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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	2^338623-86577	101936	Stefano Morozzi	12/2022
9752	2^338620-150735	101935	Stefano Morozzi	12/2021
9753	2^338619-27765	101935	Stefano Morozzi	01/2022
9754	2^338619-77959	101935	Stefano Morozzi	01/2022
9755	2^338619-186367	101935	Stefano Morozzi	12/2022
9756	2^338618-64905	101935	Stefano Morozzi	01/2023
9757	2^338615+151655	101934	Stefano Morozzi	12/2021
9758	2^338616+5047	101934	Stefano Morozzi	01/2022
9759	2^338616+39705	101934	Stefano Morozzi	05/2022
9760	2^338617+149321	101934	Stefano Morozzi	02/2023
9761	2^338611+76659	101933	Stefano Morozzi	12/2021
9762	2^338613-109791	101933	Stefano Morozzi	04/2022
9763	2^338612+119583	101933	Stefano Morozzi	09/2022
9764	2^338611-140397	101933	Stefano Morozzi	01/2023
9765	2^338614-39653	101933	Stefano Morozzi	01/2023
9766	2^338609+130139	101932	Stefano Morozzi	01/2022
9767	2^338609+131327	101932	Stefano Morozzi	01/2022
9768	2^338608-155453	101932	Stefano Morozzi	02/2022
9769	2^338609+161721	101932	Stefano Morozzi	04/2022
9770	2^338609-10405	101932	Stefano Morozzi	06/2022
9771	2^338608+94017	101932	Stefano Morozzi	09/2022
9772	2^338610+170515	101932	Stefano Morozzi	11/2022
9773	2^338607+30611	101931	Stefano Morozzi	01/2022
9774	2^338607+106695	101931	Stefano Morozzi	02/2022
9775	2^338606-32291	101931	Stefano Morozzi	03/2022
9776	2^338606+15195	101931	Stefano Morozzi	05/2022
9777	2^338605+197789	101931	Stefano Morozzi	11/2022
9778	2^338607-90621	101931	Stefano Morozzi	01/2023
9779	2^338603-1195	101930	Stefano Morozzi	12/2021
9780	2^338601+108867	101930	Stefano Morozzi	03/2022
9781	2^338603+34311	101930	Stefano Morozzi	03/2022
9782	2^338598+57127	101929	Stefano Morozzi	02/2022
9783	2^338598+162645	101929	Stefano Morozzi	04/2022
9784	2^338599+43445	101929	Stefano Morozzi	09/2022
9785	2^338599+19485	101929	Stefano Morozzi	09/2022
9786	2^338598+46195	101929	Stefano Morozzi	11/2022
9787	2^338600-36393	101929	Stefano Morozzi	12/2022
9788	2^338596-1739	101928	Stefano Morozzi	12/2021
9789	2^338595-78687	101928	Stefano Morozzi	01/2022
9790	2^338595+181683	101928	Stefano Morozzi	02/2022
9791	2^338597-106045	101928	Stefano Morozzi	02/2022
9792	2^338595+119565	101928	Stefano Morozzi	09/2022
9793	2^338595+19623	101928	Stefano Morozzi	09/2022
9794	2^338595+21711	101928	Stefano Morozzi	11/2022
9795	2^338596-111129	101928	Stefano Morozzi	12/2022
9796	2^338591+53769	101927	Stefano Morozzi	01/2022
9797	2^338593+156989	101927	Stefano Morozzi	02/2022
9798	2^338592+36157	101927	Stefano Morozzi	03/2022
9799	2^338593+42099	101927	Stefano Morozzi	09/2022
9800	2^338591+46685	101927	Stefano Morozzi	11/2022
9801	2^338593+120437	101927	Stefano Morozzi	11/2022
9802	2^338591-165517	101927	Stefano Morozzi	01/2023
9803	2^338592-166107	101927	Stefano Morozzi	01/2023
9804	2^338592-189249	101927	Stefano Morozzi	01/2023
9805	2^338594-40493	101927	Stefano Morozzi	01/2023
9806	2^338590+182007	101926	Stefano Morozzi	02/2022
9807	2^338590+60747	101926	Stefano Morozzi	03/2022
9808	2^338588+62397	101926	Stefano Morozzi	04/2022
9809	2^338589-9685	101926	Stefano Morozzi	04/2022
9810	2^338588+73765	101926	Stefano Morozzi	02/2023
9811	2^338589-16915	101926	Stefano Morozzi	02/2023
9818	(2^338587+2306)/2	101925	Stefano Morozzi	02/2021
9812	2^338586+1153	101925	Stefano Morozzi	12/2021
9813	2^338587-51709	101925	Stefano Morozzi	12/2021
9814	2^338586+105303	101925	Stefano Morozzi	01/2022
9815	2^338585-131773	101925	Stefano Morozzi	03/2022
9816	2^338587+168039	101925	Stefano Morozzi	09/2022
9817	2^338585-140719	101925	Stefano Morozzi	01/2023
9819	2^338584+100771	101924	Stefano Morozzi	11/2021
9820	2^338581-150415	101924	Stefano Morozzi	12/2021
9821	2^338581-2349	101924	Stefano Morozzi	12/2021
9822	2^338582+42933	101924	Stefano Morozzi	09/2022
9823	2^338584+93267	101924	Stefano Morozzi	09/2022
9824	2^338582-86697	101924	Stefano Morozzi	12/2022
9825	2^338582-138035	101924	Stefano Morozzi	12/2022
9826	2^338584-115569	101924	Stefano Morozzi	01/2023
9827	2^338581-92793	101924	Stefano Morozzi	02/2023
9828	2^338578+67593	101923	Stefano Morozzi	09/2022
9829	2^338580+142201	101923	Stefano Morozzi	09/2022
9830	2^338579-14635	101923	Stefano Morozzi	01/2023
9831	2^338579-164985	101923	Stefano Morozzi	01/2023
9832	2^338575-28815	101922	Stefano Morozzi	01/2022
9833	2^338575-33645	101922	Stefano Morozzi	04/2022
9834	2^338577-92239	101922	Stefano Morozzi	02/2023
9835	2^338573-156693	101921	Stefano Morozzi	03/2022
9836	2^338572+193305	101921	Stefano Morozzi	09/2022
9837	2^338573+173751	101921	Stefano Morozzi	02/2023
9838	2^338574+73707	101921	Stefano Morozzi	02/2023
9843	2^338568+37	101920	Lelio R Paula	07/2011
9839	2^338570-53933	101920	Stefano Morozzi	02/2022
9840	2^338569+87201	101920	Stefano Morozzi	04/2022
9841	2^338570-36897	101920	Stefano Morozzi	12/2022
9842	2^338570-61157	101920	Stefano Morozzi	12/2022
9844	2^338567-9619	101919	Stefano Morozzi	04/2022
9845	2^338565-141589	101919	Stefano Morozzi	01/2023
9846	2^338565+148821	101919	Stefano Morozzi	02/2023
9847	2^338564-56763	101918	Stefano Morozzi	03/2022
9848	2^338561+112007	101918	Stefano Morozzi	04/2022
9849	2^338561-9315	101918	Stefano Morozzi	04/2022
9850	2^338564+41965	101918	Stefano Morozzi	09/2022
9851	2^338561+121139	101918	Stefano Morozzi	11/2022
9852	2^338562+21799	101918	Stefano Morozzi	11/2022
9860	2^338559-1858777	101917	Enzo Doria	04/2016
9853	2^338558+4825	101917	Stefano Morozzi	01/2022
9854	2^338559-127935	101917	Stefano Morozzi	01/2022
9855	2^338560+154891	101917	Stefano Morozzi	01/2022
9856	2^338559+131885	101917	Stefano Morozzi	02/2022
9857	2^338558+93735	101917	Stefano Morozzi	09/2022
9858	2^338559-90957	101917	Stefano Morozzi	01/2023
9859	2^338559-190761	101917	Stefano Morozzi	01/2023
9861	2^338555+189981	101916	Stefano Morozzi	05/2022
9862	2^338553-125383	101915	Stefano Morozzi	12/2021
9863	2^338554-82821	101915	Stefano Morozzi	03/2022
9864	2^338548+76923	101914	Stefano Morozzi	12/2021
9865	2^338549+158517	101914	Stefano Morozzi	03/2022
9866	2^338549+85397	101914	Stefano Morozzi	03/2022
9867	2^338548+138121	101914	Stefano Morozzi	05/2022
9868	2^338550-110301	101914	Stefano Morozzi	06/2022
9869	2^338547+129321	101913	Stefano Morozzi	01/2022
9870	2^338547-153481	101913	Stefano Morozzi	01/2022
9871	2^338545-11059	101913	Stefano Morozzi	12/2022
9872	2^338544+107853	101912	Stefano Morozzi	02/2022
9873	2^338542+172813	101912	Stefano Morozzi	11/2022
9874	2^338544-12687	101912	Stefano Morozzi	12/2022
9875	2^338543-140677	101912	Stefano Morozzi	01/2023
9876	2^338541+152721	101911	Stefano Morozzi	01/2022
9877	2^338539+60825	101911	Stefano Morozzi	03/2022
9878	2^338539+160881	101911	Stefano Morozzi	03/2022
9879	2^338541-182523	101911	Stefano Morozzi	03/2022
9880	2^338540+87645	101911	Stefano Morozzi	04/2022
9881	2^338541+148305	101911	Stefano Morozzi	11/2022
9882	2^338541-163075	101911	Stefano Morozzi	12/2022
9883	2^338536-100785	101910	Stefano Morozzi	12/2021
9884	2^338535-51837	101910	Stefano Morozzi	12/2021
9885	2^338535-158745	101910	Stefano Morozzi	04/2022
9886	2^338536-189977	101910	Stefano Morozzi	01/2023
9887	2^338537-65623	101910	Stefano Morozzi	01/2023
9888	2^338532+39445	101909	Stefano Morozzi	05/2022
9889	2^338532+141415	101909	Stefano Morozzi	06/2022
9890	2^338532-136037	101909	Stefano Morozzi	06/2022
9891	2^338531+81081	101908	Stefano Morozzi	01/2022
9892	2^338530+59835	101908	Stefano Morozzi	03/2022
9893	2^338529+186551	101908	Stefano Morozzi	04/2022
9894	2^338531+61313	101908	Stefano Morozzi	04/2022
9895	2^338531-9277	101908	Stefano Morozzi	04/2022
9896	2^338528-92727	101908	Stefano Morozzi	02/2023
9897	2^338527+191205	101907	Stefano Morozzi	06/2022
9898	2^338525+99621	101907	Stefano Morozzi	02/2023
9899	2^338524+54421	101906	Stefano Morozzi	01/2022
9900	2^338522-155811	101906	Stefano Morozzi	02/2022
9901	2^338523-16291	101906	Stefano Morozzi	01/2023
9902	2^338522-142137	101906	Stefano Morozzi	02/2023
9903	2^338521+183131	101905	Stefano Morozzi	02/2022
9904	2^338520+34945	101905	Stefano Morozzi	03/2022
9905	2^338518-182885	101905	Stefano Morozzi	04/2022
9906	2^338518+114633	101905	Stefano Morozzi	05/2022
9907	2^338518-12621	101905	Stefano Morozzi	12/2022
9908	2^338518-187325	101905	Stefano Morozzi	12/2022
9916	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
9909	2^338517-125955	101904	Stefano Morozzi	12/2021
9910	2^338517+126437	101904	Stefano Morozzi	12/2021
9911	2^338517-53499	101904	Stefano Morozzi	01/2022
9912	2^338515+30369	101904	Stefano Morozzi	01/2022
9913	2^338517-184623	101904	Stefano Morozzi	04/2022
9914	2^338515+89333	101904	Stefano Morozzi	05/2022
9915	2^338515+198813	101904	Stefano Morozzi	02/2023
9919	24502^14419+14419^24502	101903	Hans Havermann	01/2019
9917	2^338512-827	101903	Stefano Morozzi	12/2021
9918	2^338514-6611	101903	Stefano Morozzi	03/2022
9920	2^338509+5139	101902	Stefano Morozzi	01/2022
9921	2^338509+40205	101902	Stefano Morozzi	06/2022
9922	2^338511+19959	101902	Stefano Morozzi	09/2022
9923	2^338510-37877	101902	Stefano Morozzi	12/2022
9924	2^338507-188655	101901	Stefano Morozzi	12/2022
9925	2^338507-114457	101901	Stefano Morozzi	01/2023
9926	2^338504-152615	101900	Stefano Morozzi	01/2022
9927	2^338502-4587	101900	Stefano Morozzi	02/2022
9928	2^338502-166275	101900	Stefano Morozzi	01/2023
9929	2^338500-26865	101899	Stefano Morozzi	12/2021
9930	2^338501-177471	101899	Stefano Morozzi	12/2021
9931	2^338499-3915	101899	Stefano Morozzi	01/2022
9932	2^338501+32051	101899	Stefano Morozzi	02/2022
9933	2^338499+183533	101899	Stefano Morozzi	03/2022
9934	2^338500+35625	101899	Stefano Morozzi	03/2022
9935	2^338499+87579	101899	Stefano Morozzi	04/2022
9936	2^338498-117683	101899	Stefano Morozzi	02/2023
9939	2^338497-17041	101898	Enzo Doria	05/2013
9937	2^338497+150405	101898	Stefano Morozzi	11/2021
9938	2^338495+100533	101898	Stefano Morozzi	12/2021
9940	2^338494+36057	101897	Stefano Morozzi	03/2022
9941	2^338492+39015	101897	Stefano Morozzi	05/2022
9942	2^338494+168007	101897	Stefano Morozzi	09/2022
9943	2^338490+61149	101896	Stefano Morozzi	03/2022
9944	2^338489+161369	101896	Stefano Morozzi	04/2022
9945	2^338491+22961	101896	Stefano Morozzi	11/2022
9946	2^338487-3555	101895	Stefano Morozzi	01/2022
9947	2^338487-183129	101895	Stefano Morozzi	04/2022
9948	2^338484+128767	101894	Stefano Morozzi	01/2022
9949	2^338484-31895	101894	Stefano Morozzi	03/2022
9950	2^338483-67899	101894	Stefano Morozzi	02/2023
9951	2^338483-192129	101894	Stefano Morozzi	02/2023
9952	2^338478+10893	101893	Stefano Morozzi	03/2022
9953	2^338479+87243	101893	Stefano Morozzi	04/2022
9954	2^338479+167619	101893	Stefano Morozzi	09/2022
9955	2^338480+197503	101893	Stefano Morozzi	11/2022
9956	2^338481-11421	101893	Stefano Morozzi	12/2022
9957	2^338479-89649	101893	Stefano Morozzi	01/2023
9958	(29*34^66532-12833)/33	101893	Eric Chen	03/2023
9961	2^338475+54615	101892	Lelio R Paula	10/2016
9959	2^338475-59775	101892	Stefano Morozzi	04/2022
9960	2^338476-134237	101892	Stefano Morozzi	04/2022
9962	2^338474+100767	101891	Stefano Morozzi	11/2021
9963	2^338474+81165	101891	Stefano Morozzi	01/2022
9964	2^338474+41137	101891	Stefano Morozzi	06/2022
9965	2^338472-110445	101891	Stefano Morozzi	06/2022
9966	2^338473-89535	101891	Stefano Morozzi	01/2023
9967	2^338470+27777	101890	Stefano Morozzi	01/2022
9968	2^338468+31351	101890	Stefano Morozzi	01/2022
9969	2^338469-106339	101890	Stefano Morozzi	03/2022
9970	2^338471+187469	101890	Stefano Morozzi	04/2022
9971	2^338468+96613	101890	Stefano Morozzi	11/2022
9972	2^338469+46167	101890	Stefano Morozzi	11/2022
9973	2^338470+71527	101890	Stefano Morozzi	11/2022
9974	2^338469-112783	101890	Stefano Morozzi	12/2022
9975	2^338470-115665	101890	Stefano Morozzi	01/2023
9976	2^338467-25665	101889	Stefano Morozzi	12/2021
9977	2^338465+152139	101889	Stefano Morozzi	12/2021
9978	2^338466-28643	101889	Stefano Morozzi	01/2022
9979	2^338465+181517	101889	Stefano Morozzi	01/2022
9980	2^338466+115917	101889	Stefano Morozzi	06/2022
9981	2^338465-88291	101889	Stefano Morozzi	12/2022
9982	2^338464-104009	101888	Stefano Morozzi	02/2022
9983	2^338463+185169	101888	Stefano Morozzi	03/2022
9984	2^338464+60595	101888	Stefano Morozzi	03/2022
9985	2^338464-66377	101888	Stefano Morozzi	01/2023
9986	2^338458+60273	101887	Stefano Morozzi	03/2022
9987	2^338461+135867	101887	Stefano Morozzi	03/2022
9988	2^338455-4621	101886	Stefano Morozzi	02/2022
9989	2^338457+187827	101886	Stefano Morozzi	04/2022
9990	2^338455+173349	101886	Stefano Morozzi	11/2022
9991	2^338454+133737	101885	Stefano Morozzi	03/2022
9992	2^338454-158501	101885	Stefano Morozzi	04/2022
9993	2^338454-184217	101885	Stefano Morozzi	04/2022
9994	2^338453+164451	101885	Stefano Morozzi	05/2022
9995	2^338452-136137	101885	Stefano Morozzi	12/2022
9996	2^338450+106275	101884	Stefano Morozzi	01/2022
9997	2^338450+168439	101884	Stefano Morozzi	09/2022
9998	(133*10^101881+17)/3	101883	Robert Price	11/2021
9999	2^338445-80461	101883	Stefano Morozzi	02/2022
10000	2^338446-131211	101883	Stefano Morozzi	02/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301883 PRPs in the top)