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 ?
8501	2^338336+54607	101850	Stefano Morozzi	01/2022
8502	2^338338+109999	101850	Stefano Morozzi	03/2022
8503	2^338336+161575	101850	Stefano Morozzi	04/2022
8504	2^338335+51975	101849	Stefano Morozzi	12/2021
8505	2^338335-152607	101849	Stefano Morozzi	01/2022
8506	2^338334+55273	101849	Stefano Morozzi	01/2022
8507	2^338332+34315	101849	Stefano Morozzi	03/2022
8508	2^338335+158759	101849	Stefano Morozzi	03/2022
8509	2^338332+67621	101849	Stefano Morozzi	09/2022
8510	2^338332-66099	101849	Stefano Morozzi	01/2023
8511	2^338334-191043	101849	Stefano Morozzi	01/2023
8512	2^338331+83403	101848	Stefano Morozzi	02/2022
8513	2^338330-110865	101848	Stefano Morozzi	06/2022
8514	2^338330+71047	101848	Stefano Morozzi	11/2022
8515	2^338328-5295	101847	Stefano Morozzi	02/2022
8516	2^338327+143585	101847	Stefano Morozzi	09/2022
8517	2^338324-179667	101846	Stefano Morozzi	02/2022
8518	2^338322+21903	101846	Stefano Morozzi	11/2022
8519	2^338324+98047	101846	Stefano Morozzi	11/2022
8520	2^338323-87729	101846	Stefano Morozzi	12/2022
8521	2^338322-16667	101846	Stefano Morozzi	01/2023
8522	2^338325-142159	101846	Stefano Morozzi	02/2023
8523	2^338316-175857	101844	Stefano Morozzi	12/2021
8524	2^338318+54405	101844	Stefano Morozzi	01/2022
8525	2^338316+32961	101844	Stefano Morozzi	02/2022
8526	2^338317+68175	101844	Stefano Morozzi	09/2022
8527	2^338318-86171	101844	Stefano Morozzi	12/2022
8528	2^338315-178635	101843	Stefano Morozzi	01/2022
8529	2^338315+34899	101843	Stefano Morozzi	03/2022
8530	2^338314-106973	101843	Stefano Morozzi	03/2022
8531	2^338313+170411	101843	Stefano Morozzi	11/2022
8532	2^338315-88807	101843	Stefano Morozzi	12/2022
8533	2^338311-51799	101842	Stefano Morozzi	12/2021
8534	2^338309+157259	101842	Stefano Morozzi	02/2022
8535	2^338310+40903	101842	Stefano Morozzi	06/2022
8536	2^338309-168051	101842	Stefano Morozzi	02/2023
8537	2^338308-55853	101841	Stefano Morozzi	02/2022
8538	2^338307+134871	101841	Stefano Morozzi	03/2022
8539	2^338307+19689	101841	Stefano Morozzi	09/2022
8540	2^338308+66873	101841	Stefano Morozzi	09/2022
8541	2^338306+124399	101841	Stefano Morozzi	02/2023
8542	2^338306-91913	101841	Stefano Morozzi	02/2023
8543	2^338304+78757	101840	Stefano Morozzi	01/2022
8544	2^338304-5807	101840	Stefano Morozzi	02/2022
8545	2^338305+110879	101840	Stefano Morozzi	03/2022
8546	2^338304+91147	101840	Stefano Morozzi	06/2022
8547	2^338304-64475	101840	Stefano Morozzi	01/2023
8548	2^338299+85611	101839	Stefano Morozzi	03/2022
8549	2^338299-189985	101839	Stefano Morozzi	01/2023
8550	2^338298-25571	101838	Stefano Morozzi	12/2021
8551	2^338297+35547	101838	Stefano Morozzi	03/2022
8552	2^338298+111199	101838	Stefano Morozzi	03/2022
8553	2^338297+145455	101838	Stefano Morozzi	11/2022
8554	2^338297-166285	101838	Stefano Morozzi	01/2023
8555	2^338294-150711	101837	Stefano Morozzi	12/2021
8556	2^338294+177597	101837	Stefano Morozzi	12/2021
8557	2^338294-177807	101837	Stefano Morozzi	01/2022
8558	2^338295-52929	101837	Stefano Morozzi	01/2022
8559	2^338293+37407	101837	Stefano Morozzi	04/2022
8560	2^338292+40573	101837	Stefano Morozzi	06/2022
8561	2^338294+172425	101837	Stefano Morozzi	11/2022
8562	2^338293-191799	101837	Stefano Morozzi	02/2023
8563	2^338289+30957	101836	Stefano Morozzi	01/2022
8564	2^338291+131825	101836	Stefano Morozzi	02/2022
8565	2^338291+110111	101836	Stefano Morozzi	03/2022
8566	2^338290-156423	101836	Stefano Morozzi	03/2022
8567	2^338291-157845	101836	Stefano Morozzi	03/2022
8568	2^338290+69243	101836	Stefano Morozzi	09/2022
8569	2^338291-189327	101836	Stefano Morozzi	01/2023
8570	2^338291+74079	101836	Stefano Morozzi	02/2023
8571	2^338288+26623	101835	Stefano Morozzi	12/2021
8572	2^338286+33325	101835	Stefano Morozzi	02/2022
8573	2^338287+132633	101835	Stefano Morozzi	02/2022
8574	2^338287+157149	101835	Stefano Morozzi	02/2022
8575	2^338288-107193	101835	Stefano Morozzi	03/2022
8576	2^338286-83333	101835	Stefano Morozzi	04/2022
8577	2^338287+114425	101835	Stefano Morozzi	05/2022
8578	2^338288+194403	101835	Stefano Morozzi	09/2022
8579	2^338288-113177	101835	Stefano Morozzi	12/2022
8580	2^338288-65747	101835	Stefano Morozzi	01/2023
8581	2^338285+82131	101834	Stefano Morozzi	02/2022
8582	2^338284-104217	101834	Stefano Morozzi	02/2022
8583	2^338282-84533	101834	Stefano Morozzi	04/2022
8584	2^338283+67545	101834	Stefano Morozzi	09/2022
8585	2^338283-65439	101834	Stefano Morozzi	01/2023
8594	2^338280-19745	101833	Enzo Doria	06/2013
8586	2^338279-125947	101833	Stefano Morozzi	12/2021
8587	2^338280-50343	101833	Stefano Morozzi	12/2021
8588	2^338279+133331	101833	Stefano Morozzi	02/2022
8589	2^338281-54561	101833	Stefano Morozzi	02/2022
8590	2^338280+192063	101833	Stefano Morozzi	09/2022
8591	2^338281+18971	101833	Stefano Morozzi	09/2022
8592	2^338281-186711	101833	Stefano Morozzi	12/2022
8593	2^338281-91273	101833	Stefano Morozzi	01/2023
8595	2^338278+188215	101832	Stefano Morozzi	05/2022
8596	2^338273+181101	101831	Stefano Morozzi	01/2022
8597	2^338275+32909	101831	Stefano Morozzi	02/2022
8598	2^338272+166431	101831	Stefano Morozzi	06/2022
8599	2^338272+22011	101831	Stefano Morozzi	11/2022
8600	2^338275+148271	101831	Stefano Morozzi	11/2022
8601	2^338270-135725	101830	Stefano Morozzi	06/2022
8602	2^338269-136951	101830	Stefano Morozzi	12/2022
8603	2^338270-192701	101830	Stefano Morozzi	02/2023
8604	2^338271-42831	101830	Stefano Morozzi	02/2023
8605	2^338266+110665	101829	Stefano Morozzi	03/2022
8606	2^338267+110481	101829	Stefano Morozzi	03/2022
8607	2^338267-166035	101829	Stefano Morozzi	01/2023
8608	2^338265-154893	101828	Stefano Morozzi	02/2022
8609	2^338264+163611	101828	Stefano Morozzi	05/2022
8610	2^338263-62767	101828	Stefano Morozzi	12/2022
8611	2^338261-188119	101827	Stefano Morozzi	12/2022
8612	2^338259-40327	101827	Stefano Morozzi	01/2023
8613	2^338256+5223	101826	Stefano Morozzi	01/2022
8614	2^338257+178425	101826	Stefano Morozzi	01/2022
8615	2^338256-180569	101826	Stefano Morozzi	02/2022
8616	2^338257-5965	101826	Stefano Morozzi	02/2022
8617	2^338258-9225	101826	Stefano Morozzi	04/2022
8618	2^338255-127021	101825	Stefano Morozzi	12/2021
8619	2^338253+159005	101825	Stefano Morozzi	03/2022
8620	2^338253+64817	101825	Stefano Morozzi	05/2022
8621	2^338254-85403	101825	Stefano Morozzi	06/2022
8622	2^338254+142947	101825	Stefano Morozzi	09/2022
8623	2^338253+121095	101825	Stefano Morozzi	11/2022
8624	2^338254+196725	101825	Stefano Morozzi	11/2022
8625	2^338254-91007	101825	Stefano Morozzi	01/2023
8626	2^338251+78975	101824	Stefano Morozzi	01/2022
8627	2^338252-178709	101824	Stefano Morozzi	01/2022
8628	2^338252+129703	101824	Stefano Morozzi	01/2022
8629	2^338252+132285	101824	Stefano Morozzi	02/2022
8630	2^338251-33381	101824	Stefano Morozzi	04/2022
8631	2^338252-13805	101824	Stefano Morozzi	12/2022
8632	2^338245-134755	101822	Stefano Morozzi	04/2022
8633	2^338244-59219	101822	Stefano Morozzi	04/2022
8634	2^338244-64703	101822	Stefano Morozzi	01/2023
8642	(2^338242+2782)/2	101821	Stefano Morozzi	02/2021
8635	2^338241+1391	101821	Stefano Morozzi	12/2021
8636	2^338242+151195	101821	Stefano Morozzi	12/2021
8637	2^338240-152495	101821	Stefano Morozzi	12/2021
8638	2^338240+81745	101821	Stefano Morozzi	02/2022
8639	2^338241-155551	101821	Stefano Morozzi	02/2022
8640	2^338242-108237	101821	Stefano Morozzi	04/2022
8641	2^338242+43045	101821	Stefano Morozzi	09/2022
8643	2^338238-126735	101820	Stefano Morozzi	12/2021
8644	2^338238+183855	101820	Stefano Morozzi	03/2022
8645	2^338238+141013	101820	Stefano Morozzi	06/2022
8646	2^338237+97227	101820	Stefano Morozzi	11/2022
8647	2^338238+48429	101820	Stefano Morozzi	11/2022
8648	2^338234-80925	101819	Stefano Morozzi	02/2022
8649	2^338234-154593	101819	Stefano Morozzi	02/2022
8650	2^338235-131787	101819	Stefano Morozzi	03/2022
8651	2^338233+89781	101819	Stefano Morozzi	05/2022
8652	2^338235+169971	101819	Stefano Morozzi	11/2022
8653	2^338233-113875	101819	Stefano Morozzi	12/2022
8660	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
8654	2^338232-175539	101818	Stefano Morozzi	12/2021
8655	2^338231+57345	101818	Stefano Morozzi	02/2022
8656	2^338232+36097	101818	Stefano Morozzi	03/2022
8657	2^338230+137403	101818	Stefano Morozzi	04/2022
8658	2^338231-59569	101818	Stefano Morozzi	04/2022
8659	2^338230-86633	101818	Stefano Morozzi	12/2022
8661	2^338228+159247	101817	Stefano Morozzi	03/2022
8662	2^338227-12631	101817	Stefano Morozzi	12/2022
8663	(34*10^101815+191)/9	101816	Robert Price	08/2021
8664	2^338224+185461	101816	Stefano Morozzi	03/2022
8665	2^338224+62295	101816	Stefano Morozzi	04/2022
8666	2^338225+162645	101816	Stefano Morozzi	04/2022
8667	2^338223+144209	101816	Stefano Morozzi	09/2022
8674	6^130841+103	101815	Lelio R Paula	10/2016
8668	2^338220+150405	101815	Stefano Morozzi	11/2021
8669	2^338219-4147	101815	Stefano Morozzi	01/2022
8670	2^338221+83391	101815	Stefano Morozzi	02/2022
8671	2^338221+62937	101815	Stefano Morozzi	04/2022
8672	2^338220-65697	101815	Stefano Morozzi	01/2023
8673	2^338220-139505	101815	Stefano Morozzi	01/2023
8675	2^338216+77473	101814	Stefano Morozzi	12/2021
8676	2^338218+155299	101814	Stefano Morozzi	01/2022
8677	2^338217-134745	101814	Stefano Morozzi	04/2022
8678	2^338218+73507	101814	Stefano Morozzi	11/2022
8679	2^338213-125631	101813	Stefano Morozzi	12/2021
8680	2^338215+25845	101813	Stefano Morozzi	12/2021
8681	2^338210-153537	101812	Stefano Morozzi	01/2022
8682	2^338209+60915	101812	Stefano Morozzi	03/2022
8683	2^338211-57297	101812	Stefano Morozzi	03/2022
8684	2^338211-110257	101812	Stefano Morozzi	06/2022
8685	2^338211+71549	101812	Stefano Morozzi	11/2022
8686	2^338208-178787	101811	Stefano Morozzi	01/2022
8687	2^338208+106153	101811	Stefano Morozzi	01/2022
8688	2^338207+16499	101811	Stefano Morozzi	06/2022
8689	2^338205+102471	101810	Stefano Morozzi	12/2021
8690	2^338199-176377	101809	Stefano Morozzi	12/2021
8691	2^338201-151233	101809	Stefano Morozzi	12/2021
8692	2^338202-152061	101809	Stefano Morozzi	12/2021
8693	2^338202+133785	101809	Stefano Morozzi	03/2022
8694	2^338200+135643	101809	Stefano Morozzi	03/2022
8695	2^338202+14169	101809	Stefano Morozzi	05/2022
8696	2^338202-85211	101809	Stefano Morozzi	06/2022
8697	2^338200+74265	101809	Stefano Morozzi	02/2023
8698	2^338196+121147	101808	Stefano Morozzi	11/2022
8699	2^338196+73551	101808	Stefano Morozzi	11/2022
8700	2^338194-175845	101807	Stefano Morozzi	12/2021
8701	2^338195+56771	101807	Stefano Morozzi	02/2022
8702	2^338195+162365	101807	Stefano Morozzi	04/2022
8703	2^338194+67497	101807	Stefano Morozzi	09/2022
8704	2^338193-116335	101807	Stefano Morozzi	01/2023
8705	2^338194-15585	101807	Stefano Morozzi	01/2023
8706	2^338192+130387	101806	Stefano Morozzi	01/2022
8707	2^338190+89359	101806	Stefano Morozzi	05/2022
8708	2^338189+144605	101806	Stefano Morozzi	09/2022
8709	2^338190-113537	101806	Stefano Morozzi	12/2022
8710	2^338186+127245	101805	Stefano Morozzi	12/2021
8711	2^338186-130013	101805	Stefano Morozzi	02/2022
8712	2^338186+39235	101805	Stefano Morozzi	05/2022
8713	2^338185+77315	101804	Stefano Morozzi	12/2021
8714	2^338185+102519	101804	Stefano Morozzi	12/2021
8715	2^338183-76539	101804	Stefano Morozzi	12/2021
8716	2^338185+104489	101804	Stefano Morozzi	01/2022
8717	2^338179+35361	101803	Stefano Morozzi	03/2022
8718	2^338181+64235	101803	Stefano Morozzi	05/2022
8719	2^338181+94047	101803	Stefano Morozzi	09/2022
8720	2^338180+146131	101803	Stefano Morozzi	11/2022
8721	2^338179+123399	101803	Stefano Morozzi	11/2022
8722	2^338182-42425	101803	Stefano Morozzi	02/2023
8723	2^338177+51807	101802	Stefano Morozzi	12/2021
8724	2^338177+107385	101802	Stefano Morozzi	02/2022
8725	2^338178+34287	101802	Stefano Morozzi	03/2022
8726	2^338178+184207	101802	Stefano Morozzi	03/2022
8727	2^338177-108901	101802	Stefano Morozzi	04/2022
8728	2^338177+141569	101802	Stefano Morozzi	06/2022
8729	2^338176+46221	101802	Stefano Morozzi	11/2022
8730	2^338175+25161	101801	Stefano Morozzi	11/2021
8731	2^338173-27901	101801	Stefano Morozzi	01/2022
8732	2^338174+23217	101801	Stefano Morozzi	11/2022
8733	2^338174+23793	101801	Stefano Morozzi	11/2022
8734	2^338173-36183	101801	Stefano Morozzi	12/2022
8735	2^338173-137053	101801	Stefano Morozzi	12/2022
8736	2^338174-36797	101801	Stefano Morozzi	12/2022
8737	2^338175-166509	101801	Stefano Morozzi	01/2023
8738	2^338169-155965	101800	Stefano Morozzi	02/2022
8739	2^338172+95797	101800	Stefano Morozzi	11/2022
8740	2^338171-117987	101800	Stefano Morozzi	02/2023
8741	2^338166+183237	101799	Stefano Morozzi	02/2022
8742	2^338168-157835	101799	Stefano Morozzi	03/2022
8743	2^338166+137107	101799	Stefano Morozzi	04/2022
8744	2^338166+22897	101799	Stefano Morozzi	11/2022
8745	2^338166-161123	101799	Stefano Morozzi	12/2022
8746	2^338165-152139	101798	Stefano Morozzi	12/2021
8747	2^338163-178947	101798	Stefano Morozzi	02/2022
8748	2^338164-64329	101798	Stefano Morozzi	01/2023
8749	2^338159-127575	101797	Stefano Morozzi	12/2021
8750	2^338161+154259	101797	Stefano Morozzi	01/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(295756 PRPs in the top)