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 ?
6501	2^338597-106045	101928	Stefano Morozzi	02/2022
6502	2^338595+119565	101928	Stefano Morozzi	09/2022
6503	2^338595+19623	101928	Stefano Morozzi	09/2022
6504	2^338591+53769	101927	Stefano Morozzi	01/2022
6505	2^338593+156989	101927	Stefano Morozzi	02/2022
6506	2^338592+36157	101927	Stefano Morozzi	03/2022
6507	2^338593+42099	101927	Stefano Morozzi	09/2022
6508	2^338590+182007	101926	Stefano Morozzi	02/2022
6509	2^338590+60747	101926	Stefano Morozzi	03/2022
6510	2^338588+62397	101926	Stefano Morozzi	04/2022
6511	2^338589-9685	101926	Stefano Morozzi	04/2022
6517	(2^338587+2306)/2	101925	Stefano Morozzi	02/2021
6512	2^338586+1153	101925	Stefano Morozzi	12/2021
6513	2^338587-51709	101925	Stefano Morozzi	12/2021
6514	2^338586+105303	101925	Stefano Morozzi	01/2022
6515	2^338585-131773	101925	Stefano Morozzi	03/2022
6516	2^338587+168039	101925	Stefano Morozzi	09/2022
6518	2^338584+100771	101924	Stefano Morozzi	11/2021
6519	2^338581-150415	101924	Stefano Morozzi	12/2021
6520	2^338581-2349	101924	Stefano Morozzi	12/2021
6521	2^338582+42933	101924	Stefano Morozzi	09/2022
6522	2^338584+93267	101924	Stefano Morozzi	09/2022
6523	2^338578+67593	101923	Stefano Morozzi	09/2022
6524	2^338580+142201	101923	Stefano Morozzi	09/2022
6525	2^338575-28815	101922	Stefano Morozzi	01/2022
6526	2^338575-33645	101922	Stefano Morozzi	04/2022
6527	2^338573-156693	101921	Stefano Morozzi	03/2022
6528	2^338572+193305	101921	Stefano Morozzi	09/2022
6531	2^338568+37	101920	Lelio R Paula	07/2011
6529	2^338570-53933	101920	Stefano Morozzi	02/2022
6530	2^338569+87201	101920	Stefano Morozzi	04/2022
6532	2^338567-9619	101919	Stefano Morozzi	04/2022
6533	2^338564-56763	101918	Stefano Morozzi	03/2022
6534	2^338561+112007	101918	Stefano Morozzi	04/2022
6535	2^338561-9315	101918	Stefano Morozzi	04/2022
6536	2^338564+41965	101918	Stefano Morozzi	09/2022
6542	2^338559-1858777	101917	Enzo Doria	04/2016
6537	2^338558+4825	101917	Stefano Morozzi	01/2022
6538	2^338559-127935	101917	Stefano Morozzi	01/2022
6539	2^338560+154891	101917	Stefano Morozzi	01/2022
6540	2^338559+131885	101917	Stefano Morozzi	02/2022
6541	2^338558+93735	101917	Stefano Morozzi	09/2022
6543	2^338555+189981	101916	Stefano Morozzi	05/2022
6544	2^338553-125383	101915	Stefano Morozzi	12/2021
6545	2^338554-82821	101915	Stefano Morozzi	03/2022
6546	2^338548+76923	101914	Stefano Morozzi	12/2021
6547	2^338549+158517	101914	Stefano Morozzi	03/2022
6548	2^338549+85397	101914	Stefano Morozzi	03/2022
6549	2^338548+138121	101914	Stefano Morozzi	05/2022
6550	2^338550-110301	101914	Stefano Morozzi	06/2022
6551	2^338547+129321	101913	Stefano Morozzi	01/2022
6552	2^338547-153481	101913	Stefano Morozzi	01/2022
6553	2^338544+107853	101912	Stefano Morozzi	02/2022
6554	2^338541+152721	101911	Stefano Morozzi	01/2022
6555	2^338539+60825	101911	Stefano Morozzi	03/2022
6556	2^338539+160881	101911	Stefano Morozzi	03/2022
6557	2^338541-182523	101911	Stefano Morozzi	03/2022
6558	2^338540+87645	101911	Stefano Morozzi	04/2022
6559	2^338536-100785	101910	Stefano Morozzi	12/2021
6560	2^338535-51837	101910	Stefano Morozzi	12/2021
6561	2^338535-158745	101910	Stefano Morozzi	04/2022
6562	2^338532+39445	101909	Stefano Morozzi	05/2022
6563	2^338532+141415	101909	Stefano Morozzi	06/2022
6564	2^338532-136037	101909	Stefano Morozzi	06/2022
6565	2^338531+81081	101908	Stefano Morozzi	01/2022
6566	2^338530+59835	101908	Stefano Morozzi	03/2022
6567	2^338529+186551	101908	Stefano Morozzi	04/2022
6568	2^338531+61313	101908	Stefano Morozzi	04/2022
6569	2^338531-9277	101908	Stefano Morozzi	04/2022
6570	2^338527+191205	101907	Stefano Morozzi	06/2022
6571	2^338524+54421	101906	Stefano Morozzi	01/2022
6572	2^338522-155811	101906	Stefano Morozzi	02/2022
6573	2^338521+183131	101905	Stefano Morozzi	02/2022
6574	2^338520+34945	101905	Stefano Morozzi	03/2022
6575	2^338518-182885	101905	Stefano Morozzi	04/2022
6576	2^338518+114633	101905	Stefano Morozzi	05/2022
6583	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
6577	2^338517-125955	101904	Stefano Morozzi	12/2021
6578	2^338517+126437	101904	Stefano Morozzi	12/2021
6579	2^338517-53499	101904	Stefano Morozzi	01/2022
6580	2^338515+30369	101904	Stefano Morozzi	01/2022
6581	2^338517-184623	101904	Stefano Morozzi	04/2022
6582	2^338515+89333	101904	Stefano Morozzi	05/2022
6586	24502^14419+14419^24502	101903	Hans Havermann	01/2019
6584	2^338512-827	101903	Stefano Morozzi	12/2021
6585	2^338514-6611	101903	Stefano Morozzi	03/2022
6587	2^338509+5139	101902	Stefano Morozzi	01/2022
6588	2^338509+40205	101902	Stefano Morozzi	06/2022
6589	2^338511+19959	101902	Stefano Morozzi	09/2022
6590	2^338504-152615	101900	Stefano Morozzi	01/2022
6591	2^338502-4587	101900	Stefano Morozzi	02/2022
6592	2^338500-26865	101899	Stefano Morozzi	12/2021
6593	2^338501-177471	101899	Stefano Morozzi	12/2021
6594	2^338499-3915	101899	Stefano Morozzi	01/2022
6595	2^338501+32051	101899	Stefano Morozzi	02/2022
6596	2^338499+183533	101899	Stefano Morozzi	03/2022
6597	2^338500+35625	101899	Stefano Morozzi	03/2022
6598	2^338499+87579	101899	Stefano Morozzi	04/2022
6601	2^338497-17041	101898	Enzo Doria	05/2013
6599	2^338497+150405	101898	Stefano Morozzi	11/2021
6600	2^338495+100533	101898	Stefano Morozzi	12/2021
6602	2^338494+36057	101897	Stefano Morozzi	03/2022
6603	2^338492+39015	101897	Stefano Morozzi	05/2022
6604	2^338494+168007	101897	Stefano Morozzi	09/2022
6605	2^338490+61149	101896	Stefano Morozzi	03/2022
6606	2^338489+161369	101896	Stefano Morozzi	04/2022
6607	2^338487-3555	101895	Stefano Morozzi	01/2022
6608	2^338487-183129	101895	Stefano Morozzi	04/2022
6609	2^338484+128767	101894	Stefano Morozzi	01/2022
6610	2^338484-31895	101894	Stefano Morozzi	03/2022
6611	2^338478+10893	101893	Stefano Morozzi	03/2022
6612	2^338479+87243	101893	Stefano Morozzi	04/2022
6613	2^338479+167619	101893	Stefano Morozzi	09/2022
6616	2^338475+54615	101892	Lelio R Paula	10/2016
6614	2^338475-59775	101892	Stefano Morozzi	04/2022
6615	2^338476-134237	101892	Stefano Morozzi	04/2022
6617	2^338474+100767	101891	Stefano Morozzi	11/2021
6618	2^338474+81165	101891	Stefano Morozzi	01/2022
6619	2^338474+41137	101891	Stefano Morozzi	06/2022
6620	2^338472-110445	101891	Stefano Morozzi	06/2022
6621	2^338470+27777	101890	Stefano Morozzi	01/2022
6622	2^338468+31351	101890	Stefano Morozzi	01/2022
6623	2^338469-106339	101890	Stefano Morozzi	03/2022
6624	2^338471+187469	101890	Stefano Morozzi	04/2022
6625	2^338467-25665	101889	Stefano Morozzi	12/2021
6626	2^338465+152139	101889	Stefano Morozzi	12/2021
6627	2^338466-28643	101889	Stefano Morozzi	01/2022
6628	2^338465+181517	101889	Stefano Morozzi	01/2022
6629	2^338466+115917	101889	Stefano Morozzi	06/2022
6630	2^338464-104009	101888	Stefano Morozzi	02/2022
6631	2^338463+185169	101888	Stefano Morozzi	03/2022
6632	2^338464+60595	101888	Stefano Morozzi	03/2022
6633	2^338458+60273	101887	Stefano Morozzi	03/2022
6634	2^338461+135867	101887	Stefano Morozzi	03/2022
6635	2^338455-4621	101886	Stefano Morozzi	02/2022
6636	2^338457+187827	101886	Stefano Morozzi	04/2022
6637	2^338454+133737	101885	Stefano Morozzi	03/2022
6638	2^338454-158501	101885	Stefano Morozzi	04/2022
6639	2^338454-184217	101885	Stefano Morozzi	04/2022
6640	2^338453+164451	101885	Stefano Morozzi	05/2022
6641	2^338450+106275	101884	Stefano Morozzi	01/2022
6642	2^338450+168439	101884	Stefano Morozzi	09/2022
6643	(133*10^101881+17)/3	101883	Robert Price	11/2021
6644	2^338445-80461	101883	Stefano Morozzi	02/2022
6645	2^338446-131211	101883	Stefano Morozzi	02/2022
6646	2^338448+187167	101883	Stefano Morozzi	04/2022
6647	2^338446-160115	101883	Stefano Morozzi	06/2022
6648	2^338444+127623	101882	Stefano Morozzi	12/2021
6649	2^338441-5893	101881	Stefano Morozzi	02/2022
6650	2^338436+153657	101880	Stefano Morozzi	01/2022
6651	2^338437-153159	101880	Stefano Morozzi	01/2022
6652	2^338436-83783	101880	Stefano Morozzi	04/2022
6653	2^338435+89109	101880	Stefano Morozzi	05/2022
6654	2^338435+13871	101880	Stefano Morozzi	05/2022
6655	2^338434+81537	101879	Stefano Morozzi	01/2022
6656	2^338432+33495	101879	Stefano Morozzi	03/2022
6657	2^338432-7043	101879	Stefano Morozzi	03/2022
6658	2^338433-32629	101879	Stefano Morozzi	03/2022
6659	2^338430-9903	101878	Stefano Morozzi	04/2022
6665	2^338426-19797	101877	Enzo Doria	06/2013
6660	2^338427-77797	101877	Stefano Morozzi	01/2022
6661	2^338427-178687	101877	Stefano Morozzi	01/2022
6662	2^338428-54873	101877	Stefano Morozzi	02/2022
6663	2^338425+41357	101877	Stefano Morozzi	06/2022
6664	2^338428+90855	101877	Stefano Morozzi	06/2022
6666	2^338420-178829	101875	Stefano Morozzi	01/2022
6667	2^338421-105423	101875	Stefano Morozzi	02/2022
6668	2^338419-82761	101875	Stefano Morozzi	03/2022
6669	2^338420+193143	101875	Stefano Morozzi	09/2022
6670	2^338418-50903	101874	Stefano Morozzi	12/2021
6671	2^338418+158355	101874	Stefano Morozzi	02/2022
6672	2^338418+159339	101874	Stefano Morozzi	03/2022
6673	2^338416+14953	101874	Stefano Morozzi	05/2022
6674	2^338416+166051	101874	Stefano Morozzi	06/2022
6675	2^338413-125919	101873	Stefano Morozzi	12/2021
6676	2^338414+26083	101873	Stefano Morozzi	12/2021
6677	2^338412-152379	101873	Stefano Morozzi	12/2021
6678	2^338413+54797	101873	Stefano Morozzi	01/2022
6679	2^338412+157951	101873	Stefano Morozzi	02/2022
6680	2^338414+81627	101873	Stefano Morozzi	02/2022
6681	2^338413+133679	101873	Stefano Morozzi	03/2022
6682	2^338409-52183	101872	Stefano Morozzi	12/2021
6683	2^338411-3789	101872	Stefano Morozzi	01/2022
6684	2^338406-184175	101871	Stefano Morozzi	04/2022
6685	2^338405+94451	101871	Stefano Morozzi	09/2022
6686	2^338404+55717	101870	Stefano Morozzi	01/2022
6687	2^338403+36261	101870	Stefano Morozzi	04/2022
6688	2^338402-34431	101870	Stefano Morozzi	04/2022
6689	2^338404-159215	101870	Stefano Morozzi	04/2022
6690	2^338403+18363	101870	Stefano Morozzi	09/2022
6691	2^338395-127449	101868	Stefano Morozzi	12/2021
6692	2^338398-127637	101868	Stefano Morozzi	01/2022
6693	2^338394+100317	101867	Stefano Morozzi	11/2021
6694	2^338393-152749	101867	Stefano Morozzi	01/2022
6695	2^338393+163025	101867	Stefano Morozzi	04/2022
6696	2^338393+89229	101867	Stefano Morozzi	05/2022
6697	2^338390+76627	101866	Stefano Morozzi	12/2021
6698	2^338389-85081	101866	Stefano Morozzi	06/2022
6699	2^338387-75685	101865	Stefano Morozzi	12/2021
6700	2^338388-53459	101865	Stefano Morozzi	01/2022
6701	2^338384+131563	101864	Stefano Morozzi	01/2022
6702	2^338382+109069	101864	Stefano Morozzi	03/2022
6703	2^338384+168987	101864	Stefano Morozzi	09/2022
6704	2^338380+77125	101863	Stefano Morozzi	12/2021
6705	2^338381-35539	101863	Stefano Morozzi	06/2022
6706	2^338378-125841	101862	Stefano Morozzi	12/2021
6707	2^338375+27815	101862	Stefano Morozzi	01/2022
6708	2^338375-28509	101862	Stefano Morozzi	01/2022
6709	2^338375+29985	101862	Stefano Morozzi	01/2022
6710	2^338377+157881	101862	Stefano Morozzi	02/2022
6711	2^338375+59589	101862	Stefano Morozzi	03/2022
6712	2^338378+36399	101862	Stefano Morozzi	04/2022
6713	2^338378-159773	101862	Stefano Morozzi	04/2022
6714	2^338378+14883	101862	Stefano Morozzi	05/2022
6715	2^338376+140173	101862	Stefano Morozzi	06/2022
6716	2^338375+18761	101862	Stefano Morozzi	09/2022
6717	2^338373-75103	101861	Stefano Morozzi	12/2021
6718	2^338372+128877	101861	Stefano Morozzi	01/2022
6719	2^338374-28731	101861	Stefano Morozzi	01/2022
6720	2^338374-128427	101861	Stefano Morozzi	01/2022
6721	2^338372+37875	101861	Stefano Morozzi	04/2022
6722	2^338373+161541	101861	Stefano Morozzi	04/2022
6723	2^338374+37759	101861	Stefano Morozzi	04/2022
6724	2^338372+93235	101861	Stefano Morozzi	09/2022
6725	2^338369+29427	101860	Stefano Morozzi	01/2022
6726	2^338370+179133	101860	Stefano Morozzi	01/2022
6727	2^338369+131501	101860	Stefano Morozzi	01/2022
6728	2^338369+181649	101860	Stefano Morozzi	02/2022
6729	2^338370-4787	101860	Stefano Morozzi	02/2022
6730	2^338371-133491	101860	Stefano Morozzi	04/2022
6731	2^338371+42023	101860	Stefano Morozzi	09/2022
6736	2^338368-20369	101859	Enzo Doria	06/2013
6737	2^338366+74179	101859	Enzo Doria	04/2016
6732	2^338366+53853	101859	Stefano Morozzi	01/2022
6733	2^338365-31665	101859	Stefano Morozzi	03/2022
6734	2^338368-156345	101859	Stefano Morozzi	03/2022
6735	2^338366-159867	101859	Stefano Morozzi	04/2022
6738	2^338362-180845	101858	Stefano Morozzi	02/2022
6739	2^338364-155769	101858	Stefano Morozzi	02/2022
6740	2^338362+142843	101858	Stefano Morozzi	09/2022
6741	2^338361-100875	101857	Stefano Morozzi	12/2021
6742	2^338361+154169	101857	Stefano Morozzi	01/2022
6743	2^338356+101271	101856	Stefano Morozzi	12/2021
6744	2^338356+53383	101856	Stefano Morozzi	01/2022
6745	2^338355+59393	101856	Stefano Morozzi	03/2022
6746	2^338356+60775	101856	Stefano Morozzi	03/2022
6747	2^338356-106257	101856	Stefano Morozzi	03/2022
6748	2^338357-58921	101856	Stefano Morozzi	04/2022
6749	2^338356+94605	101856	Stefano Morozzi	09/2022
6750	2^338356+117813	101856	Stefano Morozzi	09/2022

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PRP Records

Probable Primes Top 10000

(291192 PRPs in the top)