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 ?
9501	2^338535-158745	101910	Stefano Morozzi	04/2022
9502	2^338536-189977	101910	Stefano Morozzi	01/2023
9503	2^338537-65623	101910	Stefano Morozzi	01/2023
9504	2^338532+39445	101909	Stefano Morozzi	05/2022
9505	2^338532+141415	101909	Stefano Morozzi	06/2022
9506	2^338532-136037	101909	Stefano Morozzi	06/2022
9507	2^338531+81081	101908	Stefano Morozzi	01/2022
9508	2^338530+59835	101908	Stefano Morozzi	03/2022
9509	2^338529+186551	101908	Stefano Morozzi	04/2022
9510	2^338531+61313	101908	Stefano Morozzi	04/2022
9511	2^338531-9277	101908	Stefano Morozzi	04/2022
9512	2^338528-92727	101908	Stefano Morozzi	02/2023
9513	2^338527+191205	101907	Stefano Morozzi	06/2022
9514	2^338525+99621	101907	Stefano Morozzi	02/2023
9515	2^338524+54421	101906	Stefano Morozzi	01/2022
9516	2^338522-155811	101906	Stefano Morozzi	02/2022
9517	2^338523-16291	101906	Stefano Morozzi	01/2023
9518	2^338522-142137	101906	Stefano Morozzi	02/2023
9519	2^338521+183131	101905	Stefano Morozzi	02/2022
9520	2^338520+34945	101905	Stefano Morozzi	03/2022
9521	2^338518-182885	101905	Stefano Morozzi	04/2022
9522	2^338518+114633	101905	Stefano Morozzi	05/2022
9523	2^338518-12621	101905	Stefano Morozzi	12/2022
9524	2^338518-187325	101905	Stefano Morozzi	12/2022
9532	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
9525	2^338517-125955	101904	Stefano Morozzi	12/2021
9526	2^338517+126437	101904	Stefano Morozzi	12/2021
9527	2^338517-53499	101904	Stefano Morozzi	01/2022
9528	2^338515+30369	101904	Stefano Morozzi	01/2022
9529	2^338517-184623	101904	Stefano Morozzi	04/2022
9530	2^338515+89333	101904	Stefano Morozzi	05/2022
9531	2^338515+198813	101904	Stefano Morozzi	02/2023
9535	24502^14419+14419^24502	101903	Hans Havermann	01/2019
9533	2^338512-827	101903	Stefano Morozzi	12/2021
9534	2^338514-6611	101903	Stefano Morozzi	03/2022
9536	2^338509+5139	101902	Stefano Morozzi	01/2022
9537	2^338509+40205	101902	Stefano Morozzi	06/2022
9538	2^338511+19959	101902	Stefano Morozzi	09/2022
9539	2^338510-37877	101902	Stefano Morozzi	12/2022
9540	2^338507-188655	101901	Stefano Morozzi	12/2022
9541	2^338507-114457	101901	Stefano Morozzi	01/2023
9542	2^338504-152615	101900	Stefano Morozzi	01/2022
9543	2^338502-4587	101900	Stefano Morozzi	02/2022
9544	2^338502-166275	101900	Stefano Morozzi	01/2023
9545	2^338500-26865	101899	Stefano Morozzi	12/2021
9546	2^338501-177471	101899	Stefano Morozzi	12/2021
9547	2^338499-3915	101899	Stefano Morozzi	01/2022
9548	2^338501+32051	101899	Stefano Morozzi	02/2022
9549	2^338499+183533	101899	Stefano Morozzi	03/2022
9550	2^338500+35625	101899	Stefano Morozzi	03/2022
9551	2^338499+87579	101899	Stefano Morozzi	04/2022
9552	2^338498-117683	101899	Stefano Morozzi	02/2023
9555	2^338497-17041	101898	Enzo Doria	05/2013
9553	2^338497+150405	101898	Stefano Morozzi	11/2021
9554	2^338495+100533	101898	Stefano Morozzi	12/2021
9556	2^338494+36057	101897	Stefano Morozzi	03/2022
9557	2^338492+39015	101897	Stefano Morozzi	05/2022
9558	2^338494+168007	101897	Stefano Morozzi	09/2022
9559	2^338490+61149	101896	Stefano Morozzi	03/2022
9560	2^338489+161369	101896	Stefano Morozzi	04/2022
9561	2^338491+22961	101896	Stefano Morozzi	11/2022
9562	2^338487-3555	101895	Stefano Morozzi	01/2022
9563	2^338487-183129	101895	Stefano Morozzi	04/2022
9564	2^338484+128767	101894	Stefano Morozzi	01/2022
9565	2^338484-31895	101894	Stefano Morozzi	03/2022
9566	2^338483-67899	101894	Stefano Morozzi	02/2023
9567	2^338483-192129	101894	Stefano Morozzi	02/2023
9568	2^338478+10893	101893	Stefano Morozzi	03/2022
9569	2^338479+87243	101893	Stefano Morozzi	04/2022
9570	2^338479+167619	101893	Stefano Morozzi	09/2022
9571	2^338480+197503	101893	Stefano Morozzi	11/2022
9572	2^338481-11421	101893	Stefano Morozzi	12/2022
9573	2^338479-89649	101893	Stefano Morozzi	01/2023
9574	(29*34^66532-12833)/33	101893	Eric Chen	03/2023
9577	2^338475+54615	101892	Lelio R Paula	10/2016
9575	2^338475-59775	101892	Stefano Morozzi	04/2022
9576	2^338476-134237	101892	Stefano Morozzi	04/2022
9578	2^338474+100767	101891	Stefano Morozzi	11/2021
9579	2^338474+81165	101891	Stefano Morozzi	01/2022
9580	2^338474+41137	101891	Stefano Morozzi	06/2022
9581	2^338472-110445	101891	Stefano Morozzi	06/2022
9582	2^338473-89535	101891	Stefano Morozzi	01/2023
9583	2^338470+27777	101890	Stefano Morozzi	01/2022
9584	2^338468+31351	101890	Stefano Morozzi	01/2022
9585	2^338469-106339	101890	Stefano Morozzi	03/2022
9586	2^338471+187469	101890	Stefano Morozzi	04/2022
9587	2^338468+96613	101890	Stefano Morozzi	11/2022
9588	2^338469+46167	101890	Stefano Morozzi	11/2022
9589	2^338470+71527	101890	Stefano Morozzi	11/2022
9590	2^338469-112783	101890	Stefano Morozzi	12/2022
9591	2^338470-115665	101890	Stefano Morozzi	01/2023
9592	2^338467-25665	101889	Stefano Morozzi	12/2021
9593	2^338465+152139	101889	Stefano Morozzi	12/2021
9594	2^338466-28643	101889	Stefano Morozzi	01/2022
9595	2^338465+181517	101889	Stefano Morozzi	01/2022
9596	2^338466+115917	101889	Stefano Morozzi	06/2022
9597	2^338465-88291	101889	Stefano Morozzi	12/2022
9598	2^338464-104009	101888	Stefano Morozzi	02/2022
9599	2^338463+185169	101888	Stefano Morozzi	03/2022
9600	2^338464+60595	101888	Stefano Morozzi	03/2022
9601	2^338464-66377	101888	Stefano Morozzi	01/2023
9602	2^338458+60273	101887	Stefano Morozzi	03/2022
9603	2^338461+135867	101887	Stefano Morozzi	03/2022
9604	2^338455-4621	101886	Stefano Morozzi	02/2022
9605	2^338457+187827	101886	Stefano Morozzi	04/2022
9606	2^338455+173349	101886	Stefano Morozzi	11/2022
9607	2^338454+133737	101885	Stefano Morozzi	03/2022
9608	2^338454-158501	101885	Stefano Morozzi	04/2022
9609	2^338454-184217	101885	Stefano Morozzi	04/2022
9610	2^338453+164451	101885	Stefano Morozzi	05/2022
9611	2^338452-136137	101885	Stefano Morozzi	12/2022
9612	2^338450+106275	101884	Stefano Morozzi	01/2022
9613	2^338450+168439	101884	Stefano Morozzi	09/2022
9614	(133*10^101881+17)/3	101883	Robert Price	11/2021
9615	2^338445-80461	101883	Stefano Morozzi	02/2022
9616	2^338446-131211	101883	Stefano Morozzi	02/2022
9617	2^338448+187167	101883	Stefano Morozzi	04/2022
9618	2^338446-160115	101883	Stefano Morozzi	06/2022
9619	2^338447-164157	101883	Stefano Morozzi	01/2023
9620	2^338447-191001	101883	Stefano Morozzi	01/2023
9621	2^338444+127623	101882	Stefano Morozzi	12/2021
9622	2^338443-113827	101882	Stefano Morozzi	12/2022
9623	2^338441-5893	101881	Stefano Morozzi	02/2022
9624	2^338439-162565	101881	Stefano Morozzi	12/2022
9625	2^338436+153657	101880	Stefano Morozzi	01/2022
9626	2^338437-153159	101880	Stefano Morozzi	01/2022
9627	2^338436-83783	101880	Stefano Morozzi	04/2022
9628	2^338435+89109	101880	Stefano Morozzi	05/2022
9629	2^338435+13871	101880	Stefano Morozzi	05/2022
9630	2^338436+149691	101880	Stefano Morozzi	02/2023
9631	2^338434+81537	101879	Stefano Morozzi	01/2022
9632	2^338432+33495	101879	Stefano Morozzi	03/2022
9633	2^338432-7043	101879	Stefano Morozzi	03/2022
9634	2^338433-32629	101879	Stefano Morozzi	03/2022
9635	2^338430-9903	101878	Stefano Morozzi	04/2022
9643	2^338426-19797	101877	Enzo Doria	06/2013
9636	2^338427-77797	101877	Stefano Morozzi	01/2022
9637	2^338427-178687	101877	Stefano Morozzi	01/2022
9638	2^338428-54873	101877	Stefano Morozzi	02/2022
9639	2^338425+41357	101877	Stefano Morozzi	06/2022
9640	2^338428+90855	101877	Stefano Morozzi	06/2022
9641	2^338428-39807	101877	Stefano Morozzi	01/2023
9642	2^338425-192381	101877	Stefano Morozzi	02/2023
9644	2^338422-188787	101876	Stefano Morozzi	12/2022
9645	2^338423-187755	101876	Stefano Morozzi	12/2022
9646	2^338422-115865	101876	Stefano Morozzi	01/2023
9647	2^338420-178829	101875	Stefano Morozzi	01/2022
9648	2^338421-105423	101875	Stefano Morozzi	02/2022
9649	2^338419-82761	101875	Stefano Morozzi	03/2022
9650	2^338420+193143	101875	Stefano Morozzi	09/2022
9651	2^338419+199641	101875	Stefano Morozzi	02/2023
9652	2^338420-143103	101875	Stefano Morozzi	02/2023
9653	2^338418-50903	101874	Stefano Morozzi	12/2021
9654	2^338418+158355	101874	Stefano Morozzi	02/2022
9655	2^338418+159339	101874	Stefano Morozzi	03/2022
9656	2^338416+14953	101874	Stefano Morozzi	05/2022
9657	2^338416+166051	101874	Stefano Morozzi	06/2022
9658	2^338418-138765	101874	Stefano Morozzi	12/2022
9659	2^338417+49737	101874	Stefano Morozzi	02/2023
9660	2^338413-125919	101873	Stefano Morozzi	12/2021
9661	2^338414+26083	101873	Stefano Morozzi	12/2021
9662	2^338412-152379	101873	Stefano Morozzi	12/2021
9663	2^338413+54797	101873	Stefano Morozzi	01/2022
9664	2^338412+157951	101873	Stefano Morozzi	02/2022
9665	2^338414+81627	101873	Stefano Morozzi	02/2022
9666	2^338413+133679	101873	Stefano Morozzi	03/2022
9667	2^338413+197735	101873	Stefano Morozzi	11/2022
9668	2^338413-114301	101873	Stefano Morozzi	01/2023
9669	11*32^67682+395	101873	Eric Chen	04/2023
9670	2^338409-52183	101872	Stefano Morozzi	12/2021
9671	2^338411-3789	101872	Stefano Morozzi	01/2022
9672	2^338409+173237	101872	Stefano Morozzi	11/2022
9673	2^338406-184175	101871	Stefano Morozzi	04/2022
9674	2^338405+94451	101871	Stefano Morozzi	09/2022
9675	2^338406-161217	101871	Stefano Morozzi	12/2022
9676	2^338406+199929	101871	Stefano Morozzi	02/2023
9677	2^338404+55717	101870	Stefano Morozzi	01/2022
9678	2^338403+36261	101870	Stefano Morozzi	04/2022
9679	2^338402-34431	101870	Stefano Morozzi	04/2022
9680	2^338404-159215	101870	Stefano Morozzi	04/2022
9681	2^338403+18363	101870	Stefano Morozzi	09/2022
9682	2^338403+170235	101870	Stefano Morozzi	11/2022
9683	2^338399+23045	101869	Stefano Morozzi	11/2022
9684	2^338399-65535	101869	Stefano Morozzi	01/2023
9685	2^338395-127449	101868	Stefano Morozzi	12/2021
9686	2^338398-127637	101868	Stefano Morozzi	01/2022
9687	2^338398-166533	101868	Stefano Morozzi	01/2023
9688	2^338394+100317	101867	Stefano Morozzi	11/2021
9689	2^338393-152749	101867	Stefano Morozzi	01/2022
9690	2^338393+163025	101867	Stefano Morozzi	04/2022
9691	2^338393+89229	101867	Stefano Morozzi	05/2022
9692	2^338393+99647	101867	Stefano Morozzi	02/2023
9693	2^338394-192471	101867	Stefano Morozzi	02/2023
9694	2^338390+76627	101866	Stefano Morozzi	12/2021
9695	2^338389-85081	101866	Stefano Morozzi	06/2022
9696	2^338390+148113	101866	Stefano Morozzi	11/2022
9697	2^338389-14253	101866	Stefano Morozzi	01/2023
9698	2^338390-114297	101866	Stefano Morozzi	01/2023
9699	2^338391-64225	101866	Stefano Morozzi	01/2023
9700	2^338389-16971	101866	Stefano Morozzi	02/2023
9701	2^338387-75685	101865	Stefano Morozzi	12/2021
9702	2^338388-53459	101865	Stefano Morozzi	01/2022
9703	2^338388-36575	101865	Stefano Morozzi	12/2022
9704	2^338385-190311	101865	Stefano Morozzi	01/2023
9705	2^338384+131563	101864	Stefano Morozzi	01/2022
9706	2^338382+109069	101864	Stefano Morozzi	03/2022
9707	2^338384+168987	101864	Stefano Morozzi	09/2022
9708	2^338383-42367	101864	Stefano Morozzi	02/2023
9709	2^338380+77125	101863	Stefano Morozzi	12/2021
9710	2^338381-35539	101863	Stefano Morozzi	06/2022
9711	2^338378-125841	101862	Stefano Morozzi	12/2021
9712	2^338375+27815	101862	Stefano Morozzi	01/2022
9713	2^338375-28509	101862	Stefano Morozzi	01/2022
9714	2^338375+29985	101862	Stefano Morozzi	01/2022
9715	2^338377+157881	101862	Stefano Morozzi	02/2022
9716	2^338375+59589	101862	Stefano Morozzi	03/2022
9717	2^338378+36399	101862	Stefano Morozzi	04/2022
9718	2^338378-159773	101862	Stefano Morozzi	04/2022
9719	2^338378+14883	101862	Stefano Morozzi	05/2022
9720	2^338376+140173	101862	Stefano Morozzi	06/2022
9721	2^338375+18761	101862	Stefano Morozzi	09/2022
9722	2^338373-75103	101861	Stefano Morozzi	12/2021
9723	2^338372+128877	101861	Stefano Morozzi	01/2022
9724	2^338374-28731	101861	Stefano Morozzi	01/2022
9725	2^338374-128427	101861	Stefano Morozzi	01/2022
9726	2^338372+37875	101861	Stefano Morozzi	04/2022
9727	2^338373+161541	101861	Stefano Morozzi	04/2022
9728	2^338374+37759	101861	Stefano Morozzi	04/2022
9729	2^338372+93235	101861	Stefano Morozzi	09/2022
9730	2^338373-63273	101861	Stefano Morozzi	12/2022
9731	2^338369+29427	101860	Stefano Morozzi	01/2022
9732	2^338370+179133	101860	Stefano Morozzi	01/2022
9733	2^338369+131501	101860	Stefano Morozzi	01/2022
9734	2^338369+181649	101860	Stefano Morozzi	02/2022
9735	2^338370-4787	101860	Stefano Morozzi	02/2022
9736	2^338371-133491	101860	Stefano Morozzi	04/2022
9737	2^338371+42023	101860	Stefano Morozzi	09/2022
9738	2^338371+145323	101860	Stefano Morozzi	11/2022
9739	2^338371-138145	101860	Stefano Morozzi	12/2022
9746	2^338368-20369	101859	Enzo Doria	06/2013
9747	2^338366+74179	101859	Enzo Doria	04/2016
9740	2^338366+53853	101859	Stefano Morozzi	01/2022
9741	2^338365-31665	101859	Stefano Morozzi	03/2022
9742	2^338368-156345	101859	Stefano Morozzi	03/2022
9743	2^338366-159867	101859	Stefano Morozzi	04/2022
9744	2^338368-63509	101859	Stefano Morozzi	12/2022
9745	2^338365-190975	101859	Stefano Morozzi	01/2023
9748	2^338362-180845	101858	Stefano Morozzi	02/2022
9749	2^338364-155769	101858	Stefano Morozzi	02/2022
9750	2^338362+142843	101858	Stefano Morozzi	09/2022

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Probable Primes Top 10000

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