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 ?
9752	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
9751	2^338831-63687	101999	Stefano Morozzi	12/2022
9760	2^338829-113239	101998	Enzo Doria	07/2014
9761	2^338828-113297	101998	Enzo Doria	07/2014
9753	2^338830+25017	101998	Stefano Morozzi	11/2021
9754	2^338831+321	101998	Stefano Morozzi	11/2021
9755	2^338827-26197	101998	Stefano Morozzi	12/2021
9756	2^338829+52727	101998	Stefano Morozzi	01/2022
9757	2^338827-55461	101998	Stefano Morozzi	02/2022
9758	2^338828-65859	101998	Stefano Morozzi	01/2023
9759	2^338829+99365	101998	Stefano Morozzi	02/2023
9762	2^338825-27453	101997	Stefano Morozzi	12/2021
9763	2^338824+89355	101997	Stefano Morozzi	05/2022
9764	2^338825-10995	101997	Stefano Morozzi	06/2022
9765	2^338824+149865	101997	Stefano Morozzi	02/2023
9766	2^338822+111175	101996	Stefano Morozzi	03/2022
9767	2^338822+187819	101996	Stefano Morozzi	04/2022
9768	2^338823+139545	101996	Stefano Morozzi	05/2022
9769	2^338823-184905	101996	Stefano Morozzi	06/2022
9770	2^338821-38919	101996	Stefano Morozzi	12/2022
9771	2^338820+41317	101995	Stefano Morozzi	06/2022
9772	2^338817+46019	101995	Stefano Morozzi	11/2022
9773	2^338820+148083	101995	Stefano Morozzi	11/2022
9774	2^338817-163251	101995	Stefano Morozzi	12/2022
9775	2^338819-63705	101995	Stefano Morozzi	12/2022
9776	2^338817-92509	101995	Stefano Morozzi	02/2023
9777	2^338815+151175	101994	Stefano Morozzi	12/2021
9778	2^338814-30011	101994	Stefano Morozzi	02/2022
9779	2^338814+12309	101994	Stefano Morozzi	04/2022
9780	2^338816-60647	101994	Stefano Morozzi	06/2022
9781	2^338816+171043	101994	Stefano Morozzi	11/2022
9782	2^338814-11513	101994	Stefano Morozzi	12/2022
9783	2^338811-126999	101993	Stefano Morozzi	12/2021
9784	2^338811+131621	101993	Stefano Morozzi	02/2022
9785	2^338812-107637	101993	Stefano Morozzi	03/2022
9786	2^338813+192725	101993	Stefano Morozzi	09/2022
9787	2^338812+94731	101993	Stefano Morozzi	11/2022
9788	2^338813+49205	101993	Stefano Morozzi	02/2023
9789	2^338809-152755	101992	Stefano Morozzi	01/2022
9790	2^338808+156531	101992	Stefano Morozzi	01/2022
9791	2^338808+7885	101992	Stefano Morozzi	02/2022
9792	2^338808-105797	101992	Stefano Morozzi	02/2022
9793	2^338807-35899	101992	Stefano Morozzi	06/2022
9794	2^338808-89175	101992	Stefano Morozzi	01/2023
9795	2^338808-91475	101992	Stefano Morozzi	01/2023
9796	2^338805+29879	101991	Stefano Morozzi	01/2022
9797	2^338805+157925	101991	Stefano Morozzi	02/2022
9798	2^338804-6809	101991	Stefano Morozzi	03/2022
9799	2^338806-157095	101991	Stefano Morozzi	03/2022
9800	2^338804-133173	101991	Stefano Morozzi	04/2022
9801	2^338805-115189	101991	Stefano Morozzi	01/2023
9802	2^338802+150403	101990	Stefano Morozzi	11/2021
9803	2^338801+154587	101990	Stefano Morozzi	01/2022
9804	2^338802-180603	101990	Stefano Morozzi	02/2022
9805	2^338803-31921	101990	Stefano Morozzi	03/2022
9806	2^338803-81735	101990	Stefano Morozzi	03/2022
9807	2^338803+195141	101990	Stefano Morozzi	11/2022
9808	2^338800+160141	101989	Stefano Morozzi	03/2022
9809	2^338797-82489	101989	Stefano Morozzi	03/2022
9814	2^338796+93	101988	Donovan Johnson	06/2008
9810	2^338795+455	101988	Stefano Morozzi	11/2021
9811	2^338795-102075	101988	Stefano Morozzi	12/2021
9812	2^338794-3483	101988	Stefano Morozzi	01/2022
9813	2^338796+179641	101988	Stefano Morozzi	01/2022
9815	2^338793-5155	101987	Stefano Morozzi	02/2022
9816	2^338793+111107	101987	Stefano Morozzi	03/2022
9817	2^338791+112083	101987	Stefano Morozzi	04/2022
9818	2^338792-85097	101987	Stefano Morozzi	06/2022
9819	(61*10^101986+47)/9	101987	Robert Price	07/2022
9820	2^338787+53309	101986	Stefano Morozzi	01/2022
9821	2^338787-153817	101986	Stefano Morozzi	01/2022
9822	2^338789+56229	101986	Stefano Morozzi	01/2022
9823	2^338790+6429	101986	Stefano Morozzi	01/2022
9824	2^338788+131701	101986	Stefano Morozzi	02/2022
9825	2^338785+104639	101985	Stefano Morozzi	01/2022
9826	2^338784+37591	101985	Stefano Morozzi	04/2022
9827	2^338786-9831	101985	Stefano Morozzi	04/2022
9828	2^338783+109065	101984	Stefano Morozzi	03/2022
9829	2^338779+86711	101983	Stefano Morozzi	04/2022
9830	2^338778+113589	101983	Stefano Morozzi	05/2022
9831	2^338775-30369	101982	Stefano Morozzi	02/2022
9832	2^338774+159135	101982	Stefano Morozzi	03/2022
9833	2^338776+113001	101982	Stefano Morozzi	04/2022
9834	2^338774+117039	101982	Stefano Morozzi	09/2022
9835	2^338775+167109	101982	Stefano Morozzi	09/2022
9836	2^338774+147595	101982	Stefano Morozzi	11/2022
9837	2^338772+42733	101981	Stefano Morozzi	09/2022
9838	2^338771-138805	101981	Stefano Morozzi	12/2022
9839	2^338768-181007	101980	Stefano Morozzi	02/2022
9840	2^338768+108807	101980	Stefano Morozzi	03/2022
9841	2^338767+169155	101980	Stefano Morozzi	09/2022
9842	2^338769+95369	101980	Stefano Morozzi	11/2022
9843	2^338769+195965	101980	Stefano Morozzi	11/2022
9844	2^338770-12725	101980	Stefano Morozzi	12/2022
9845	2^338768-140843	101980	Stefano Morozzi	01/2023
9846	2^338764+138013	101979	Stefano Morozzi	04/2022
9847	2^338765-160323	101979	Stefano Morozzi	06/2022
9848	2^338765+124545	101979	Stefano Morozzi	02/2023
9854	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
9849	2^338761+103671	101978	Stefano Morozzi	01/2022
9850	2^338763-7651	101978	Stefano Morozzi	03/2022
9851	2^338763+65591	101978	Stefano Morozzi	06/2022
9852	2^338762-111875	101978	Stefano Morozzi	12/2022
9853	2^338762-192237	101978	Stefano Morozzi	02/2023
9855	2^338757-5151	101977	Stefano Morozzi	02/2022
9856	2^338760-79037	101977	Stefano Morozzi	02/2022
9857	2^338757-82143	101977	Stefano Morozzi	03/2022
9858	2^338757+137007	101977	Stefano Morozzi	04/2022
9859	2^338755+158531	101976	Stefano Morozzi	03/2022
9860	2^338755+74081	101976	Stefano Morozzi	02/2023
9861	2^338752-153353	101975	Stefano Morozzi	01/2022
9862	2^338751+8001	101975	Stefano Morozzi	02/2022
9863	2^338752+32977	101975	Stefano Morozzi	02/2022
9864	2^338753-79233	101975	Stefano Morozzi	02/2022
9865	2^338752-88157	101975	Stefano Morozzi	12/2022
9866	2^338750-175625	101974	Stefano Morozzi	12/2021
9867	2^338747-2731	101974	Stefano Morozzi	12/2021
9868	2^338750-29597	101974	Stefano Morozzi	02/2022
9869	2^338748+35095	101974	Stefano Morozzi	03/2022
9870	2^338747+137475	101974	Stefano Morozzi	04/2022
9871	2^338747+162005	101974	Stefano Morozzi	04/2022
9872	2^338750+162237	101974	Stefano Morozzi	04/2022
9873	2^338747-184365	101974	Stefano Morozzi	04/2022
9874	2^338748+64341	101974	Stefano Morozzi	05/2022
9875	2^338750+24445	101974	Stefano Morozzi	02/2023
9876	2^338746+59577	101973	Stefano Morozzi	03/2022
9877	2^338746+62055	101973	Stefano Morozzi	04/2022
9878	2^338744+194065	101973	Stefano Morozzi	09/2022
9879	2^338741+25359	101972	Stefano Morozzi	12/2021
9880	2^338743+176981	101972	Stefano Morozzi	12/2021
9881	2^338741+183029	101972	Stefano Morozzi	02/2022
9882	2^338743-130309	101972	Stefano Morozzi	02/2022
9883	2^338741+86349	101972	Stefano Morozzi	04/2022
9884	2^338741+111561	101972	Stefano Morozzi	04/2022
9885	2^338743+172301	101972	Stefano Morozzi	11/2022
9886	2^338741-189969	101972	Stefano Morozzi	01/2023
9887	2^338739+76959	101971	Stefano Morozzi	12/2021
9888	2^338739-105957	101971	Stefano Morozzi	02/2022
9889	2^338739+190149	101971	Stefano Morozzi	05/2022
9890	2^338738+64947	101971	Stefano Morozzi	05/2022
9891	2^338740+119947	101971	Stefano Morozzi	11/2022
9892	2^338740-186837	101971	Stefano Morozzi	12/2022
9893	2^338737+127547	101970	Stefano Morozzi	12/2021
9894	2^338737+128591	101970	Stefano Morozzi	01/2022
9895	2^338735-153165	101970	Stefano Morozzi	01/2022
9896	2^338734+13719	101970	Stefano Morozzi	05/2022
9897	2^338734-138225	101970	Stefano Morozzi	12/2022
9898	2^338735-186129	101970	Stefano Morozzi	12/2022
9904	25295^10744+10744^25295	101969	Hans Havermann	01/2019
9905	25712^9243+9243^25712	101969	Hans Havermann	01/2019
9899	2^338731-150895	101969	Stefano Morozzi	12/2021
9900	2^338731+54911	101969	Stefano Morozzi	01/2022
9901	2^338731+85863	101969	Stefano Morozzi	03/2022
9902	2^338732+185047	101969	Stefano Morozzi	03/2022
9903	2^338733+193791	101969	Stefano Morozzi	09/2022
9906	2^338729+69221	101968	Stefano Morozzi	09/2022
9907	2^338728+123355	101968	Stefano Morozzi	11/2022
9908	2^338730-87063	101968	Stefano Morozzi	12/2022
9909	2^338726+128199	101967	Stefano Morozzi	01/2022
9910	2^338727+127745	101967	Stefano Morozzi	01/2022
9911	2^338724+32971	101967	Stefano Morozzi	02/2022
9912	2^338727+189683	101967	Stefano Morozzi	05/2022
9913	2^338727+118293	101967	Stefano Morozzi	09/2022
9914	2^338723-76651	101966	Stefano Morozzi	12/2021
9915	2^338721+79037	101966	Stefano Morozzi	01/2022
9916	2^338723-132621	101966	Stefano Morozzi	03/2022
9917	2^338722+137313	101966	Stefano Morozzi	04/2022
9918	2^338722+162915	101966	Stefano Morozzi	04/2022
9919	2^338723+199161	101966	Stefano Morozzi	02/2023
9920	2^338718-126861	101965	Stefano Morozzi	12/2021
9921	2^338718-109127	101965	Stefano Morozzi	04/2022
9926	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
9922	2^338714+30835	101964	Stefano Morozzi	01/2022
9923	2^338714+156715	101964	Stefano Morozzi	02/2022
9924	2^338715+19923	101964	Stefano Morozzi	09/2022
9925	2^338716+173253	101964	Stefano Morozzi	11/2022
9927	2^338711+125399	101963	Stefano Morozzi	12/2021
9928	2^338713-30895	101963	Stefano Morozzi	02/2022
9929	2^338712-132545	101963	Stefano Morozzi	03/2022
9930	2^338713+87825	101963	Stefano Morozzi	04/2022
9931	2^338712+190333	101963	Stefano Morozzi	06/2022
9932	2^338709-154429	101962	Stefano Morozzi	02/2022
9933	2^338710+140545	101962	Stefano Morozzi	06/2022
9934	2^338706-102917	101961	Stefano Morozzi	01/2022
9935	2^338705+34727	101961	Stefano Morozzi	03/2022
9936	2^338706-165633	101961	Stefano Morozzi	01/2023
9937	2^338707-116115	101961	Stefano Morozzi	01/2023
9938	2^338698+104083	101959	Stefano Morozzi	01/2022
9939	2^338700-184565	101959	Stefano Morozzi	04/2022
9940	2^338700+189777	101959	Stefano Morozzi	05/2022
9941	2^338698+41779	101959	Stefano Morozzi	09/2022
9942	2^338699+148533	101959	Stefano Morozzi	11/2022
9943	2^338700+97381	101959	Stefano Morozzi	11/2022
9944	2^338698-142181	101959	Stefano Morozzi	02/2023
9945	2^338696+181671	101958	Stefano Morozzi	02/2022
9946	2^338697+146651	101958	Stefano Morozzi	11/2022
9947	2^338695-116977	101958	Stefano Morozzi	02/2023
9948	2^338692+106297	101957	Stefano Morozzi	01/2022
9949	2^338692+33195	101957	Stefano Morozzi	02/2022
9950	2^338692+110505	101957	Stefano Morozzi	03/2022
9951	2^338692+190093	101957	Stefano Morozzi	05/2022
9952	2^338692+173343	101957	Stefano Morozzi	11/2022
9953	2^338693+144975	101957	Stefano Morozzi	11/2022
9954	2^338692+149281	101957	Stefano Morozzi	02/2023
9955	2^338688+82203	101956	Stefano Morozzi	02/2022
9956	2^338689+82365	101956	Stefano Morozzi	02/2022
9957	2^338688-92159	101956	Stefano Morozzi	02/2023
9958	2^338686-81303	101955	Stefano Morozzi	03/2022
9959	2^338687+40461	101955	Stefano Morozzi	06/2022
9960	2^338687+65283	101955	Stefano Morozzi	06/2022
9966	2^338682-19865	101954	Enzo Doria	06/2013
9967	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
9961	(8*10^101954-269)/9	101954	Robert Price	09/2021
9962	2^338683+50303	101954	Stefano Morozzi	11/2021
9963	2^338682-107205	101954	Stefano Morozzi	03/2022
9964	2^338682+13839	101954	Stefano Morozzi	05/2022
9965	2^338683-42837	101954	Stefano Morozzi	02/2023
9968	2^338678-180005	101953	Stefano Morozzi	02/2022
9969	2^338680+15855	101953	Stefano Morozzi	06/2022
9970	2^338678+93175	101953	Stefano Morozzi	09/2022
9971	2^338680+99217	101953	Stefano Morozzi	02/2023
9972	2^338674-175967	101952	Stefano Morozzi	12/2021
9973	2^338677-177373	101952	Stefano Morozzi	12/2021
9974	2^338677+102999	101952	Stefano Morozzi	01/2022
9975	2^338676+33381	101952	Stefano Morozzi	03/2022
9976	2^338677-82699	101952	Stefano Morozzi	03/2022
9977	2^338676-34299	101952	Stefano Morozzi	04/2022
9978	2^338675+188445	101952	Stefano Morozzi	05/2022
9979	2^338676+165271	101952	Stefano Morozzi	06/2022
9980	2^338674-187551	101952	Stefano Morozzi	12/2022
9981	2^338676-42243	101952	Stefano Morozzi	02/2023
9982	2^338671-55041	101951	Stefano Morozzi	02/2022
9983	2^338673-80203	101951	Stefano Morozzi	02/2022
9984	2^338672-182063	101951	Stefano Morozzi	03/2022
9985	2^338672+36667	101951	Stefano Morozzi	04/2022
9986	2^338668+2583	101950	Stefano Morozzi	12/2021
9987	2^338670-157001	101950	Stefano Morozzi	03/2022
9988	2^338669-8353	101950	Stefano Morozzi	04/2022
9989	2^338670+40635	101950	Stefano Morozzi	06/2022
9997	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
9990	2^338665+1577	101949	Stefano Morozzi	12/2021
9991	2^338665-51133	101949	Stefano Morozzi	12/2021
9992	2^338664+4345	101949	Stefano Morozzi	01/2022
9993	2^338666-128943	101949	Stefano Morozzi	01/2022
9994	2^338664+131535	101949	Stefano Morozzi	01/2022
9995	2^338667+14943	101949	Stefano Morozzi	05/2022
9996	2^338665+166637	101949	Stefano Morozzi	09/2022
9998	2^338662+31587	101948	Stefano Morozzi	02/2022
9999	2^338663-58375	101948	Stefano Morozzi	04/2022
10000	2^338663-107869	101948	Stefano Morozzi	04/2022

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PRP Records

Probable Primes Top 10000

(302900 PRPs in the top)