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 ?
8757	35^65917-7092	101781	Enzo Doria	03/2013
8751	2^338109-7261	101781	Stefano Morozzi	03/2022
8752	2^338109-131961	101781	Stefano Morozzi	03/2022
8753	2^338108+39585	101781	Stefano Morozzi	05/2022
8754	2^338109+38147	101781	Stefano Morozzi	05/2022
8755	2^338108+17301	101781	Stefano Morozzi	09/2022
8756	2^338108-65859	101781	Stefano Morozzi	01/2023
8758	2^338105+79599	101780	Stefano Morozzi	01/2022
8759	2^338103-180675	101780	Stefano Morozzi	02/2022
8760	2^338103+19499	101780	Stefano Morozzi	09/2022
8761	2^338103-165319	101780	Stefano Morozzi	01/2023
8762	2^338100-100389	101779	Stefano Morozzi	12/2021
8763	2^338100+27595	101779	Stefano Morozzi	12/2021
8764	2^338101+101139	101779	Stefano Morozzi	12/2021
8765	2^338101+134985	101779	Stefano Morozzi	03/2022
8766	2^338102+186135	101779	Stefano Morozzi	03/2022
8767	2^338100+36885	101779	Stefano Morozzi	04/2022
8768	2^338102-8151	101779	Stefano Morozzi	04/2022
8769	2^338100+90637	101779	Stefano Morozzi	06/2022
8770	2^338101+68505	101779	Stefano Morozzi	09/2022
8771	2^338100-42867	101779	Stefano Morozzi	02/2023
8772	2^338097+100229	101778	Stefano Morozzi	11/2021
8773	2^338097-25695	101778	Stefano Morozzi	12/2021
8774	2^338098-110043	101778	Stefano Morozzi	06/2022
8775	2^338099-191389	101778	Stefano Morozzi	01/2023
8776	2^338093-128403	101777	Stefano Morozzi	01/2022
8777	2^338093+33051	101777	Stefano Morozzi	02/2022
8778	2^338094+135555	101777	Stefano Morozzi	03/2022
8779	2^338095-32395	101777	Stefano Morozzi	03/2022
8780	2^338090-175353	101776	Stefano Morozzi	12/2021
8781	2^338090+33277	101776	Stefano Morozzi	02/2022
8782	2^338091-105601	101776	Stefano Morozzi	02/2022
8783	2^338091-32127	101776	Stefano Morozzi	03/2022
8784	2^338092+12873	101776	Stefano Morozzi	04/2022
8785	2^338091-58485	101776	Stefano Morozzi	04/2022
8786	2^338086+177643	101775	Stefano Morozzi	12/2021
8787	2^338089+82905	101775	Stefano Morozzi	02/2022
8788	2^338088+87565	101775	Stefano Morozzi	04/2022
8789	2^338088-166205	101775	Stefano Morozzi	01/2023
8790	2^338089-140053	101775	Stefano Morozzi	01/2023
8791	2^338087+124935	101775	Stefano Morozzi	02/2023
8792	2^338085-3301	101774	Stefano Morozzi	01/2022
8793	2^338084+108691	101774	Stefano Morozzi	03/2022
8794	2^338083+164369	101774	Stefano Morozzi	05/2022
8795	2^338080+107521	101773	Stefano Morozzi	02/2022
8796	2^338080-156917	101773	Stefano Morozzi	03/2022
8797	2^338081+199775	101773	Stefano Morozzi	02/2023
8798	2^338076+62311	101772	Stefano Morozzi	04/2022
8799	2^338079+161745	101772	Stefano Morozzi	04/2022
8800	2^338078-60075	101772	Stefano Morozzi	06/2022
8801	2^338079+167079	101772	Stefano Morozzi	09/2022
8802	2^338076+122535	101772	Stefano Morozzi	11/2022
8803	2^338077+95619	101772	Stefano Morozzi	11/2022
8804	2^338078+20539	101772	Stefano Morozzi	11/2022
8805	2^338076-36813	101772	Stefano Morozzi	12/2022
8806	2^338078-64911	101772	Stefano Morozzi	01/2023
8807	2^338073-77971	101771	Stefano Morozzi	01/2022
8808	2^338074+55579	101771	Stefano Morozzi	01/2022
8809	2^338073-81813	101771	Stefano Morozzi	03/2022
8810	2^338073+138645	101771	Stefano Morozzi	05/2022
8811	2^338075+148043	101771	Stefano Morozzi	11/2022
8812	2^338070-152607	101770	Stefano Morozzi	01/2022
8813	2^338070+138787	101770	Stefano Morozzi	05/2022
8814	2^338071+165249	101770	Stefano Morozzi	06/2022
8815	2^338070+70359	101770	Stefano Morozzi	11/2022
8816	2^338071+98573	101770	Stefano Morozzi	11/2022
8817	2^338069+79365	101769	Stefano Morozzi	01/2022
8818	2^338069+107571	101769	Stefano Morozzi	02/2022
8819	2^338068+73035	101769	Stefano Morozzi	11/2022
8820	2^338064+100087	101768	Stefano Morozzi	11/2021
8821	2^338064-83793	101768	Stefano Morozzi	04/2022
8822	2^338064+193701	101768	Stefano Morozzi	09/2022
8823	2^338065+199947	101768	Stefano Morozzi	02/2023
8824	2^338060-151047	101767	Stefano Morozzi	12/2021
8825	2^338060-130805	101767	Stefano Morozzi	02/2022
8826	2^338060-136593	101767	Stefano Morozzi	12/2022
8827	2^338062-15725	101767	Stefano Morozzi	01/2023
8828	2^338058-76415	101766	Stefano Morozzi	12/2021
8829	2^338057+83865	101766	Stefano Morozzi	03/2022
8830	2^338057+86997	101766	Stefano Morozzi	04/2022
8831	2^338058+188589	101766	Stefano Morozzi	05/2022
8832	2^338058+68089	101766	Stefano Morozzi	09/2022
8833	2^338059+121803	101766	Stefano Morozzi	11/2022
8834	2^338057-39021	101766	Stefano Morozzi	01/2023
8835	2^338056+50605	101765	Stefano Morozzi	11/2021
8836	2^338053+53231	101765	Stefano Morozzi	01/2022
8837	2^338054-180497	101765	Stefano Morozzi	02/2022
8838	2^338053+59891	101765	Stefano Morozzi	03/2022
8839	2^338056+33987	101765	Stefano Morozzi	03/2022
8840	2^338055-157779	101765	Stefano Morozzi	03/2022
8841	2^338056+90307	101765	Stefano Morozzi	06/2022
8842	2^338055+124443	101765	Stefano Morozzi	02/2023
8843	2^338052-55373	101764	Stefano Morozzi	02/2022
8844	2^338050-138281	101764	Stefano Morozzi	12/2022
8845	2^338050+148959	101764	Stefano Morozzi	02/2023
8846	2^338051-118159	101764	Stefano Morozzi	02/2023
8847	2^338048+31185	101763	Stefano Morozzi	01/2022
8848	2^338047+31935	101763	Stefano Morozzi	02/2022
8849	2^338047+108011	101763	Stefano Morozzi	02/2022
8850	2^338049+56777	101763	Stefano Morozzi	02/2022
8851	2^338049-7531	101763	Stefano Morozzi	03/2022
8852	2^338048-304019	101763	Harrison Mesh	06/2022
8853	2^338049+191291	101763	Stefano Morozzi	06/2022
8854	2^338047-187699	101763	Stefano Morozzi	12/2022
8855	2^338047-66405	101763	Stefano Morozzi	01/2023
8856	2^338049-192633	101763	Stefano Morozzi	02/2023
8857	2^338046-25841	101762	Stefano Morozzi	12/2021
8858	2^338046-2285	101762	Stefano Morozzi	12/2021
8859	2^338046-177851	101762	Stefano Morozzi	01/2022
8860	2^338043+84045	101762	Stefano Morozzi	03/2022
8861	2^338046-57573	101762	Stefano Morozzi	03/2022
8862	2^338044-8177	101762	Stefano Morozzi	04/2022
8863	2^338045-58443	101762	Stefano Morozzi	04/2022
8864	2^338044+193497	101762	Stefano Morozzi	09/2022
8865	2^338043+45701	101762	Stefano Morozzi	11/2022
8866	2^338044-114197	101762	Stefano Morozzi	01/2023
8867	2^338042+194973	101761	Stefano Morozzi	11/2022
8868	2^338040-164483	101761	Stefano Morozzi	01/2023
8869	2^338038-57887	101760	Stefano Morozzi	04/2022
8870	2^338037+139169	101760	Stefano Morozzi	05/2022
8871	2^338037+188595	101760	Stefano Morozzi	05/2022
8872	2^338038-187241	101760	Stefano Morozzi	12/2022
8873	2^338039+124035	101760	Stefano Morozzi	02/2023
8874	2^338037-42523	101760	Stefano Morozzi	02/2023
8875	2^338034+125653	101759	Stefano Morozzi	11/2021
8876	2^338034-25211	101759	Stefano Morozzi	12/2021
8877	2^338033-154099	101759	Stefano Morozzi	02/2022
8878	2^338034-31803	101759	Stefano Morozzi	03/2022
8879	2^338033+162311	101759	Stefano Morozzi	04/2022
8880	2^338033-83071	101759	Stefano Morozzi	04/2022
8881	2^338035-158095	101759	Stefano Morozzi	04/2022
8882	2^338036-34193	101759	Stefano Morozzi	04/2022
8883	2^338036+42873	101759	Stefano Morozzi	09/2022
8884	2^338036+93373	101759	Stefano Morozzi	09/2022
8885	2^338035+146129	101759	Stefano Morozzi	11/2022
8886	2^338036+23983	101759	Stefano Morozzi	11/2022
8887	2^338036+170433	101759	Stefano Morozzi	11/2022
8888	2^338031+79989	101758	Stefano Morozzi	01/2022
8889	2^338032+158073	101758	Stefano Morozzi	02/2022
8890	2^338030-54371	101758	Stefano Morozzi	02/2022
8891	2^338032-180747	101758	Stefano Morozzi	02/2022
8892	2^338029-27909	101757	Stefano Morozzi	01/2022
8893	2^338027+70475	101757	Stefano Morozzi	11/2022
8894	2^338028-38705	101757	Stefano Morozzi	12/2022
8895	2^338028-140459	101757	Stefano Morozzi	01/2023
8896	2^338024-128495	101756	Stefano Morozzi	01/2022
8897	2^338025+34785	101756	Stefano Morozzi	03/2022
8898	2^338025-181765	101756	Stefano Morozzi	03/2022
8899	2^338024+63765	101756	Stefano Morozzi	05/2022
8900	2^338023-160621	101756	Stefano Morozzi	06/2022
8901	2^338026+117553	101756	Stefano Morozzi	09/2022
8902	2^338020-52437	101755	Stefano Morozzi	12/2021
8903	2^338021+160241	101755	Stefano Morozzi	03/2022
8904	2^338022+185845	101755	Stefano Morozzi	03/2022
8905	2^338021+189587	101755	Stefano Morozzi	05/2022
8906	2^338021-85891	101755	Stefano Morozzi	06/2022
8907	2^338020-87797	101755	Stefano Morozzi	12/2022
8908	2^338018-102741	101754	Stefano Morozzi	01/2022
8909	2^338018+29937	101754	Stefano Morozzi	01/2022
8910	2^338017-29505	101754	Stefano Morozzi	02/2022
8911	2^338018-30873	101754	Stefano Morozzi	02/2022
8912	2^338018-157013	101754	Stefano Morozzi	03/2022
8913	2^338019+168929	101754	Stefano Morozzi	09/2022
8914	2^338017+172721	101754	Stefano Morozzi	11/2022
8915	2^338018-136131	101754	Stefano Morozzi	12/2022
8916	2^338016+50797	101753	Stefano Morozzi	11/2021
8917	2^338016+26707	101753	Stefano Morozzi	12/2021
8918	2^338014+104677	101753	Stefano Morozzi	01/2022
8919	2^338013+145091	101753	Stefano Morozzi	11/2022
8920	2^338016-16335	101753	Stefano Morozzi	01/2023
8923	2^338010-19833	101752	Enzo Doria	06/2013
8921	2^338011+28665	101752	Stefano Morozzi	01/2022
8922	2^338010+89505	101752	Stefano Morozzi	05/2022
8924	2^338007+58985	101751	Stefano Morozzi	03/2022
8925	2^338008+109741	101751	Stefano Morozzi	03/2022
8926	2^338009+9527	101751	Stefano Morozzi	03/2022
8927	2^338007+14511	101751	Stefano Morozzi	05/2022
8928	2^338008+67957	101751	Stefano Morozzi	09/2022
8929	2^338009-11935	101751	Stefano Morozzi	12/2022
8930	2^338007-14199	101751	Stefano Morozzi	01/2023
8931	2^338005-75829	101750	Stefano Morozzi	12/2021
8932	2^338006-125055	101750	Stefano Morozzi	12/2021
8933	2^338006+5013	101750	Stefano Morozzi	01/2022
8934	2^338003+40269	101750	Stefano Morozzi	06/2022
8935	2^338006+166495	101750	Stefano Morozzi	06/2022
8936	2^338003-188551	101750	Stefano Morozzi	12/2022
8937	2^338006-118041	101750	Stefano Morozzi	02/2023
8938	2^338000+25113	101749	Stefano Morozzi	12/2021
8940	3^213215-76	101730	Lelio R Paula	09/2016
8939	23907^17998+17998^23907	101730	Hans Havermann	01/2019
8941	10^101728+154953	101729	Patrick De Geest	02/2020
8944	2^337930+63	101728	Lelio R Paula	07/2011
8942	10^101728-987654321	101728	Robert Price	12/2019
8943	10^101728-60741	101728	Patrick De Geest	02/2020
8945	2^337920+1869661	101725	Enzo Doria	05/2016
8946	2^337922+100280245065	101725	Paul Bourdelais	10/2021
8947	24116^16509+16509^24116	101715	Hans Havermann	01/2019
8948	(2^337875+3174)/2	101711	Stefano Morozzi	09/2020
8949	2^337859-19645	101706	Enzo Doria	05/2013
8950	2^337754+1869169	101675	Enzo Doria	05/2016
8951	(710^(250830+1)-9*10^50830-7)/9	101661	Robert Price	10/2023
8952	3*10^101657-37	101658	Robert Price	07/2018
8953	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
8954	11^97605-24	101646	Lelio R Paula	10/2016
8955	(83*10^101636+133)/9	101637	Robert Price	08/2021
8956	(2^337624+3606)/2	101635	Stefano Morozzi	09/2020
8957	8^112539-112539	101633	Robert Price	01/2014
8958	(2^337575+1818)/2	101620	Stefano Morozzi	02/2021
8959	(11*10^101613+61)/9	101614	Tyler Busby	01/2023
8960	25694^9003+9003^25694	101605	Hans Havermann	12/2018
8961	2^337515-19869	101603	Enzo Doria	06/2013
8962	2^337473+719	101590	Lelio R Paula	08/2011
8963	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
8964	2^337452-108815	101584	Enzo Doria	03/2014
8965	2^337453+1185	101584	Lelio R Paula	09/2016
8966	(41*10^101583+319)/9	101584	Robert Price	06/2021
8967	2^337410-113561	101571	Enzo Doria	08/2014
8968	2^337387+855	101564	Lelio R Paula	09/2016
8969	2^337367-17295	101558	Lelio R Paula	09/2016
8970	2^337342-109035	101551	Enzo Doria	04/2014
8971	23703^19238+19238^23703	101548	Hans Havermann	12/2018
8972	(26*10^101537-167)/3	101538	Robert Price	10/2019
8973	2^337267-19	101528	Lelio R Paula	07/2011
8974	(2^337259+1766)/2	101525	Stefano Morozzi	09/2020
8975	(2^337257+2306)/2	101525	Stefano Morozzi	02/2021
8976	2^337222-340871	101514	Harrison Mesh	06/2022
8977	(2^337195+2646)/2	101506	Stefano Morozzi	09/2020
8978	2^337183-19989	101503	Enzo Doria	06/2013
8979	2^337149+72425	101492	Enzo Doria	04/2016
8980	24041^16642+16642^24041	101483	Hans Havermann	12/2018
8981	33982^969+969^33982	101482	Hans Havermann	12/2018
8982	2^337101-20241	101478	Enzo Doria	06/2013
8983	2^337035-20001	101458	Enzo Doria	06/2013
8984	(7*10^101456+89)/3	101457	Robert Price	08/2020
8985	2^337017-16995	101453	Lelio R Paula	09/2016
8986	(347^40448+1)/(347^512+1)	101451	Martin Hopf	12/2023
8987	(8677^25759-1)/8676	101445	Serge Batalov	06/2022
8988	2^336979-115315	101441	Enzo Doria	06/2015
8989	2^336970-20885	101439	Enzo Doria	06/2013
8990	2^336958+79	101435	Lelio R Paula	10/2009
8991	(1589^31687-1)/1588	101431	Serge Batalov	06/2022
8992	2^336942+169	101430	Lelio R Paula	10/2009
8993	(193929^19321-1)/(193929^139-1)	101428	Ryan Propper	11/2023
8994	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
8995	4*10^101415-89	101416	Robert Price	11/2018
8996	(14*10^101410-89)/3	101411	Robert Price	05/2020
8997	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
8998	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
8999	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
9000	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016

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Probable Primes Top 10000

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