paula	03/2016
9776	(2^317000+3210)/2	95427	Stefano Morozzi	09/2020
9775	10^95427-10001	95427	Robert Price	02/2021
9778	2^316995-110427	95426	Enzo Doria	05/2014
9779	(69841^19699-1)/69840	95420	Serge Batalov	06/2022
9780	(59242^19993-1)/59241	95415	Serge Batalov	06/2022
9782	22300^18987+18987^22300	95410	Hans Havermann	06/2020
9781	(9478^23993-1)/9477	95410	Serge Batalov	06/2022
9784	2^316937+177	95408	Lelio R Paula	11/2012
9783	4*10^95407+91	95408	Robert Price	11/2017
9785	(94085^19321-1)/(94085^139-1)	95403	Ryan Propper	11/2023
9786	2^316908+1915	95399	Lelio R Paula	03/2016
9787	2^316894+99	95395	Lelio R Paula	11/2012
9788	(2^316887+2546)/2	95393	Stefano Morozzi	09/2020
9789	2*10^95374-21	95375	Robert Price	09/2020
9790	6^122547+11	95361	Lelio R Paula	05/2016
9791	2^316771+82875	95358	Lelio R Paula	03/2016
9792	(15609^22741-1)/15608	95358	Serge Batalov	06/2022
9793	(2^316765+3102)/2	95356	Stefano Morozzi	09/2020
9794	(2267^28411-1)/2266	95329	Serge Batalov	06/2022
9795	(824^32693-1)/823	95328	Serge Batalov	06/2022
9796	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
9797	1*10^95326+57	95327	Robert Price	03/2011
9798	10^95326-393687	95326	Patrick De Geest	09/2013
9799	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
9800	2^316654-109481	95323	Enzo Doria	04/2014
9801	8*10^95316+51	95317	Robert Price	05/2017
9802	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
9803	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
9804	(71*10^95277-539)/9	95278	Robert Price	11/2017
9805	23422^11691+11691^23422	95278	Hans Havermann	10/2019
9806	19^74503-56	95271	Lelio R Paula	06/2016
9807	(5038^25733-1)/5037	95267	Serge Batalov	06/2022
9808	11^91475-4380	95262	Enzo Doria	01/2013
9809	(62*10^95251-611)/9	95252	Robert Price	05/2017
9810	(160090^18301-1)/160089	95240	Serge Batalov	06/2022
9811	(173205^18181-1)/173204	95238	Serge Batalov	06/2022
9812	(158710^18313-1)/158709	95234	Serge Batalov	06/2022
9813	(9979^23813-1)/9978	95227	Serge Batalov	06/2022
9814	(57376^20011-1)/57375	95223	Serge Batalov	06/2022
9815	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
9816	26541^3868+3868^26541	95216	Hans Havermann	07/2020
9817	(79*10^95214-43)/9	95215	Erik Branger	11/2013
9818	(7176^24691-1)/7175	95202	Anonymous	11/2020
9819	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
9820	5*2^316213+9	95191	Lelio R Paula	08/2014
9821	2*10^95188-91	95189	Robert Price	04/2020
9822	2^316205-1848163	95188	Enzo Doria	07/2015
9823	2^316185-2787913	95182	Enzo Doria	04/2016
9824	(2^316174+3538)/2	95178	Stefano Morozzi	09/2020
9825	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
9826	2^316140-5	95168	Henri Lifchitz	02/2006
9827	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
9828	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
9829	2^316069+76817	95147	Enzo Doria	05/2016
9830	(199*10^95134-7)/3	95136	Robert Price	02/2017
9831	2^316027-97305	95134	Lelio R Paula	03/2016
9832	2^316006-2798051	95128	Enzo Doria	04/2016
9833	24994^6397+6397^24994	95127	Hans Havermann	02/2020
9835	2^315921-2797603	95102	Enzo Doria	04/2016
9834	(2^315921+1314)/2	95102	Stefano Morozzi	02/2021
9836	2*10^95095+63	95096	Robert Price	10/2017
9837	2^315857+1299	95083	Lelio R Paula	03/2016
9838	(2^315858+2598)/2	95083	Stefano Morozzi	09/2020
9840	14^82955-43	95078	Lelio R Paula	06/2016
9839	(8*10^95078-269)/9	95078	Robert Price	09/2021
9841	(23*10^95074-101)/3	95075	Robert Price	04/2021
9842	2^315827-933075	95074	Paul Bourdelais	04/2021
9843	(2*10^95072-17)/3	95072	Robert Price	08/2014
9844	(286*10^95059-1)/3	95061	Robert Price	11/2020
9845	(2^315779+1610)/2	95059	Stefano Morozzi	09/2020
9846	2^315775-111546435	95058	Paul Bourdelais	10/2021
9847	21938^21513+21513^21938	95051	Hans Havermann	09/2020
9848	2^315727+65	95044	Lelio R Paula	11/2012
9849	2^315725+1885757	95043	Enzo Doria	03/2017
9850	10^(2*47509+1)-10^47509-1	95019	Robert Price	07/2023
9851	23277^12058+12058^23277	95000	Hans Havermann	09/2020
9852	1*10^94983+21	94984	Robert Price	03/2011
9853	10^94983-717	94983	Patrick De Geest	08/2013
9854	17^77187-82	94975	Lelio R Paula	07/2016
9855	3*10^94964+37	94965	Robert Price	10/2017
9856	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
9857	2^315423-110329	94952	Enzo Doria	05/2014
9858	2^315420+3493	94951	Riley Fisher	08/2023
9859	11^91169-7230	94943	Enzo Doria	02/2013
9860	7*10^94938+61	94939	Robert Price	02/2017
9861	2^315351+1025	94931	Lelio R Paula	03/2016
9862	2^315350-112253	94930	Enzo Doria	06/2014
9863	(2^315343+1766)/2	94928	Stefano Morozzi	09/2020
9864	(2^315343+3066)/2	94928	Stefano Morozzi	09/2020
9866	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
9865	2^315268+7	94906	Lelio R Paula	10/2012
9867	11^91133+62	94906	Lelio R Paula	05/2016
9868	(2^315264+1558)/2	94904	Stefano Morozzi	09/2020
9869	30^64244+41	94897	Lelio R Paula	08/2012
9870	(151*10^94885-7)/9	94887	Robert Price	07/2017
9871	fibonacci(453998)+2	94880	Jon Grantham	08/2023
9872	4^157583+22147	94875	Mike Oakes	01/2011
9873	(14*32^63026-190819)/31	94864	Eric Chen	04/2023
9874	2^315123+20513	94862	Enzo Doria	07/2023
9875	2^315098+123	94854	Lelio R Paula	11/2012
9876	3^198791-34	94848	Robert Price	11/2013
9877	3*2^315067+7	94846	Lelio R Paula	08/2014
9878	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
9879	22576^15875+15875^22576	94836	Hans Havermann	09/2020
9880	(16*10^94822+53)/3	94823	Robert Price	12/2016
9881	8*6^121849-7	94818	Lelio R Paula	10/2014
9882	(85*10^94802+473)/9	94803	Robert Price	03/2017
9883	21767^21852-21852^21767	94790	Norbert Schneider	06/2020
9884	(2*34^61893-647)/3	94788	Eric Chen	03/2023
9885	2^314870-108761	94786	Enzo Doria	03/2014
9886	5*2^314841-3	94778	Lelio R Paula	08/2014
9888	(2^314842+550)/2	94777	Stefano Morozzi	09/2020
9887	11738^23289-23289^11738	94777	Norbert Schneider	05/2022
9889	(2^314787+2630)/2	94761	Stefano Morozzi	09/2020
9890	6^121772+113	94758	Lelio R Paula	05/2016
9891	(19812^22201-1)/(19812^149-1)	94756	Ryan Propper	11/2023
9892	2^314751+221873	94750	Enzo Doria	09/2023
9893	(2^314740+3642)/2	94746	Stefano Morozzi	09/2020
9894	6^121756-16253	94745	Enzo Doria	02/2013
9895	(5*25^67773-2267)/6	94743	Eric Chen	04/2023
9896	2^314718-112793	94740	Enzo Doria	06/2014
9897	2^314697-1847293	94734	Enzo Doria	07/2015
9898	22836^14065+14065^22836	94727	Hans Havermann	09/2020
9899	2^314548-249	94689	Yves Minet	02/2012
9900	5^135469+42	94689	Lelio R Paula	04/2016
9901	2^314545+22697	94688	Enzo Doria	09/2023
9902	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
9903	25773^4712+4712^25773	94670	Hans Havermann	08/2020
9904	(2^314485+3614)/2	94670	Stefano Morozzi	09/2020
9905	(2*10^94604+547)/9	94604	Robert Price	10/2017
9906	(2^314164+2562)/2	94573	Stefano Morozzi	09/2020
9907	3*2^314152+5	94570	Lelio R Paula	08/2014
9908	2*6^121530-5	94570	Lelio R Paula	10/2014
9909	7*10^94563+87	94564	Robert Price	11/2016
9910	2^314114-109677	94558	Enzo Doria	04/2014
9911	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
9912	2^314059+76583	94542	Enzo Doria	05/2016
9913	2^314041-4035	94536	Lelio R Paula	03/2016
9914	(2^314028+3102)/2	94532	Stefano Morozzi	09/2020
9915	(807*33^62250-7)/32	94529	Eric Chen	05/2023
9916	(2^314012+618)/2	94527	Stefano Morozzi	09/2020
9917	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
9918	11^90760-4710	94517	Enzo Doria	01/2013
9919	21675^21796+21796^21675	94507	Norbert Schneider	04/2020
9920	2^313942+100280245065	94506	Paul Bourdelais	10/2021
9921	(457829*27^66017-385)/26	94499	Eric Chen	02/2023
9922	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
9923	94*10^94493-3	94495	Robert Price	11/2016
9924	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
9925	(2^313859+2706)/2	94481	Stefano Morozzi	09/2020
9926	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
9927	7^111792-32	94476	Lelio R Paula	04/2016
9928	(2^313800+822)/2	94463	Stefano Morozzi	01/2021
9929	9*10^94462-47	94463	Robert Price	11/2021
9930	11*10^94460+3	94462	Robert Price	07/2021
9931	(202*10^94441-1)/3	94443	Robert Price	05/2020
9932	11^90680-5850	94434	Enzo Doria	01/2013
9933	(752^32833-1)/751	94432	Michael Stocker	05/2020
9934	2^313675-110125	94426	Enzo Doria	04/2014
9935	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
9936	2^313609-112225	94406	Enzo Doria	06/2014
9937	2^313584+72901	94399	Enzo Doria	04/2016
9938	(2^313567+1310)/2	94393	Stefano Morozzi	02/2021
9939	(2^313562+730)/2	94392	Stefano Morozzi	09/2020
9940	2^313510-112865	94376	Enzo Doria	06/2014
9941	7*10^94373+87	94374	Robert Price	11/2016
9942	(9^98897+8^98897)/17	94371	Robert Price	12/2012
9943	2^313453-114703	94359	Enzo Doria	04/2015
9944	8*10^94357-51	94358	Robert Price	10/2017
9945	25903^4392+4392^25903	94356	Hans Havermann	09/2020
9946	31706^945+945^31706	94340	Hans Havermann	09/2020
9947	(379*10^94337-1)/9	94339	Robert Price	08/2017
9948	2^313344-313344+1	94326	Robert Price	10/2014
9949	(2^313313+3662)/2	94317	Stefano Morozzi	09/2020
9950	20^72481-49	94300	Lelio R Paula	05/2016
9951	(34*10^94293-259)/9	94294	Robert Price	12/2021
9952	44725!2+128	94289	Robert Price	03/2015
9953	4*10^94286+9	94287	Robert Price	05/2015
9954	17^76621+24	94279	Lelio R Paula	07/2016
9955	26274^3875+3875^26274	94279	Hans Havermann	09/2020
9956	4*10^94270-33	94271	Robert Price	04/2021
9957	2^313156-112859	94270	Enzo Doria	06/2014
9958	(49*10^94262-211)/9	94263	Robert Price	06/2022
9959	6^121130-59	94258	Lelio R Paula	05/2016
9960	3^197542+28	94252	Robert Price	11/2013
9961	(2^313076+3550)/2	94245	Stefano Morozzi	09/2020
9962	(81822^19321-1)/(81822^139-1)	94239	Ryan Propper	11/2023
9963	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
9964	2^313045-5955	94236	Lelio R Paula	03/2016
9965	22099^18358+18358^22099	94227	Hans Havermann	08/2020
9966	(9*33^62046+53831)/16	94218	Eric Chen	05/2023
9967	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
9968	2^312909-1865203	94195	Enzo Doria	03/2016
9969	25013^5830+5830^25013	94191	Hans Havermann	09/2020
9970	2^312848-149	94177	Lelio R Paula	11/2012
9971	(2^312819+3278)/2	94168	Stefano Morozzi	02/2021
9972	4^156403-77597	94164	Mike Oakes	04/2011
9973	18^75004-85	94151	Lelio R Paula	06/2016
9974	(19573*10^94146-7)/9	94150	Patrick De Geest	05/2023
9975	19^73622-48	94145	Lelio R Paula	06/2016
9976	(11^90397-3^90397)/8	94138	Robert Price	04/2011
9977	(3^197287+5)/16	94129	Lelio R Paula	04/2013
9978	(23*10^94123-29)/3	94124	Robert Price	03/2022
9979	24220^7691+7691^24220	94119	Hans Havermann	09/2020
9980	12^87212-37	94118	Lelio R Paula	06/2016
9981	11^90376+76	94117	Lelio R Paula	05/2016
9982	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
9983	(2^312622+534)/2	94109	Stefano Morozzi	09/2020
9984	(10^94096+191)/3	94096	Robert Price	11/2017
9985	23794^9005+9005^23794	94093	Hans Havermann	09/2020
9986	2^312562-112685	94091	Enzo Doria	06/2014
9987	137^44026-2	94072	Lelio R Paula	10/2017
9988	s(164441)	94052	Robert Price	05/2020
9989	2^312404-869688105	94043	Lelio R Paula	09/2016
9990	2^312387+2793533	94038	Enzo Doria	03/2016
9992	10^94016+91	94017	Robert Price	04/2011
9991	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
9993	10^94016-188963	94016	Patrick De Geest	08/2013
9994	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
9995	(401*10^94010+13)/9	94012	Robert Price	09/2021
9996	23866^8691+8691^23866	94010	Hans Havermann	08/2020
9997	6^120802+7661	94003	Mike Oakes	04/2011
9998	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
9999	(2^312245+702)/2	93995	Stefano Morozzi	09/2020
10000	(56*10^93993+493)/9	93994	Robert Price	10/2021

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Probable Primes Top 10000

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