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 ?
6501	2^338370-4787	101860	Stefano Morozzi	02/2022
6502	2^338371-133491	101860	Stefano Morozzi	04/2022
6507	2^338368-20369	101859	Enzo Doria	06/2013
6508	2^338366+74179	101859	Enzo Doria	04/2016
6503	2^338366+53853	101859	Stefano Morozzi	01/2022
6504	2^338365-31665	101859	Stefano Morozzi	03/2022
6505	2^338368-156345	101859	Stefano Morozzi	03/2022
6506	2^338366-159867	101859	Stefano Morozzi	04/2022
6509	2^338362-180845	101858	Stefano Morozzi	02/2022
6510	2^338364-155769	101858	Stefano Morozzi	02/2022
6511	2^338361-100875	101857	Stefano Morozzi	12/2021
6512	2^338361+154169	101857	Stefano Morozzi	01/2022
6513	2^338356+101271	101856	Stefano Morozzi	12/2021
6514	2^338356+53383	101856	Stefano Morozzi	01/2022
6515	2^338355+59393	101856	Stefano Morozzi	03/2022
6516	2^338356+60775	101856	Stefano Morozzi	03/2022
6517	2^338356-106257	101856	Stefano Morozzi	03/2022
6518	2^338357-58921	101856	Stefano Morozzi	04/2022
6519	2^338350-152933	101854	Stefano Morozzi	01/2022
6520	2^338350+6337	101854	Stefano Morozzi	01/2022
6522	27088^5755+5755^27088	101853	Hans Havermann	01/2019
6521	2^338347+125901	101853	Stefano Morozzi	11/2021
6523	2^338343+152271	101852	Stefano Morozzi	12/2021
6524	2^338345+154107	101852	Stefano Morozzi	01/2022
6525	2^338342+155397	101852	Stefano Morozzi	01/2022
6526	2^338342-130767	101852	Stefano Morozzi	02/2022
6527	2^338345-30123	101852	Stefano Morozzi	02/2022
6528	2^338345+35747	101852	Stefano Morozzi	03/2022
6529	2^338345-133131	101852	Stefano Morozzi	04/2022
6530	2^338345-134559	101852	Stefano Morozzi	04/2022
6531	2^338339+2753	101851	Stefano Morozzi	12/2021
6532	2^338341+128415	101851	Stefano Morozzi	01/2022
6533	2^338338+2677	101850	Stefano Morozzi	12/2021
6534	2^338336+54607	101850	Stefano Morozzi	01/2022
6535	2^338338+109999	101850	Stefano Morozzi	03/2022
6536	2^338336+161575	101850	Stefano Morozzi	04/2022
6537	2^338335+51975	101849	Stefano Morozzi	12/2021
6538	2^338335-152607	101849	Stefano Morozzi	01/2022
6539	2^338334+55273	101849	Stefano Morozzi	01/2022
6540	2^338332+34315	101849	Stefano Morozzi	03/2022
6541	2^338335+158759	101849	Stefano Morozzi	03/2022
6542	2^338331+83403	101848	Stefano Morozzi	02/2022
6543	2^338328-5295	101847	Stefano Morozzi	02/2022
6544	2^338324-179667	101846	Stefano Morozzi	02/2022
6545	2^338316-175857	101844	Stefano Morozzi	12/2021
6546	2^338318+54405	101844	Stefano Morozzi	01/2022
6547	2^338316+32961	101844	Stefano Morozzi	02/2022
6548	2^338315-178635	101843	Stefano Morozzi	01/2022
6549	2^338315+34899	101843	Stefano Morozzi	03/2022
6550	2^338314-106973	101843	Stefano Morozzi	03/2022
6551	2^338311-51799	101842	Stefano Morozzi	12/2021
6552	2^338309+157259	101842	Stefano Morozzi	02/2022
6553	2^338308-55853	101841	Stefano Morozzi	02/2022
6554	2^338307+134871	101841	Stefano Morozzi	03/2022
6555	2^338304+78757	101840	Stefano Morozzi	01/2022
6556	2^338304-5807	101840	Stefano Morozzi	02/2022
6557	2^338305+110879	101840	Stefano Morozzi	03/2022
6558	2^338299+85611	101839	Stefano Morozzi	03/2022
6559	2^338298-25571	101838	Stefano Morozzi	12/2021
6560	2^338297+35547	101838	Stefano Morozzi	03/2022
6561	2^338298+111199	101838	Stefano Morozzi	03/2022
6562	2^338294-150711	101837	Stefano Morozzi	12/2021
6563	2^338294+177597	101837	Stefano Morozzi	12/2021
6564	2^338294-177807	101837	Stefano Morozzi	01/2022
6565	2^338295-52929	101837	Stefano Morozzi	01/2022
6566	2^338293+37407	101837	Stefano Morozzi	04/2022
6567	2^338289+30957	101836	Stefano Morozzi	01/2022
6568	2^338291+131825	101836	Stefano Morozzi	02/2022
6569	2^338291+110111	101836	Stefano Morozzi	03/2022
6570	2^338290-156423	101836	Stefano Morozzi	03/2022
6571	2^338291-157845	101836	Stefano Morozzi	03/2022
6572	2^338288+26623	101835	Stefano Morozzi	12/2021
6573	2^338286+33325	101835	Stefano Morozzi	02/2022
6574	2^338287+132633	101835	Stefano Morozzi	02/2022
6575	2^338287+157149	101835	Stefano Morozzi	02/2022
6576	2^338288-107193	101835	Stefano Morozzi	03/2022
6577	2^338286-83333	101835	Stefano Morozzi	04/2022
6578	2^338287+114425	101835	Stefano Morozzi	05/2022
6579	2^338285+82131	101834	Stefano Morozzi	02/2022
6580	2^338284-104217	101834	Stefano Morozzi	02/2022
6581	2^338282-84533	101834	Stefano Morozzi	04/2022
6586	2^338280-19745	101833	Enzo Doria	06/2013
6582	2^338279-125947	101833	Stefano Morozzi	12/2021
6583	2^338280-50343	101833	Stefano Morozzi	12/2021
6584	2^338279+133331	101833	Stefano Morozzi	02/2022
6585	2^338281-54561	101833	Stefano Morozzi	02/2022
6587	2^338278+188215	101832	Stefano Morozzi	05/2022
6588	2^338273+181101	101831	Stefano Morozzi	01/2022
6589	2^338275+32909	101831	Stefano Morozzi	02/2022
6590	2^338266+110665	101829	Stefano Morozzi	03/2022
6591	2^338267+110481	101829	Stefano Morozzi	03/2022
6592	2^338265-154893	101828	Stefano Morozzi	02/2022
6593	2^338264+163611	101828	Stefano Morozzi	05/2022
6594	2^338256+5223	101826	Stefano Morozzi	01/2022
6595	2^338257+178425	101826	Stefano Morozzi	01/2022
6596	2^338256-180569	101826	Stefano Morozzi	02/2022
6597	2^338257-5965	101826	Stefano Morozzi	02/2022
6598	2^338258-9225	101826	Stefano Morozzi	04/2022
6599	2^338255-127021	101825	Stefano Morozzi	12/2021
6600	2^338253+159005	101825	Stefano Morozzi	03/2022
6601	2^338253+64817	101825	Stefano Morozzi	05/2022
6602	2^338251+78975	101824	Stefano Morozzi	01/2022
6603	2^338252-178709	101824	Stefano Morozzi	01/2022
6604	2^338252+129703	101824	Stefano Morozzi	01/2022
6605	2^338252+132285	101824	Stefano Morozzi	02/2022
6606	2^338251-33381	101824	Stefano Morozzi	04/2022
6607	2^338245-134755	101822	Stefano Morozzi	04/2022
6608	2^338244-59219	101822	Stefano Morozzi	04/2022
6615	(2^338242+2782)/2	101821	Stefano Morozzi	02/2021
6609	2^338241+1391	101821	Stefano Morozzi	12/2021
6610	2^338242+151195	101821	Stefano Morozzi	12/2021
6611	2^338240-152495	101821	Stefano Morozzi	12/2021
6612	2^338240+81745	101821	Stefano Morozzi	02/2022
6613	2^338241-155551	101821	Stefano Morozzi	02/2022
6614	2^338242-108237	101821	Stefano Morozzi	04/2022
6616	2^338238-126735	101820	Stefano Morozzi	12/2021
6617	2^338238+183855	101820	Stefano Morozzi	03/2022
6618	2^338234-80925	101819	Stefano Morozzi	02/2022
6619	2^338234-154593	101819	Stefano Morozzi	02/2022
6620	2^338235-131787	101819	Stefano Morozzi	03/2022
6621	2^338233+89781	101819	Stefano Morozzi	05/2022
6627	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
6622	2^338232-175539	101818	Stefano Morozzi	12/2021
6623	2^338231+57345	101818	Stefano Morozzi	02/2022
6624	2^338232+36097	101818	Stefano Morozzi	03/2022
6625	2^338230+137403	101818	Stefano Morozzi	04/2022
6626	2^338231-59569	101818	Stefano Morozzi	04/2022
6628	2^338228+159247	101817	Stefano Morozzi	03/2022
6629	(34*10^101815+191)/9	101816	Robert Price	08/2021
6630	2^338224+185461	101816	Stefano Morozzi	03/2022
6631	2^338224+62295	101816	Stefano Morozzi	04/2022
6632	2^338225+162645	101816	Stefano Morozzi	04/2022
6637	6^130841+103	101815	Lelio R Paula	10/2016
6633	2^338220+150405	101815	Stefano Morozzi	11/2021
6634	2^338219-4147	101815	Stefano Morozzi	01/2022
6635	2^338221+83391	101815	Stefano Morozzi	02/2022
6636	2^338221+62937	101815	Stefano Morozzi	04/2022
6638	2^338216+77473	101814	Stefano Morozzi	12/2021
6639	2^338218+155299	101814	Stefano Morozzi	01/2022
6640	2^338217-134745	101814	Stefano Morozzi	04/2022
6641	2^338213-125631	101813	Stefano Morozzi	12/2021
6642	2^338215+25845	101813	Stefano Morozzi	12/2021
6643	2^338210-153537	101812	Stefano Morozzi	01/2022
6644	2^338209+60915	101812	Stefano Morozzi	03/2022
6645	2^338211-57297	101812	Stefano Morozzi	03/2022
6646	2^338208-178787	101811	Stefano Morozzi	01/2022
6647	2^338208+106153	101811	Stefano Morozzi	01/2022
6648	2^338205+102471	101810	Stefano Morozzi	12/2021
6649	2^338199-176377	101809	Stefano Morozzi	12/2021
6650	2^338201-151233	101809	Stefano Morozzi	12/2021
6651	2^338202-152061	101809	Stefano Morozzi	12/2021
6652	2^338202+133785	101809	Stefano Morozzi	03/2022
6653	2^338200+135643	101809	Stefano Morozzi	03/2022
6654	2^338202+14169	101809	Stefano Morozzi	05/2022
6655	2^338194-175845	101807	Stefano Morozzi	12/2021
6656	2^338195+56771	101807	Stefano Morozzi	02/2022
6657	2^338195+162365	101807	Stefano Morozzi	04/2022
6658	2^338192+130387	101806	Stefano Morozzi	01/2022
6659	2^338190+89359	101806	Stefano Morozzi	05/2022
6660	2^338186+127245	101805	Stefano Morozzi	12/2021
6661	2^338186-130013	101805	Stefano Morozzi	02/2022
6662	2^338186+39235	101805	Stefano Morozzi	05/2022
6663	2^338185+77315	101804	Stefano Morozzi	12/2021
6664	2^338185+102519	101804	Stefano Morozzi	12/2021
6665	2^338183-76539	101804	Stefano Morozzi	12/2021
6666	2^338185+104489	101804	Stefano Morozzi	01/2022
6667	2^338179+35361	101803	Stefano Morozzi	03/2022
6668	2^338181+64235	101803	Stefano Morozzi	05/2022
6669	2^338177+51807	101802	Stefano Morozzi	12/2021
6670	2^338177+107385	101802	Stefano Morozzi	02/2022
6671	2^338178+34287	101802	Stefano Morozzi	03/2022
6672	2^338178+184207	101802	Stefano Morozzi	03/2022
6673	2^338177-108901	101802	Stefano Morozzi	04/2022
6674	2^338175+25161	101801	Stefano Morozzi	11/2021
6675	2^338173-27901	101801	Stefano Morozzi	01/2022
6676	2^338169-155965	101800	Stefano Morozzi	02/2022
6677	2^338166+183237	101799	Stefano Morozzi	02/2022
6678	2^338168-157835	101799	Stefano Morozzi	03/2022
6679	2^338166+137107	101799	Stefano Morozzi	04/2022
6680	2^338165-152139	101798	Stefano Morozzi	12/2021
6681	2^338163-178947	101798	Stefano Morozzi	02/2022
6682	2^338159-127575	101797	Stefano Morozzi	12/2021
6683	2^338161+154259	101797	Stefano Morozzi	01/2022
6684	2^338160+139947	101797	Stefano Morozzi	05/2022
6685	2^338156-75269	101796	Stefano Morozzi	12/2021
6686	2^338156-151247	101796	Stefano Morozzi	12/2021
6687	2^338156+103273	101796	Stefano Morozzi	01/2022
6688	2^338155+132621	101795	Stefano Morozzi	02/2022
6689	2^338155-82605	101795	Stefano Morozzi	03/2022
6690	2^338155-182631	101795	Stefano Morozzi	03/2022
6691	2^338155+187755	101795	Stefano Morozzi	04/2022
6692	2^338154-83975	101795	Stefano Morozzi	04/2022
6693	2^338154+163759	101795	Stefano Morozzi	05/2022
6694	2^338152-25767	101794	Stefano Morozzi	12/2021
6695	2^338152+181927	101794	Stefano Morozzi	02/2022
6696	2^338151+60779	101794	Stefano Morozzi	03/2022
6697	2^338151+189149	101794	Stefano Morozzi	05/2022
6698	2^338147+29343	101793	Stefano Morozzi	01/2022
6699	2^338148+130803	101793	Stefano Morozzi	01/2022
6700	2^338144+180697	101792	Stefano Morozzi	01/2022
6701	2^338143+8589	101792	Stefano Morozzi	02/2022
6702	2^338143-55611	101792	Stefano Morozzi	02/2022
6703	2^338143+60623	101792	Stefano Morozzi	03/2022
6704	2^338141-77301	101791	Stefano Morozzi	12/2021
6705	2^338141+157145	101791	Stefano Morozzi	02/2022
6706	2^338140+84745	101791	Stefano Morozzi	03/2022
6707	2^338140+90073	101791	Stefano Morozzi	05/2022
6708	2^338139-134719	101790	Stefano Morozzi	04/2022
6709	2^338133+1445	101789	Stefano Morozzi	12/2021
6710	2^338132+105643	101788	Stefano Morozzi	01/2022
6711	2^338131+181871	101788	Stefano Morozzi	02/2022
6712	2^338132-184539	101788	Stefano Morozzi	04/2022
6713	2^338128+128953	101787	Stefano Morozzi	01/2022
6714	2^338127+11021	101787	Stefano Morozzi	03/2022
6715	2^338123-25959	101786	Stefano Morozzi	12/2021
6716	2^338124-180765	101786	Stefano Morozzi	02/2022
6717	2^338125-7129	101786	Stefano Morozzi	03/2022
6719	2^338122-20117	101785	Enzo Doria	06/2013
6720	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
6718	2^338122+32799	101785	Stefano Morozzi	02/2022
6721	2^338117+103761	101784	Stefano Morozzi	01/2022
6722	2^338118+53817	101784	Stefano Morozzi	01/2022
6723	2^338116+82585	101784	Stefano Morozzi	02/2022
6724	2^338118+39483	101784	Stefano Morozzi	05/2022
6725	2^338115+61083	101783	Stefano Morozzi	03/2022
6726	2^338110-175365	101782	Stefano Morozzi	12/2021
6727	2^338110-3963	101782	Stefano Morozzi	01/2022
6728	2^338112+155061	101782	Stefano Morozzi	01/2022
6729	2^338112+137335	101782	Stefano Morozzi	04/2022
6736	35^65917-7092	101781	Enzo Doria	03/2013
6730	2^338107-1221	101781	Stefano Morozzi	12/2021
6731	2^338109+108539	101781	Stefano Morozzi	03/2022
6732	2^338109-7261	101781	Stefano Morozzi	03/2022
6733	2^338109-131961	101781	Stefano Morozzi	03/2022
6734	2^338108+39585	101781	Stefano Morozzi	05/2022
6735	2^338109+38147	101781	Stefano Morozzi	05/2022
6737	2^338105+79599	101780	Stefano Morozzi	01/2022
6738	2^338103-180675	101780	Stefano Morozzi	02/2022
6739	2^338100-100389	101779	Stefano Morozzi	12/2021
6740	2^338100+27595	101779	Stefano Morozzi	12/2021
6741	2^338101+101139	101779	Stefano Morozzi	12/2021
6742	2^338101+134985	101779	Stefano Morozzi	03/2022
6743	2^338102+186135	101779	Stefano Morozzi	03/2022
6744	2^338100+36885	101779	Stefano Morozzi	04/2022
6745	2^338102-8151	101779	Stefano Morozzi	04/2022
6746	2^338097+100229	101778	Stefano Morozzi	11/2021
6747	2^338097-25695	101778	Stefano Morozzi	12/2021
6748	2^338093-128403	101777	Stefano Morozzi	01/2022
6749	2^338093+33051	101777	Stefano Morozzi	02/2022
6750	2^338094+135555	101777	Stefano Morozzi	03/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(290751 PRPs in the top)