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	2^338670-157001	101950	Stefano Morozzi	03/2022
9752	2^338669-8353	101950	Stefano Morozzi	04/2022
9753	2^338670+40635	101950	Stefano Morozzi	06/2022
9761	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
9754	2^338665+1577	101949	Stefano Morozzi	12/2021
9755	2^338665-51133	101949	Stefano Morozzi	12/2021
9756	2^338664+4345	101949	Stefano Morozzi	01/2022
9757	2^338666-128943	101949	Stefano Morozzi	01/2022
9758	2^338664+131535	101949	Stefano Morozzi	01/2022
9759	2^338667+14943	101949	Stefano Morozzi	05/2022
9760	2^338665+166637	101949	Stefano Morozzi	09/2022
9762	2^338662+31587	101948	Stefano Morozzi	02/2022
9763	2^338663-58375	101948	Stefano Morozzi	04/2022
9764	2^338663-107869	101948	Stefano Morozzi	04/2022
9765	2^338663+90435	101948	Stefano Morozzi	06/2022
9766	2^338661+70457	101948	Stefano Morozzi	11/2022
9767	2^338662+70519	101948	Stefano Morozzi	11/2022
9768	2^338663-39447	101948	Stefano Morozzi	01/2023
9769	2^338658-159191	101947	Stefano Morozzi	04/2022
9770	2^338659-159687	101947	Stefano Morozzi	04/2022
9771	2^338659+15543	101947	Stefano Morozzi	05/2022
9772	2^338658+44395	101947	Stefano Morozzi	09/2022
9773	2^338658+192537	101947	Stefano Morozzi	09/2022
9774	2^338659-90531	101947	Stefano Morozzi	01/2023
9775	2^338659-114759	101947	Stefano Morozzi	01/2023
9776	2^338659+124079	101947	Stefano Morozzi	02/2023
9777	2^338654+51027	101946	Stefano Morozzi	12/2021
9778	2^338656-152115	101946	Stefano Morozzi	12/2021
9779	2^338654+32415	101946	Stefano Morozzi	02/2022
9780	2^338654+39799	101946	Stefano Morozzi	05/2022
9781	2^338655+144579	101946	Stefano Morozzi	09/2022
9782	2^338657+97509	101946	Stefano Morozzi	11/2022
9783	2^338653+126629	101945	Stefano Morozzi	12/2021
9784	2^338653+33279	101945	Stefano Morozzi	02/2022
9785	2^338652-107097	101945	Stefano Morozzi	03/2022
9786	2^338653+94475	101945	Stefano Morozzi	09/2022
9787	2^338651+194073	101945	Stefano Morozzi	09/2022
9788	2^338652-89157	101945	Stefano Morozzi	01/2023
9789	2^338649-154663	101944	Stefano Morozzi	02/2022
9790	2^338650+61399	101944	Stefano Morozzi	04/2022
9791	2^338650-35655	101944	Stefano Morozzi	06/2022
9792	2^338650+169623	101944	Stefano Morozzi	09/2022
9793	2^338649-40743	101944	Stefano Morozzi	01/2023
9794	2^338645+150311	101943	Stefano Morozzi	11/2021
9795	2^338645+28481	101943	Stefano Morozzi	01/2022
9796	2^338647-77895	101943	Stefano Morozzi	01/2022
9797	2^338647-84607	101943	Stefano Morozzi	04/2022
9798	2^338647+164523	101943	Stefano Morozzi	05/2022
9799	2^338645+64845	101943	Stefano Morozzi	05/2022
9800	2^338644-35969	101943	Stefano Morozzi	12/2022
9801	2^338645-15715	101943	Stefano Morozzi	01/2023
9802	2^338641-152541	101942	Stefano Morozzi	12/2021
9803	2^338643-56487	101942	Stefano Morozzi	03/2022
9804	2^338642-186525	101942	Stefano Morozzi	12/2022
9805	2^338643-41715	101942	Stefano Morozzi	02/2023
9806	2^338638+100575	101941	Stefano Morozzi	12/2021
9807	2^338639-127461	101941	Stefano Morozzi	12/2021
9808	2^338640+187657	101941	Stefano Morozzi	04/2022
9809	2^338640+44431	101941	Stefano Morozzi	09/2022
9810	2^338635+1961	101940	Stefano Morozzi	12/2021
9811	2^338637+102125	101940	Stefano Morozzi	12/2021
9812	2^338636-135329	101940	Stefano Morozzi	06/2022
9813	2^338635+199485	101940	Stefano Morozzi	02/2023
9818	28594^3673+3673^28594	101939	Hans Havermann	02/2019
9814	2^338631+110741	101939	Stefano Morozzi	03/2022
9815	2^338631+112119	101939	Stefano Morozzi	04/2022
9816	2^338634-83097	101939	Stefano Morozzi	04/2022
9817	2^338633+139701	101939	Stefano Morozzi	05/2022
9819	2^338630-150341	101938	Stefano Morozzi	12/2021
9820	2^338630+12867	101938	Stefano Morozzi	04/2022
9821	2^338629+42147	101938	Stefano Morozzi	09/2022
9822	2^338628+121083	101938	Stefano Morozzi	11/2022
9823	2^338630+147235	101938	Stefano Morozzi	11/2022
9824	2^338628-37679	101938	Stefano Morozzi	12/2022
9825	2^338629-41383	101938	Stefano Morozzi	01/2023
9826	2^338628-91877	101938	Stefano Morozzi	02/2023
9827	2^338626-105875	101937	Stefano Morozzi	02/2022
9828	2^338625-111729	101937	Stefano Morozzi	12/2022
9829	2^338627+49299	101937	Stefano Morozzi	02/2023
9830	2^338621+33069	101936	Stefano Morozzi	02/2022
9831	2^338623-106405	101936	Stefano Morozzi	03/2022
9832	2^338621+61751	101936	Stefano Morozzi	04/2022
9833	2^338623-86577	101936	Stefano Morozzi	12/2022
9834	2^338620-150735	101935	Stefano Morozzi	12/2021
9835	2^338619-27765	101935	Stefano Morozzi	01/2022
9836	2^338619-77959	101935	Stefano Morozzi	01/2022
9837	2^338619-186367	101935	Stefano Morozzi	12/2022
9838	2^338618-64905	101935	Stefano Morozzi	01/2023
9839	2^338615+151655	101934	Stefano Morozzi	12/2021
9840	2^338616+5047	101934	Stefano Morozzi	01/2022
9841	2^338616+39705	101934	Stefano Morozzi	05/2022
9842	2^338617+149321	101934	Stefano Morozzi	02/2023
9843	2^338611+76659	101933	Stefano Morozzi	12/2021
9844	2^338613-109791	101933	Stefano Morozzi	04/2022
9845	2^338612+119583	101933	Stefano Morozzi	09/2022
9846	2^338611-140397	101933	Stefano Morozzi	01/2023
9847	2^338614-39653	101933	Stefano Morozzi	01/2023
9848	2^338609+130139	101932	Stefano Morozzi	01/2022
9849	2^338609+131327	101932	Stefano Morozzi	01/2022
9850	2^338608-155453	101932	Stefano Morozzi	02/2022
9851	2^338609+161721	101932	Stefano Morozzi	04/2022
9852	2^338609-10405	101932	Stefano Morozzi	06/2022
9853	2^338608+94017	101932	Stefano Morozzi	09/2022
9854	2^338610+170515	101932	Stefano Morozzi	11/2022
9855	2^338607+30611	101931	Stefano Morozzi	01/2022
9856	2^338607+106695	101931	Stefano Morozzi	02/2022
9857	2^338606-32291	101931	Stefano Morozzi	03/2022
9858	2^338606+15195	101931	Stefano Morozzi	05/2022
9859	2^338605+197789	101931	Stefano Morozzi	11/2022
9860	2^338607-90621	101931	Stefano Morozzi	01/2023
9861	2^338603-1195	101930	Stefano Morozzi	12/2021
9862	2^338601+108867	101930	Stefano Morozzi	03/2022
9863	2^338603+34311	101930	Stefano Morozzi	03/2022
9864	2^338598+57127	101929	Stefano Morozzi	02/2022
9865	2^338598+162645	101929	Stefano Morozzi	04/2022
9866	2^338599+43445	101929	Stefano Morozzi	09/2022
9867	2^338599+19485	101929	Stefano Morozzi	09/2022
9868	2^338598+46195	101929	Stefano Morozzi	11/2022
9869	2^338600-36393	101929	Stefano Morozzi	12/2022
9870	2^338596-1739	101928	Stefano Morozzi	12/2021
9871	2^338595-78687	101928	Stefano Morozzi	01/2022
9872	2^338595+181683	101928	Stefano Morozzi	02/2022
9873	2^338597-106045	101928	Stefano Morozzi	02/2022
9874	2^338595+119565	101928	Stefano Morozzi	09/2022
9875	2^338595+19623	101928	Stefano Morozzi	09/2022
9876	2^338595+21711	101928	Stefano Morozzi	11/2022
9877	2^338596-111129	101928	Stefano Morozzi	12/2022
9878	2^338591+53769	101927	Stefano Morozzi	01/2022
9879	2^338593+156989	101927	Stefano Morozzi	02/2022
9880	2^338592+36157	101927	Stefano Morozzi	03/2022
9881	2^338593+42099	101927	Stefano Morozzi	09/2022
9882	2^338591+46685	101927	Stefano Morozzi	11/2022
9883	2^338593+120437	101927	Stefano Morozzi	11/2022
9884	2^338591-165517	101927	Stefano Morozzi	01/2023
9885	2^338592-166107	101927	Stefano Morozzi	01/2023
9886	2^338592-189249	101927	Stefano Morozzi	01/2023
9887	2^338594-40493	101927	Stefano Morozzi	01/2023
9888	2^338590+182007	101926	Stefano Morozzi	02/2022
9889	2^338590+60747	101926	Stefano Morozzi	03/2022
9890	2^338588+62397	101926	Stefano Morozzi	04/2022
9891	2^338589-9685	101926	Stefano Morozzi	04/2022
9892	2^338588+73765	101926	Stefano Morozzi	02/2023
9893	2^338589-16915	101926	Stefano Morozzi	02/2023
9900	(2^338587+2306)/2	101925	Stefano Morozzi	02/2021
9894	2^338586+1153	101925	Stefano Morozzi	12/2021
9895	2^338587-51709	101925	Stefano Morozzi	12/2021
9896	2^338586+105303	101925	Stefano Morozzi	01/2022
9897	2^338585-131773	101925	Stefano Morozzi	03/2022
9898	2^338587+168039	101925	Stefano Morozzi	09/2022
9899	2^338585-140719	101925	Stefano Morozzi	01/2023
9901	2^338584+100771	101924	Stefano Morozzi	11/2021
9902	2^338581-150415	101924	Stefano Morozzi	12/2021
9903	2^338581-2349	101924	Stefano Morozzi	12/2021
9904	2^338582+42933	101924	Stefano Morozzi	09/2022
9905	2^338584+93267	101924	Stefano Morozzi	09/2022
9906	2^338582-86697	101924	Stefano Morozzi	12/2022
9907	2^338582-138035	101924	Stefano Morozzi	12/2022
9908	2^338584-115569	101924	Stefano Morozzi	01/2023
9909	2^338581-92793	101924	Stefano Morozzi	02/2023
9910	2^338578+67593	101923	Stefano Morozzi	09/2022
9911	2^338580+142201	101923	Stefano Morozzi	09/2022
9912	2^338579-14635	101923	Stefano Morozzi	01/2023
9913	2^338579-164985	101923	Stefano Morozzi	01/2023
9914	2^338575-28815	101922	Stefano Morozzi	01/2022
9915	2^338575-33645	101922	Stefano Morozzi	04/2022
9916	2^338577-92239	101922	Stefano Morozzi	02/2023
9917	2^338573-156693	101921	Stefano Morozzi	03/2022
9918	2^338572+193305	101921	Stefano Morozzi	09/2022
9919	2^338573+173751	101921	Stefano Morozzi	02/2023
9920	2^338574+73707	101921	Stefano Morozzi	02/2023
9925	2^338568+37	101920	Lelio R Paula	07/2011
9921	2^338570-53933	101920	Stefano Morozzi	02/2022
9922	2^338569+87201	101920	Stefano Morozzi	04/2022
9923	2^338570-36897	101920	Stefano Morozzi	12/2022
9924	2^338570-61157	101920	Stefano Morozzi	12/2022
9926	2^338567-9619	101919	Stefano Morozzi	04/2022
9927	2^338565-141589	101919	Stefano Morozzi	01/2023
9928	2^338565+148821	101919	Stefano Morozzi	02/2023
9929	2^338564-56763	101918	Stefano Morozzi	03/2022
9930	2^338561+112007	101918	Stefano Morozzi	04/2022
9931	2^338561-9315	101918	Stefano Morozzi	04/2022
9932	2^338564+41965	101918	Stefano Morozzi	09/2022
9933	2^338561+121139	101918	Stefano Morozzi	11/2022
9934	2^338562+21799	101918	Stefano Morozzi	11/2022
9942	2^338559-1858777	101917	Enzo Doria	04/2016
9935	2^338558+4825	101917	Stefano Morozzi	01/2022
9936	2^338559-127935	101917	Stefano Morozzi	01/2022
9937	2^338560+154891	101917	Stefano Morozzi	01/2022
9938	2^338559+131885	101917	Stefano Morozzi	02/2022
9939	2^338558+93735	101917	Stefano Morozzi	09/2022
9940	2^338559-90957	101917	Stefano Morozzi	01/2023
9941	2^338559-190761	101917	Stefano Morozzi	01/2023
9943	2^338555+189981	101916	Stefano Morozzi	05/2022
9944	2^338553-125383	101915	Stefano Morozzi	12/2021
9945	2^338554-82821	101915	Stefano Morozzi	03/2022
9946	2^338548+76923	101914	Stefano Morozzi	12/2021
9947	2^338549+158517	101914	Stefano Morozzi	03/2022
9948	2^338549+85397	101914	Stefano Morozzi	03/2022
9949	2^338548+138121	101914	Stefano Morozzi	05/2022
9950	2^338550-110301	101914	Stefano Morozzi	06/2022
9951	2^338547+129321	101913	Stefano Morozzi	01/2022
9952	2^338547-153481	101913	Stefano Morozzi	01/2022
9953	2^338545-11059	101913	Stefano Morozzi	12/2022
9954	2^338544+107853	101912	Stefano Morozzi	02/2022
9955	2^338542+172813	101912	Stefano Morozzi	11/2022
9956	2^338544-12687	101912	Stefano Morozzi	12/2022
9957	2^338543-140677	101912	Stefano Morozzi	01/2023
9958	2^338541+152721	101911	Stefano Morozzi	01/2022
9959	2^338539+60825	101911	Stefano Morozzi	03/2022
9960	2^338539+160881	101911	Stefano Morozzi	03/2022
9961	2^338541-182523	101911	Stefano Morozzi	03/2022
9962	2^338540+87645	101911	Stefano Morozzi	04/2022
9963	2^338541+148305	101911	Stefano Morozzi	11/2022
9964	2^338541-163075	101911	Stefano Morozzi	12/2022
9965	2^338536-100785	101910	Stefano Morozzi	12/2021
9966	2^338535-51837	101910	Stefano Morozzi	12/2021
9967	2^338535-158745	101910	Stefano Morozzi	04/2022
9968	2^338536-189977	101910	Stefano Morozzi	01/2023
9969	2^338537-65623	101910	Stefano Morozzi	01/2023
9970	2^338532+39445	101909	Stefano Morozzi	05/2022
9971	2^338532+141415	101909	Stefano Morozzi	06/2022
9972	2^338532-136037	101909	Stefano Morozzi	06/2022
9973	2^338531+81081	101908	Stefano Morozzi	01/2022
9974	2^338530+59835	101908	Stefano Morozzi	03/2022
9975	2^338529+186551	101908	Stefano Morozzi	04/2022
9976	2^338531+61313	101908	Stefano Morozzi	04/2022
9977	2^338531-9277	101908	Stefano Morozzi	04/2022
9978	2^338528-92727	101908	Stefano Morozzi	02/2023
9979	2^338527+191205	101907	Stefano Morozzi	06/2022
9980	2^338525+99621	101907	Stefano Morozzi	02/2023
9981	2^338524+54421	101906	Stefano Morozzi	01/2022
9982	2^338522-155811	101906	Stefano Morozzi	02/2022
9983	2^338523-16291	101906	Stefano Morozzi	01/2023
9984	2^338522-142137	101906	Stefano Morozzi	02/2023
9985	2^338521+183131	101905	Stefano Morozzi	02/2022
9986	2^338520+34945	101905	Stefano Morozzi	03/2022
9987	2^338518-182885	101905	Stefano Morozzi	04/2022
9988	2^338518+114633	101905	Stefano Morozzi	05/2022
9989	2^338518-12621	101905	Stefano Morozzi	12/2022
9990	2^338518-187325	101905	Stefano Morozzi	12/2022
9998	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
9991	2^338517-125955	101904	Stefano Morozzi	12/2021
9992	2^338517+126437	101904	Stefano Morozzi	12/2021
9993	2^338517-53499	101904	Stefano Morozzi	01/2022
9994	2^338515+30369	101904	Stefano Morozzi	01/2022
9995	2^338517-184623	101904	Stefano Morozzi	04/2022
9996	2^338515+89333	101904	Stefano Morozzi	05/2022
9997	2^338515+198813	101904	Stefano Morozzi	02/2023
9999	2^338512-827	101903	Stefano Morozzi	12/2021
10000	2^338514-6611	101903	Stefano Morozzi	03/2022

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Probable Primes Top 10000

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