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	2^338143+60623	101792	Stefano Morozzi	03/2022
9752	2^338145-63609	101792	Stefano Morozzi	12/2022
9753	2^338141-77301	101791	Stefano Morozzi	12/2021
9754	2^338141+157145	101791	Stefano Morozzi	02/2022
9755	2^338140+84745	101791	Stefano Morozzi	03/2022
9756	2^338140+90073	101791	Stefano Morozzi	05/2022
9757	2^338142+96583	101791	Stefano Morozzi	11/2022
9758	2^338139-134719	101790	Stefano Morozzi	04/2022
9759	2^338138+95443	101790	Stefano Morozzi	11/2022
9760	2^338133+1445	101789	Stefano Morozzi	12/2021
9761	2^338133+172469	101789	Stefano Morozzi	11/2022
9762	2^338134+23235	101789	Stefano Morozzi	11/2022
9763	2^338132+105643	101788	Stefano Morozzi	01/2022
9764	2^338131+181871	101788	Stefano Morozzi	02/2022
9765	2^338132-184539	101788	Stefano Morozzi	04/2022
9766	2^338130+22383	101788	Stefano Morozzi	11/2022
9767	2^338132+170143	101788	Stefano Morozzi	11/2022
9768	2^338131-62599	101788	Stefano Morozzi	12/2022
9769	2^338128+128953	101787	Stefano Morozzi	01/2022
9770	2^338127+11021	101787	Stefano Morozzi	03/2022
9771	2^338127+192935	101787	Stefano Morozzi	09/2022
9772	2^338127+98621	101787	Stefano Morozzi	11/2022
9773	2^338128+98853	101787	Stefano Morozzi	02/2023
9774	2^338123-25959	101786	Stefano Morozzi	12/2021
9775	2^338124-180765	101786	Stefano Morozzi	02/2022
9776	2^338125-7129	101786	Stefano Morozzi	03/2022
9777	2^338125-40071	101786	Stefano Morozzi	01/2023
9781	2^338122-20117	101785	Enzo Doria	06/2013
9782	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
9778	2^338122+32799	101785	Stefano Morozzi	02/2022
9779	2^338120+166411	101785	Stefano Morozzi	06/2022
9780	2^338122+90705	101785	Stefano Morozzi	06/2022
9783	2^338117+103761	101784	Stefano Morozzi	01/2022
9784	2^338118+53817	101784	Stefano Morozzi	01/2022
9785	2^338116+82585	101784	Stefano Morozzi	02/2022
9786	2^338118+39483	101784	Stefano Morozzi	05/2022
9787	2^338119+96659	101784	Stefano Morozzi	11/2022
9788	2^338115+61083	101783	Stefano Morozzi	03/2022
9789	2^338114+173287	101783	Stefano Morozzi	11/2022
9790	2^338113-139681	101783	Stefano Morozzi	01/2023
9791	2^338110-175365	101782	Stefano Morozzi	12/2021
9792	2^338110-3963	101782	Stefano Morozzi	01/2022
9793	2^338112+155061	101782	Stefano Morozzi	01/2022
9794	2^338112+137335	101782	Stefano Morozzi	04/2022
9795	2^338111-85627	101782	Stefano Morozzi	06/2022
9796	2^338111-90145	101782	Stefano Morozzi	01/2023
9805	35^65917-7092	101781	Enzo Doria	03/2013
9797	2^338107-1221	101781	Stefano Morozzi	12/2021
9798	2^338109+108539	101781	Stefano Morozzi	03/2022
9799	2^338109-7261	101781	Stefano Morozzi	03/2022
9800	2^338109-131961	101781	Stefano Morozzi	03/2022
9801	2^338108+39585	101781	Stefano Morozzi	05/2022
9802	2^338109+38147	101781	Stefano Morozzi	05/2022
9803	2^338108+17301	101781	Stefano Morozzi	09/2022
9804	2^338108-65859	101781	Stefano Morozzi	01/2023
9806	2^338105+79599	101780	Stefano Morozzi	01/2022
9807	2^338103-180675	101780	Stefano Morozzi	02/2022
9808	2^338103+19499	101780	Stefano Morozzi	09/2022
9809	2^338103-165319	101780	Stefano Morozzi	01/2023
9810	2^338100-100389	101779	Stefano Morozzi	12/2021
9811	2^338100+27595	101779	Stefano Morozzi	12/2021
9812	2^338101+101139	101779	Stefano Morozzi	12/2021
9813	2^338101+134985	101779	Stefano Morozzi	03/2022
9814	2^338102+186135	101779	Stefano Morozzi	03/2022
9815	2^338100+36885	101779	Stefano Morozzi	04/2022
9816	2^338102-8151	101779	Stefano Morozzi	04/2022
9817	2^338100+90637	101779	Stefano Morozzi	06/2022
9818	2^338101+68505	101779	Stefano Morozzi	09/2022
9819	2^338100-42867	101779	Stefano Morozzi	02/2023
9820	2^338097+100229	101778	Stefano Morozzi	11/2021
9821	2^338097-25695	101778	Stefano Morozzi	12/2021
9822	2^338098-110043	101778	Stefano Morozzi	06/2022
9823	2^338099-191389	101778	Stefano Morozzi	01/2023
9824	2^338093-128403	101777	Stefano Morozzi	01/2022
9825	2^338093+33051	101777	Stefano Morozzi	02/2022
9826	2^338094+135555	101777	Stefano Morozzi	03/2022
9827	2^338095-32395	101777	Stefano Morozzi	03/2022
9828	2^338090-175353	101776	Stefano Morozzi	12/2021
9829	2^338090+33277	101776	Stefano Morozzi	02/2022
9830	2^338091-105601	101776	Stefano Morozzi	02/2022
9831	2^338091-32127	101776	Stefano Morozzi	03/2022
9832	2^338092+12873	101776	Stefano Morozzi	04/2022
9833	2^338091-58485	101776	Stefano Morozzi	04/2022
9834	2^338086+177643	101775	Stefano Morozzi	12/2021
9835	2^338089+82905	101775	Stefano Morozzi	02/2022
9836	2^338088+87565	101775	Stefano Morozzi	04/2022
9837	2^338088-166205	101775	Stefano Morozzi	01/2023
9838	2^338089-140053	101775	Stefano Morozzi	01/2023
9839	2^338087+124935	101775	Stefano Morozzi	02/2023
9840	2^338085-3301	101774	Stefano Morozzi	01/2022
9841	2^338084+108691	101774	Stefano Morozzi	03/2022
9842	2^338083+164369	101774	Stefano Morozzi	05/2022
9843	2^338080+107521	101773	Stefano Morozzi	02/2022
9844	2^338080-156917	101773	Stefano Morozzi	03/2022
9845	2^338081+199775	101773	Stefano Morozzi	02/2023
9846	2^338076+62311	101772	Stefano Morozzi	04/2022
9847	2^338079+161745	101772	Stefano Morozzi	04/2022
9848	2^338078-60075	101772	Stefano Morozzi	06/2022
9849	2^338079+167079	101772	Stefano Morozzi	09/2022
9850	2^338076+122535	101772	Stefano Morozzi	11/2022
9851	2^338077+95619	101772	Stefano Morozzi	11/2022
9852	2^338078+20539	101772	Stefano Morozzi	11/2022
9853	2^338076-36813	101772	Stefano Morozzi	12/2022
9854	2^338078-64911	101772	Stefano Morozzi	01/2023
9855	2^338073-77971	101771	Stefano Morozzi	01/2022
9856	2^338074+55579	101771	Stefano Morozzi	01/2022
9857	2^338073-81813	101771	Stefano Morozzi	03/2022
9858	2^338073+138645	101771	Stefano Morozzi	05/2022
9859	2^338075+148043	101771	Stefano Morozzi	11/2022
9860	2^338070-152607	101770	Stefano Morozzi	01/2022
9861	2^338070+138787	101770	Stefano Morozzi	05/2022
9862	2^338071+165249	101770	Stefano Morozzi	06/2022
9863	2^338070+70359	101770	Stefano Morozzi	11/2022
9864	2^338071+98573	101770	Stefano Morozzi	11/2022
9865	2^338069+79365	101769	Stefano Morozzi	01/2022
9866	2^338069+107571	101769	Stefano Morozzi	02/2022
9867	2^338068+73035	101769	Stefano Morozzi	11/2022
9868	2^338064+100087	101768	Stefano Morozzi	11/2021
9869	2^338064-83793	101768	Stefano Morozzi	04/2022
9870	2^338064+193701	101768	Stefano Morozzi	09/2022
9871	2^338065+199947	101768	Stefano Morozzi	02/2023
9872	2^338060-151047	101767	Stefano Morozzi	12/2021
9873	2^338060-130805	101767	Stefano Morozzi	02/2022
9874	2^338060-136593	101767	Stefano Morozzi	12/2022
9875	2^338062-15725	101767	Stefano Morozzi	01/2023
9876	2^338058-76415	101766	Stefano Morozzi	12/2021
9877	2^338057+83865	101766	Stefano Morozzi	03/2022
9878	2^338057+86997	101766	Stefano Morozzi	04/2022
9879	2^338058+188589	101766	Stefano Morozzi	05/2022
9880	2^338058+68089	101766	Stefano Morozzi	09/2022
9881	2^338059+121803	101766	Stefano Morozzi	11/2022
9882	2^338057-39021	101766	Stefano Morozzi	01/2023
9883	2^338056+50605	101765	Stefano Morozzi	11/2021
9884	2^338053+53231	101765	Stefano Morozzi	01/2022
9885	2^338054-180497	101765	Stefano Morozzi	02/2022
9886	2^338053+59891	101765	Stefano Morozzi	03/2022
9887	2^338056+33987	101765	Stefano Morozzi	03/2022
9888	2^338055-157779	101765	Stefano Morozzi	03/2022
9889	2^338056+90307	101765	Stefano Morozzi	06/2022
9890	2^338055+124443	101765	Stefano Morozzi	02/2023
9891	2^338052-55373	101764	Stefano Morozzi	02/2022
9892	2^338050-138281	101764	Stefano Morozzi	12/2022
9893	2^338050+148959	101764	Stefano Morozzi	02/2023
9894	2^338051-118159	101764	Stefano Morozzi	02/2023
9895	2^338048+31185	101763	Stefano Morozzi	01/2022
9896	2^338047+31935	101763	Stefano Morozzi	02/2022
9897	2^338047+108011	101763	Stefano Morozzi	02/2022
9898	2^338049+56777	101763	Stefano Morozzi	02/2022
9899	2^338049-7531	101763	Stefano Morozzi	03/2022
9900	2^338048-304019	101763	Harrison Mesh	06/2022
9901	2^338049+191291	101763	Stefano Morozzi	06/2022
9902	2^338047-187699	101763	Stefano Morozzi	12/2022
9903	2^338047-66405	101763	Stefano Morozzi	01/2023
9904	2^338049-192633	101763	Stefano Morozzi	02/2023
9905	2^338046-25841	101762	Stefano Morozzi	12/2021
9906	2^338046-2285	101762	Stefano Morozzi	12/2021
9907	2^338046-177851	101762	Stefano Morozzi	01/2022
9908	2^338043+84045	101762	Stefano Morozzi	03/2022
9909	2^338046-57573	101762	Stefano Morozzi	03/2022
9910	2^338044-8177	101762	Stefano Morozzi	04/2022
9911	2^338045-58443	101762	Stefano Morozzi	04/2022
9912	2^338044+193497	101762	Stefano Morozzi	09/2022
9913	2^338043+45701	101762	Stefano Morozzi	11/2022
9914	2^338044-114197	101762	Stefano Morozzi	01/2023
9915	2^338042+194973	101761	Stefano Morozzi	11/2022
9916	2^338040-164483	101761	Stefano Morozzi	01/2023
9917	2^338038-57887	101760	Stefano Morozzi	04/2022
9918	2^338037+139169	101760	Stefano Morozzi	05/2022
9919	2^338037+188595	101760	Stefano Morozzi	05/2022
9920	2^338038-187241	101760	Stefano Morozzi	12/2022
9921	2^338039+124035	101760	Stefano Morozzi	02/2023
9922	2^338037-42523	101760	Stefano Morozzi	02/2023
9923	2^338034+125653	101759	Stefano Morozzi	11/2021
9924	2^338034-25211	101759	Stefano Morozzi	12/2021
9925	2^338033-154099	101759	Stefano Morozzi	02/2022
9926	2^338034-31803	101759	Stefano Morozzi	03/2022
9927	2^338033+162311	101759	Stefano Morozzi	04/2022
9928	2^338033-83071	101759	Stefano Morozzi	04/2022
9929	2^338035-158095	101759	Stefano Morozzi	04/2022
9930	2^338036-34193	101759	Stefano Morozzi	04/2022
9931	2^338036+42873	101759	Stefano Morozzi	09/2022
9932	2^338036+93373	101759	Stefano Morozzi	09/2022
9933	2^338035+146129	101759	Stefano Morozzi	11/2022
9934	2^338036+23983	101759	Stefano Morozzi	11/2022
9935	2^338036+170433	101759	Stefano Morozzi	11/2022
9936	2^338031+79989	101758	Stefano Morozzi	01/2022
9937	2^338032+158073	101758	Stefano Morozzi	02/2022
9938	2^338030-54371	101758	Stefano Morozzi	02/2022
9939	2^338032-180747	101758	Stefano Morozzi	02/2022
9940	2^338029-27909	101757	Stefano Morozzi	01/2022
9941	2^338027+70475	101757	Stefano Morozzi	11/2022
9942	2^338028-38705	101757	Stefano Morozzi	12/2022
9943	2^338028-140459	101757	Stefano Morozzi	01/2023
9944	2^338024-128495	101756	Stefano Morozzi	01/2022
9945	2^338025+34785	101756	Stefano Morozzi	03/2022
9946	2^338025-181765	101756	Stefano Morozzi	03/2022
9947	2^338024+63765	101756	Stefano Morozzi	05/2022
9948	2^338023-160621	101756	Stefano Morozzi	06/2022
9949	2^338026+117553	101756	Stefano Morozzi	09/2022
9950	2^338020-52437	101755	Stefano Morozzi	12/2021
9951	2^338021+160241	101755	Stefano Morozzi	03/2022
9952	2^338022+185845	101755	Stefano Morozzi	03/2022
9953	2^338021+189587	101755	Stefano Morozzi	05/2022
9954	2^338021-85891	101755	Stefano Morozzi	06/2022
9955	2^338020-87797	101755	Stefano Morozzi	12/2022
9956	2^338018-102741	101754	Stefano Morozzi	01/2022
9957	2^338018+29937	101754	Stefano Morozzi	01/2022
9958	2^338017-29505	101754	Stefano Morozzi	02/2022
9959	2^338018-30873	101754	Stefano Morozzi	02/2022
9960	2^338018-157013	101754	Stefano Morozzi	03/2022
9961	2^338019+168929	101754	Stefano Morozzi	09/2022
9962	2^338017+172721	101754	Stefano Morozzi	11/2022
9963	2^338018-136131	101754	Stefano Morozzi	12/2022
9964	2^338016+50797	101753	Stefano Morozzi	11/2021
9965	2^338016+26707	101753	Stefano Morozzi	12/2021
9966	2^338014+104677	101753	Stefano Morozzi	01/2022
9967	2^338013+145091	101753	Stefano Morozzi	11/2022
9968	2^338016-16335	101753	Stefano Morozzi	01/2023
9971	2^338010-19833	101752	Enzo Doria	06/2013
9969	2^338011+28665	101752	Stefano Morozzi	01/2022
9970	2^338010+89505	101752	Stefano Morozzi	05/2022
9972	2^338007+58985	101751	Stefano Morozzi	03/2022
9973	2^338008+109741	101751	Stefano Morozzi	03/2022
9974	2^338009+9527	101751	Stefano Morozzi	03/2022
9975	2^338007+14511	101751	Stefano Morozzi	05/2022
9976	2^338008+67957	101751	Stefano Morozzi	09/2022
9977	2^338009-11935	101751	Stefano Morozzi	12/2022
9978	2^338007-14199	101751	Stefano Morozzi	01/2023
9979	2^338005-75829	101750	Stefano Morozzi	12/2021
9980	2^338006-125055	101750	Stefano Morozzi	12/2021
9981	2^338006+5013	101750	Stefano Morozzi	01/2022
9982	2^338003+40269	101750	Stefano Morozzi	06/2022
9983	2^338006+166495	101750	Stefano Morozzi	06/2022
9984	2^338003-188551	101750	Stefano Morozzi	12/2022
9985	2^338006-118041	101750	Stefano Morozzi	02/2023
9986	2^338000+25113	101749	Stefano Morozzi	12/2021
9988	3^213215-76	101730	Lelio R Paula	09/2016
9987	23907^17998+17998^23907	101730	Hans Havermann	01/2019
9989	10^101728+154953	101729	Patrick De Geest	02/2020
9992	2^337930+63	101728	Lelio R Paula	07/2011
9990	10^101728-987654321	101728	Robert Price	12/2019
9991	10^101728-60741	101728	Patrick De Geest	02/2020
9993	2^337920+1869661	101725	Enzo Doria	05/2016
9994	2^337922+100280245065	101725	Paul Bourdelais	10/2021
9995	24116^16509+16509^24116	101715	Hans Havermann	01/2019
9996	(2^337875+3174)/2	101711	Stefano Morozzi	09/2020
9997	2^337859-19645	101706	Enzo Doria	05/2013
9998	2^337754+1869169	101675	Enzo Doria	05/2016
9999	(710^(250830+1)-9*10^50830-7)/9	101661	Robert Price	10/2023
10000	3*10^101657-37	101658	Robert Price	07/2018

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Probable Primes Top 10000

(300674 PRPs in the top)