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	2^338299-189985	101839	Stefano Morozzi	01/2023
9502	2^338298-25571	101838	Stefano Morozzi	12/2021
9503	2^338297+35547	101838	Stefano Morozzi	03/2022
9504	2^338298+111199	101838	Stefano Morozzi	03/2022
9505	2^338297+145455	101838	Stefano Morozzi	11/2022
9506	2^338297-166285	101838	Stefano Morozzi	01/2023
9507	2^338294-150711	101837	Stefano Morozzi	12/2021
9508	2^338294+177597	101837	Stefano Morozzi	12/2021
9509	2^338294-177807	101837	Stefano Morozzi	01/2022
9510	2^338295-52929	101837	Stefano Morozzi	01/2022
9511	2^338293+37407	101837	Stefano Morozzi	04/2022
9512	2^338292+40573	101837	Stefano Morozzi	06/2022
9513	2^338294+172425	101837	Stefano Morozzi	11/2022
9514	2^338293-191799	101837	Stefano Morozzi	02/2023
9515	2^338289+30957	101836	Stefano Morozzi	01/2022
9516	2^338291+131825	101836	Stefano Morozzi	02/2022
9517	2^338291+110111	101836	Stefano Morozzi	03/2022
9518	2^338290-156423	101836	Stefano Morozzi	03/2022
9519	2^338291-157845	101836	Stefano Morozzi	03/2022
9520	2^338290+69243	101836	Stefano Morozzi	09/2022
9521	2^338291-189327	101836	Stefano Morozzi	01/2023
9522	2^338291+74079	101836	Stefano Morozzi	02/2023
9523	2^338288+26623	101835	Stefano Morozzi	12/2021
9524	2^338286+33325	101835	Stefano Morozzi	02/2022
9525	2^338287+132633	101835	Stefano Morozzi	02/2022
9526	2^338287+157149	101835	Stefano Morozzi	02/2022
9527	2^338288-107193	101835	Stefano Morozzi	03/2022
9528	2^338286-83333	101835	Stefano Morozzi	04/2022
9529	2^338287+114425	101835	Stefano Morozzi	05/2022
9530	2^338288+194403	101835	Stefano Morozzi	09/2022
9531	2^338288-113177	101835	Stefano Morozzi	12/2022
9532	2^338288-65747	101835	Stefano Morozzi	01/2023
9533	2^338285+82131	101834	Stefano Morozzi	02/2022
9534	2^338284-104217	101834	Stefano Morozzi	02/2022
9535	2^338282-84533	101834	Stefano Morozzi	04/2022
9536	2^338283+67545	101834	Stefano Morozzi	09/2022
9537	2^338283-65439	101834	Stefano Morozzi	01/2023
9546	2^338280-19745	101833	Enzo Doria	06/2013
9538	2^338279-125947	101833	Stefano Morozzi	12/2021
9539	2^338280-50343	101833	Stefano Morozzi	12/2021
9540	2^338279+133331	101833	Stefano Morozzi	02/2022
9541	2^338281-54561	101833	Stefano Morozzi	02/2022
9542	2^338280+192063	101833	Stefano Morozzi	09/2022
9543	2^338281+18971	101833	Stefano Morozzi	09/2022
9544	2^338281-186711	101833	Stefano Morozzi	12/2022
9545	2^338281-91273	101833	Stefano Morozzi	01/2023
9547	2^338278+188215	101832	Stefano Morozzi	05/2022
9548	2^338273+181101	101831	Stefano Morozzi	01/2022
9549	2^338275+32909	101831	Stefano Morozzi	02/2022
9550	2^338272+166431	101831	Stefano Morozzi	06/2022
9551	2^338272+22011	101831	Stefano Morozzi	11/2022
9552	2^338275+148271	101831	Stefano Morozzi	11/2022
9553	2^338270-135725	101830	Stefano Morozzi	06/2022
9554	2^338269-136951	101830	Stefano Morozzi	12/2022
9555	2^338270-192701	101830	Stefano Morozzi	02/2023
9556	2^338271-42831	101830	Stefano Morozzi	02/2023
9557	2^338266+110665	101829	Stefano Morozzi	03/2022
9558	2^338267+110481	101829	Stefano Morozzi	03/2022
9559	2^338267-166035	101829	Stefano Morozzi	01/2023
9560	2^338265-154893	101828	Stefano Morozzi	02/2022
9561	2^338264+163611	101828	Stefano Morozzi	05/2022
9562	2^338263-62767	101828	Stefano Morozzi	12/2022
9563	2^338261-188119	101827	Stefano Morozzi	12/2022
9564	2^338259-40327	101827	Stefano Morozzi	01/2023
9565	2^338256+5223	101826	Stefano Morozzi	01/2022
9566	2^338257+178425	101826	Stefano Morozzi	01/2022
9567	2^338256-180569	101826	Stefano Morozzi	02/2022
9568	2^338257-5965	101826	Stefano Morozzi	02/2022
9569	2^338258-9225	101826	Stefano Morozzi	04/2022
9570	2^338255-127021	101825	Stefano Morozzi	12/2021
9571	2^338253+159005	101825	Stefano Morozzi	03/2022
9572	2^338253+64817	101825	Stefano Morozzi	05/2022
9573	2^338254-85403	101825	Stefano Morozzi	06/2022
9574	2^338254+142947	101825	Stefano Morozzi	09/2022
9575	2^338253+121095	101825	Stefano Morozzi	11/2022
9576	2^338254+196725	101825	Stefano Morozzi	11/2022
9577	2^338254-91007	101825	Stefano Morozzi	01/2023
9578	2^338251+78975	101824	Stefano Morozzi	01/2022
9579	2^338252-178709	101824	Stefano Morozzi	01/2022
9580	2^338252+129703	101824	Stefano Morozzi	01/2022
9581	2^338252+132285	101824	Stefano Morozzi	02/2022
9582	2^338251-33381	101824	Stefano Morozzi	04/2022
9583	2^338252-13805	101824	Stefano Morozzi	12/2022
9584	2^338245-134755	101822	Stefano Morozzi	04/2022
9585	2^338244-59219	101822	Stefano Morozzi	04/2022
9586	2^338244-64703	101822	Stefano Morozzi	01/2023
9594	(2^338242+2782)/2	101821	Stefano Morozzi	02/2021
9587	2^338241+1391	101821	Stefano Morozzi	12/2021
9588	2^338242+151195	101821	Stefano Morozzi	12/2021
9589	2^338240-152495	101821	Stefano Morozzi	12/2021
9590	2^338240+81745	101821	Stefano Morozzi	02/2022
9591	2^338241-155551	101821	Stefano Morozzi	02/2022
9592	2^338242-108237	101821	Stefano Morozzi	04/2022
9593	2^338242+43045	101821	Stefano Morozzi	09/2022
9595	2^338238-126735	101820	Stefano Morozzi	12/2021
9596	2^338238+183855	101820	Stefano Morozzi	03/2022
9597	2^338238+141013	101820	Stefano Morozzi	06/2022
9598	2^338237+97227	101820	Stefano Morozzi	11/2022
9599	2^338238+48429	101820	Stefano Morozzi	11/2022
9600	2^338234-80925	101819	Stefano Morozzi	02/2022
9601	2^338234-154593	101819	Stefano Morozzi	02/2022
9602	2^338235-131787	101819	Stefano Morozzi	03/2022
9603	2^338233+89781	101819	Stefano Morozzi	05/2022
9604	2^338235+169971	101819	Stefano Morozzi	11/2022
9605	2^338233-113875	101819	Stefano Morozzi	12/2022
9612	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
9606	2^338232-175539	101818	Stefano Morozzi	12/2021
9607	2^338231+57345	101818	Stefano Morozzi	02/2022
9608	2^338232+36097	101818	Stefano Morozzi	03/2022
9609	2^338230+137403	101818	Stefano Morozzi	04/2022
9610	2^338231-59569	101818	Stefano Morozzi	04/2022
9611	2^338230-86633	101818	Stefano Morozzi	12/2022
9613	2^338228+159247	101817	Stefano Morozzi	03/2022
9614	2^338227-12631	101817	Stefano Morozzi	12/2022
9615	(34*10^101815+191)/9	101816	Robert Price	08/2021
9616	2^338224+185461	101816	Stefano Morozzi	03/2022
9617	2^338224+62295	101816	Stefano Morozzi	04/2022
9618	2^338225+162645	101816	Stefano Morozzi	04/2022
9619	2^338223+144209	101816	Stefano Morozzi	09/2022
9626	6^130841+103	101815	Lelio R Paula	10/2016
9620	2^338220+150405	101815	Stefano Morozzi	11/2021
9621	2^338219-4147	101815	Stefano Morozzi	01/2022
9622	2^338221+83391	101815	Stefano Morozzi	02/2022
9623	2^338221+62937	101815	Stefano Morozzi	04/2022
9624	2^338220-65697	101815	Stefano Morozzi	01/2023
9625	2^338220-139505	101815	Stefano Morozzi	01/2023
9627	2^338216+77473	101814	Stefano Morozzi	12/2021
9628	2^338218+155299	101814	Stefano Morozzi	01/2022
9629	2^338217-134745	101814	Stefano Morozzi	04/2022
9630	2^338218+73507	101814	Stefano Morozzi	11/2022
9631	2^338213-125631	101813	Stefano Morozzi	12/2021
9632	2^338215+25845	101813	Stefano Morozzi	12/2021
9633	2^338210-153537	101812	Stefano Morozzi	01/2022
9634	2^338209+60915	101812	Stefano Morozzi	03/2022
9635	2^338211-57297	101812	Stefano Morozzi	03/2022
9636	2^338211-110257	101812	Stefano Morozzi	06/2022
9637	2^338211+71549	101812	Stefano Morozzi	11/2022
9638	2^338208-178787	101811	Stefano Morozzi	01/2022
9639	2^338208+106153	101811	Stefano Morozzi	01/2022
9640	2^338207+16499	101811	Stefano Morozzi	06/2022
9641	2^338205+102471	101810	Stefano Morozzi	12/2021
9642	2^338199-176377	101809	Stefano Morozzi	12/2021
9643	2^338201-151233	101809	Stefano Morozzi	12/2021
9644	2^338202-152061	101809	Stefano Morozzi	12/2021
9645	2^338202+133785	101809	Stefano Morozzi	03/2022
9646	2^338200+135643	101809	Stefano Morozzi	03/2022
9647	2^338202+14169	101809	Stefano Morozzi	05/2022
9648	2^338202-85211	101809	Stefano Morozzi	06/2022
9649	2^338200+74265	101809	Stefano Morozzi	02/2023
9650	2^338196+121147	101808	Stefano Morozzi	11/2022
9651	2^338196+73551	101808	Stefano Morozzi	11/2022
9652	2^338194-175845	101807	Stefano Morozzi	12/2021
9653	2^338195+56771	101807	Stefano Morozzi	02/2022
9654	2^338195+162365	101807	Stefano Morozzi	04/2022
9655	2^338194+67497	101807	Stefano Morozzi	09/2022
9656	2^338193-116335	101807	Stefano Morozzi	01/2023
9657	2^338194-15585	101807	Stefano Morozzi	01/2023
9658	2^338192+130387	101806	Stefano Morozzi	01/2022
9659	2^338190+89359	101806	Stefano Morozzi	05/2022
9660	2^338189+144605	101806	Stefano Morozzi	09/2022
9661	2^338190-113537	101806	Stefano Morozzi	12/2022
9662	2^338186+127245	101805	Stefano Morozzi	12/2021
9663	2^338186-130013	101805	Stefano Morozzi	02/2022
9664	2^338186+39235	101805	Stefano Morozzi	05/2022
9665	2^338185+77315	101804	Stefano Morozzi	12/2021
9666	2^338185+102519	101804	Stefano Morozzi	12/2021
9667	2^338183-76539	101804	Stefano Morozzi	12/2021
9668	2^338185+104489	101804	Stefano Morozzi	01/2022
9669	2^338179+35361	101803	Stefano Morozzi	03/2022
9670	2^338181+64235	101803	Stefano Morozzi	05/2022
9671	2^338181+94047	101803	Stefano Morozzi	09/2022
9672	2^338180+146131	101803	Stefano Morozzi	11/2022
9673	2^338179+123399	101803	Stefano Morozzi	11/2022
9674	2^338182-42425	101803	Stefano Morozzi	02/2023
9675	2^338177+51807	101802	Stefano Morozzi	12/2021
9676	2^338177+107385	101802	Stefano Morozzi	02/2022
9677	2^338178+34287	101802	Stefano Morozzi	03/2022
9678	2^338178+184207	101802	Stefano Morozzi	03/2022
9679	2^338177-108901	101802	Stefano Morozzi	04/2022
9680	2^338177+141569	101802	Stefano Morozzi	06/2022
9681	2^338176+46221	101802	Stefano Morozzi	11/2022
9682	2^338175+25161	101801	Stefano Morozzi	11/2021
9683	2^338173-27901	101801	Stefano Morozzi	01/2022
9684	2^338174+23217	101801	Stefano Morozzi	11/2022
9685	2^338174+23793	101801	Stefano Morozzi	11/2022
9686	2^338173-36183	101801	Stefano Morozzi	12/2022
9687	2^338173-137053	101801	Stefano Morozzi	12/2022
9688	2^338174-36797	101801	Stefano Morozzi	12/2022
9689	2^338175-166509	101801	Stefano Morozzi	01/2023
9690	2^338169-155965	101800	Stefano Morozzi	02/2022
9691	2^338172+95797	101800	Stefano Morozzi	11/2022
9692	2^338171-117987	101800	Stefano Morozzi	02/2023
9693	2^338166+183237	101799	Stefano Morozzi	02/2022
9694	2^338168-157835	101799	Stefano Morozzi	03/2022
9695	2^338166+137107	101799	Stefano Morozzi	04/2022
9696	2^338166+22897	101799	Stefano Morozzi	11/2022
9697	2^338166-161123	101799	Stefano Morozzi	12/2022
9698	2^338165-152139	101798	Stefano Morozzi	12/2021
9699	2^338163-178947	101798	Stefano Morozzi	02/2022
9700	2^338164-64329	101798	Stefano Morozzi	01/2023
9701	2^338159-127575	101797	Stefano Morozzi	12/2021
9702	2^338161+154259	101797	Stefano Morozzi	01/2022
9703	2^338160+139947	101797	Stefano Morozzi	05/2022
9704	2^338160+191815	101797	Stefano Morozzi	09/2022
9705	2^338160+22207	101797	Stefano Morozzi	11/2022
9706	2^338161+196157	101797	Stefano Morozzi	11/2022
9707	2^338162-138635	101797	Stefano Morozzi	12/2022
9708	2^338156-75269	101796	Stefano Morozzi	12/2021
9709	2^338156-151247	101796	Stefano Morozzi	12/2021
9710	2^338156+103273	101796	Stefano Morozzi	01/2022
9711	2^338156+167053	101796	Stefano Morozzi	09/2022
9712	2^338158+69303	101796	Stefano Morozzi	09/2022
9713	2^338158+171189	101796	Stefano Morozzi	11/2022
9714	2^338157-188989	101796	Stefano Morozzi	12/2022
9715	2^338158-188711	101796	Stefano Morozzi	12/2022
9716	2^338155+132621	101795	Stefano Morozzi	02/2022
9717	2^338155-82605	101795	Stefano Morozzi	03/2022
9718	2^338155-182631	101795	Stefano Morozzi	03/2022
9719	2^338155+187755	101795	Stefano Morozzi	04/2022
9720	2^338154-83975	101795	Stefano Morozzi	04/2022
9721	2^338154+163759	101795	Stefano Morozzi	05/2022
9722	2^338152-25767	101794	Stefano Morozzi	12/2021
9723	2^338152+181927	101794	Stefano Morozzi	02/2022
9724	2^338151+60779	101794	Stefano Morozzi	03/2022
9725	2^338151+189149	101794	Stefano Morozzi	05/2022
9726	2^338152+45567	101794	Stefano Morozzi	11/2022
9727	2^338147+29343	101793	Stefano Morozzi	01/2022
9728	2^338148+130803	101793	Stefano Morozzi	01/2022
9729	2^338146+166167	101793	Stefano Morozzi	06/2022
9730	2^338149-185073	101793	Stefano Morozzi	06/2022
9731	2^338149+41757	101793	Stefano Morozzi	09/2022
9732	2^338149+125015	101793	Stefano Morozzi	02/2023
9733	2^338144+180697	101792	Stefano Morozzi	01/2022
9734	2^338143+8589	101792	Stefano Morozzi	02/2022
9735	2^338143-55611	101792	Stefano Morozzi	02/2022
9736	2^338143+60623	101792	Stefano Morozzi	03/2022
9737	2^338145-63609	101792	Stefano Morozzi	12/2022
9738	2^338141-77301	101791	Stefano Morozzi	12/2021
9739	2^338141+157145	101791	Stefano Morozzi	02/2022
9740	2^338140+84745	101791	Stefano Morozzi	03/2022
9741	2^338140+90073	101791	Stefano Morozzi	05/2022
9742	2^338142+96583	101791	Stefano Morozzi	11/2022
9743	2^338139-134719	101790	Stefano Morozzi	04/2022
9744	2^338138+95443	101790	Stefano Morozzi	11/2022
9745	2^338133+1445	101789	Stefano Morozzi	12/2021
9746	2^338133+172469	101789	Stefano Morozzi	11/2022
9747	2^338134+23235	101789	Stefano Morozzi	11/2022
9748	2^338132+105643	101788	Stefano Morozzi	01/2022
9749	2^338131+181871	101788	Stefano Morozzi	02/2022
9750	2^338132-184539	101788	Stefano Morozzi	04/2022

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Probable Primes Top 10000

(300560 PRPs in the top)