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	8*10^98111-67	98112	Robert Price	10/2017
9752	(2^325902+1138)/2	98106	Stefano Morozzi	09/2020
9753	(215^42061-1)/214	98103	Serge Batalov	06/2022
9754	(6775^25609-1)/6774	98102	Serge Batalov	06/2022
9755	(6718^25633-1)/6717	98100	Serge Batalov	06/2022
9756	2^325866+15	98096	Lelio R Paula	12/2012
9757	22591^21952+21952^22591	98079	Hans Havermann	02/2020
9758	2^325765+1974305	98066	Enzo Doria	06/2016
9759	2^325733-58695	98056	Lelio R Paula	07/2016
9760	(7*10^98055-529)/9	98055	Robert Price	08/2021
9761	2^325717-3645	98051	Lelio R Paula	07/2016
9762	(2^325704+718)/2	98047	Stefano Morozzi	09/2020
9763	(15679^23371-1)/15678	98045	Serge Batalov	06/2022
9764	(23342^22441-1)/23341	98022	Serge Batalov	06/2022
9765	23968^12293+12293^23968	98021	Hans Havermann	11/2019
9767	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
9766	(128678^19321-1)/(128678^139-1)	98011	Ryan Propper	11/2023
9768	(7*10^98007-13)/3	98008	Robert Price	06/2016
9769	(2^325544+1110)/2	97999	Stefano Morozzi	09/2020
9770	2^325512-459959	97989	Enzo Doria	05/2015
9771	(2^325492+682)/2	97983	Stefano Morozzi	09/2020
9772	(3^205354-8)/17	97978	Lelio R Paula	09/2013
9773	2^325433+76817	97966	Enzo Doria	05/2016
9774	5*10^97963+81	97964	Robert Price	08/2017
9775	(9996^24649-1)/(9996^157-1)	97964	Ryan Propper	11/2023
9776	(13208^23773-1)/13207	97961	Serge Batalov	06/2022
9777	2^325390-109061	97953	Enzo Doria	04/2014
9778	(55*10^97940+323)/9	97941	Robert Price	10/2021
9779	13^87921+24	97940	Lelio R Paula	08/2016
9780	10^97930+188277	97931	Patrick De Geest	09/2022
9782	10^97930-7000001	97930	Robert Price	06/2021
9781	10^97930-66951	97930	Patrick De Geest	09/2022
9783	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
9784	(17968^23017-1)/17967	97922	Serge Batalov	06/2022
9785	(3337^27793-1)/3336	97922	Serge Batalov	06/2022
9787	22600^21499+21499^22600	97913	Hans Havermann	05/2020
9786	(18703^22921-1)/18702	97913	Serge Batalov	06/2022
9788	2^325215+12909	97900	Lelio R Paula	07/2016
9789	22619^21286+21286^22619	97898	Hans Havermann	04/2020
9790	(126852^19321-1)/(126852^139-1)	97892	Ryan Propper	11/2023
9791	(85*10^97876-49)/9	97877	Robert Price	12/2020
9792	7*10^97874-69	97875	Robert Price	01/2017
9793	5*10^97869-63	97870	Robert Price	04/2021
9794	(643*32^65022-23)/31	97870	Eric Chen	04/2023
9796	(17^79537+5^79537)/22	97865	Robert Price	06/2013
9795	15^83212+22	97865	Lelio R Paula	08/2016
9797	2^325087-109057	97861	Enzo Doria	04/2014
9798	2^325074+1870657	97858	Enzo Doria	05/2016
9800	2^325066-2111	97855	Yves Minet	08/2013
9799	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
9801	(8694^24841-1)/8693	97851	Serge Batalov	06/2022
9802	(21159^22621-1)/21158	97843	Serge Batalov	06/2022
9803	26660^4677+4677^26660	97842	Hans Havermann	12/2019
9804	18^77944-89	97841	Lelio R Paula	07/2016
9805	119^47136+118	97833	Norbert Schneider	09/2018
9806	6^125720-17663	97830	Enzo Doria	02/2013
9807	(73640^20101-1)/73639	97829	Serge Batalov	06/2022
9808	2^324972-2069	97827	Yves Minet	05/2013
9809	2^324958-4691	97823	Yves Minet	05/2019
9810	(8087^25033-1)/8086	97820	Serge Batalov	06/2022
9811	2^324944-2788319	97818	Enzo Doria	03/2016
9813	22845^19112+19112^22845	97807	Hans Havermann	10/2019
9812	(317^39107-1)/316	97807	Anonymous	04/2024
9814	(2^324898+1270)/2	97804	Stefano Morozzi	09/2020
9816	4*10^97799-9	97800	Erik Branger	11/2013
9815	2^324882+577294575	97800	Lelio R Paula	09/2016
9817	2^324863-1867921	97794	Enzo Doria	04/2016
9818	6^125662-18473	97785	Enzo Doria	03/2013
9819	12^90604+11	97779	Lelio R Paula	07/2016
9820	(29*10^97751+49)/3	97752	Robert Price	09/2021
9821	(37108^21391-1)/37107	97741	Serge Batalov	06/2022
9822	5^139830+24	97737	Lelio R Paula	04/2016
9823	(2^324672+1198)/2	97736	Stefano Morozzi	09/2020
9824	(101*10^97724+7)/9	97726	Robert Price	02/2022
9825	2^324612+1155	97718	Lelio R Paula	07/2016
9826	(2^324597+3542)/2	97714	Stefano Morozzi	09/2020
9827	19^76404-44	97702	Lelio R Paula	07/2016
9828	(5939^25889-1)/5938	97694	Serge Batalov	06/2022
9830	2^324505-2983	97686	Yves Minet	04/2011
9829	(7740^25121-1)/7739	97686	Serge Batalov	06/2022
9831	(144^45259+1)/145	97684	Paul Bourdelais	08/2019
9832	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
9833	(11234^24109-1)/11233	97651	Serge Batalov	06/2022
9834	6^125488-17843	97649	Enzo Doria	02/2013
9835	(2^324350+3198)/2	97639	Stefano Morozzi	09/2020
9836	(75638^20011-1)/75637	97624	Serge Batalov	06/2022
9837	7^115515-2	97622	Lelio R Paula	09/2013
9838	(15672^23269-1)/15671	97613	Serge Batalov	06/2022
9839	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
9840	6^125418-5	97595	Lelio R Paula	11/2014
9841	(2^324193+3522)/2	97592	Stefano Morozzi	09/2020
9842	(2422^28837-1)/2421	97587	Serge Batalov	06/2022
9843	(2^324172+666)/2	97586	Stefano Morozzi	09/2020
9844	2^324091+111546435	97562	Paul Bourdelais	10/2021
9845	2^324076+1155	97557	Lelio R Paula	07/2016
9846	(2^324074+9)/13	97555	Lelio R Paula	10/2013
9847	(11*10^97539-71)/3	97540	Robert Price	04/2022
9848	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
9849	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
9850	2^323946+73939	97518	Enzo Doria	04/2016
9851	2^323937+1866947	97515	Enzo Doria	03/2016
9852	(98339^19531-1)/98338	97508	Serge Batalov	06/2022
9854	6^125290-18533	97495	Enzo Doria	03/2013
9853	(2^323870+1650)/2	97495	Stefano Morozzi	09/2020
9855	2^323845+101	97488	Lelio R Paula	12/2012
9856	18^77662+65	97487	Lelio R Paula	07/2016
9857	22634^20265+20265^22634	97479	Hans Havermann	04/2020
9858	(5533^26041-1)/5532	97467	Serge Batalov	06/2022
9859	2^323772+76771	97466	Enzo Doria	05/2016
9860	2^323765-112213	97463	Enzo Doria	06/2014
9861	22730^19389+19389^22730	97457	Hans Havermann	02/2020
9862	2^323720-6555	97450	Lelio R Paula	07/2016
9863	2^323694-1860401	97442	Enzo Doria	03/2016
9864	20^74886+3	97429	Lelio R Paula	06/2016
9865	24476^9561+9561^24476	97427	Hans Havermann	01/2020
9866	(2^323623+1766)/2	97420	Stefano Morozzi	09/2020
9867	(3250^27739-1)/3249	97413	Serge Batalov	06/2022
9869	3*10^97399+73	97400	Robert Price	04/2016
9868	7^115252-50	97400	Lelio R Paula	07/2016
9870	(4715^26513-1)/4714	97392	Serge Batalov	06/2022
9871	2^323521+213317	97390	Enzo Doria	09/2023
9872	224737#+393581	97389	Nicolas PALAU	12/2016
9873	(119374^19321-1)/(119374^139-1)	97386	Ryan Propper	11/2023
9874	(2^323468+3186)/2	97374	Stefano Morozzi	09/2020
9875	(2^323456+538)/2	97370	Stefano Morozzi	09/2020
9876	23277^15236+15236^23277	97365	Hans Havermann	07/2020
9878	(26*10^97353+31)/3	97354	Robert Price	07/2016
9877	(2^323403+3510)/2	97354	Stefano Morozzi	09/2020
9879	23756^12519+12519^23756	97342	Hans Havermann	07/2020
9880	10^97335+271641	97336	Patrick De Geest	09/2022
9882	10^97335-4000001	97335	Robert Price	07/2021
9881	10^97335-98193	97335	Patrick De Geest	09/2022
9883	(637*10^97331+11)/9	97333	Robert Price	10/2021
9884	23991^11402+11402^23991	97332	Hans Havermann	07/2020
9885	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
9886	(38*10^97329+187)/9	97330	Robert Price	11/2017
9887	(31147^21661-1)/31146	97328	Serge Batalov	06/2022
9888	86455!4+8	97319	Robert Price	09/2019
9889	22591^20310+20310^22591	97316	Hans Havermann	06/2020
9890	2^323261-431173	97312	Harrison Mesh	06/2022
9891	(3996^27017-1)/3995	97302	Serge Batalov	06/2022
9892	25101^7520+7520^25101	97297	Hans Havermann	05/2020
9893	(233*10^97294+7)/3	97296	Robert Price	03/2022
9894	p(19982)#/2-1024	97293	Robert Price	09/2017
9895	(65*10^97288+277)/9	97289	Robert Price	08/2021
9896	6^125021-85	97286	Lelio R Paula	08/2016
9897	2^323164-47355	97283	Lelio R Paula	07/2016
9898	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
9899	2^323054-6555	97249	Lelio R Paula	07/2016
9900	22822^18247+18247^22822	97249	Hans Havermann	02/2020
9901	9*10^97247-29	97248	Robert Price	05/2017
9902	24382^9735+9735^24382	97244	Hans Havermann	02/2020
9903	(31*10^97242+41)/9	97243	Robert Price	04/2015
9904	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
9905	12^90098-41	97233	Lelio R Paula	07/2016
9906	2^322928-216929	97212	Enzo Doria	05/2014
9907	(16731^23017-1)/16730	97209	Serge Batalov	06/2022
9908	3*10^97205-61	97206	Robert Price	04/2021
9909	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
9910	(35*10^97194-341)/9	97195	Robert Price	08/2021
9911	(4872^26357-1)/4871	97194	Serge Batalov	06/2022
9912	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
9913	(796*10^97183-31)/9	97185	Robert Price	07/2022
9914	(2^322789+2214)/2	97169	Stefano Morozzi	09/2020
9915	2^322725+75761	97150	Enzo Doria	04/2016
9916	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
9917	(2175^29101-1)/2174	97121	Serge Batalov	06/2022
9918	22402^21639+21639^22402	97118	Hans Havermann	07/2020
9919	23399^14128+14128^23399	97108	Hans Havermann	06/2020
9920	(2892^28057-1)/2891	97108	Serge Batalov	06/2022
9921	(9578^24391-1)/9577	97104	Serge Batalov	06/2022
9922	(2^322525+2606)/2	97090	Stefano Morozzi	09/2020
9923	(9563^24391-1)/9562	97087	Serge Batalov	06/2022
9924	(41*10^97085+373)/9	97086	Robert Price	04/2017
9925	(2^322473+854)/2	97074	Stefano Morozzi	02/2021
9926	2^322413+77	97056	Lelio R Paula	12/2012
9927	2^322406+177	97054	Lelio R Paula	12/2012
9928	(349^38167-1)/348	97050	Serge Batalov	06/2022
9929	(14*10^97044+31)/9	97045	Robert Price	02/2015
9930	2^322302+255255	97023	Lelio R Paula	07/2016
9931	2^322286+212659	97018	Enzo Doria	09/2023
9932	(1302^31147-1)/1301	97008	Serge Batalov	06/2022
9933	2^322196-113093	96991	Enzo Doria	07/2014
9934	(2^322169+2690)/2	96983	Stefano Morozzi	09/2020
9935	(49*10^96980+221)/9	96981	Robert Price	02/2022
9936	9*10^96968-47	96969	Robert Price	11/2021
9937	(5895^25717-1)/5894	96962	Serge Batalov	06/2022
9938	(27473^21841-1)/27472	96946	Serge Batalov	06/2022
9939	23109^15668+15668^23109	96943	Hans Havermann	07/2020
9940	2^322000-1861469	96932	Enzo Doria	03/2016
9941	2^321971-112747	96923	Enzo Doria	06/2014
9942	23754^12023+12023^23754	96917	Hans Havermann	07/2020
9943	11^93062-92	96915	Lelio R Paula	06/2016
9944	(37871^21169-1)/37870	96914	Serge Batalov	06/2022
9945	(2^321922+2214)/2	96908	Stefano Morozzi	09/2020
9946	(2^321900+2086)/2	96902	Stefano Morozzi	09/2020
9947	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
9948	3^203051+34	96880	Lelio R Paula	05/2016
9949	2*10^96867-51	96868	Robert Price	11/2017
9950	(2^321779+2618)/2	96865	Stefano Morozzi	09/2020
9951	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
9952	2^321716-2786939	96847	Enzo Doria	03/2016
9953	22496^20181+20181^22496	96844	Hans Havermann	03/2020
9954	2^321701-113053	96842	Enzo Doria	07/2014
9955	2^321700-28635	96842	Lelio R Paula	06/2016
9956	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
9957	6*10^96835+13	96836	Robert Price	10/2021
9958	6^124433-124433	96828	Robert Price	01/2014
9959	2^321631+69	96821	Lelio R Paula	12/2012
9960	(27109^21841-1)/27108	96820	Serge Batalov	06/2022
9961	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
9962	(5052^26141-1)/5051	96809	Serge Batalov	06/2022
9963	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
9964	(59*10^96798+31)/9	96799	Robert Price	09/2015
9965	(2^321536+2062)/2	96792	Stefano Morozzi	09/2020
9966	223319#+231223	96790	Makoto Morimoto	02/2016
9967	2^321519-28635	96787	Lelio R Paula	06/2016
9968	2^321487-1867237	96778	Enzo Doria	03/2016
9969	2^321461-63	96770	Lelio R Paula	12/2012
9970	(16053^23011-1)/16052	96770	Serge Batalov	06/2022
9971	2^321439+123	96763	Lelio R Paula	12/2012
9972	2^321434+709	96762	Lelio R Paula	02/2013
9973	2^321419+22703	96757	Enzo Doria	09/2023
9974	(2^321415+554)/2	96756	Stefano Morozzi	09/2020
9975	14^84413+89	96749	Lelio R Paula	07/2016
9976	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
9977	13^86847+96	96743	Lelio R Paula	06/2016
9978	9*2^321336-7	96733	Lelio R Paula	08/2014
9979	(209*10^96722-17)/3	96724	Robert Price	05/2017
9980	(54163^20431-1)/54162	96710	Serge Batalov	06/2022
9981	2^321237-4615	96702	Yves Minet	05/2019
9982	(27273^21799-1)/27272	96691	Serge Batalov	06/2022
9983	2^321187-1159	96687	Yves Minet	11/2012
9984	2^321182-1850081	96686	Enzo Doria	08/2015
9986	23359^13768+13768^23359	96680	Hans Havermann	06/2020
9985	(65630^20071-1)/65629	96680	Serge Batalov	06/2022
9987	2^321116-112829	96666	Enzo Doria	06/2014
9988	2^321108-109499	96664	Enzo Doria	04/2014
9989	2^321098+2793859	96661	Enzo Doria	03/2016
9990	(2^321100+1170)/2	96661	Stefano Morozzi	09/2020
9991	2^321057+4097	96648	Lelio R Paula	06/2016
9992	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
9993	22743^17750+17750^22743	96640	Hans Havermann	04/2020
9994	22882^16679+16679^22882	96612	Hans Havermann	02/2020
9995	23452^13163+13163^23452	96608	Hans Havermann	02/2020
9996	(1042^32009-1)/1041	96596	Serge Batalov	06/2022
9997	(85*10^96594-373)/9	96595	Robert Price	05/2021
9998	(2^320863+666)/2	96590	Stefano Morozzi	09/2020
9999	p(19849)#/2-64	96581	Robert Price	04/2017
10000	2^320817+189	96576	Lelio R Paula	12/2012

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