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 ?
6751	2^338095-32395	101777	Stefano Morozzi	03/2022
6752	2^338090-175353	101776	Stefano Morozzi	12/2021
6753	2^338090+33277	101776	Stefano Morozzi	02/2022
6754	2^338091-105601	101776	Stefano Morozzi	02/2022
6755	2^338091-32127	101776	Stefano Morozzi	03/2022
6756	2^338092+12873	101776	Stefano Morozzi	04/2022
6757	2^338091-58485	101776	Stefano Morozzi	04/2022
6758	2^338086+177643	101775	Stefano Morozzi	12/2021
6759	2^338089+82905	101775	Stefano Morozzi	02/2022
6760	2^338088+87565	101775	Stefano Morozzi	04/2022
6761	2^338085-3301	101774	Stefano Morozzi	01/2022
6762	2^338084+108691	101774	Stefano Morozzi	03/2022
6763	2^338083+164369	101774	Stefano Morozzi	05/2022
6764	2^338080+107521	101773	Stefano Morozzi	02/2022
6765	2^338080-156917	101773	Stefano Morozzi	03/2022
6766	2^338076+62311	101772	Stefano Morozzi	04/2022
6767	2^338079+161745	101772	Stefano Morozzi	04/2022
6768	2^338073-77971	101771	Stefano Morozzi	01/2022
6769	2^338074+55579	101771	Stefano Morozzi	01/2022
6770	2^338073-81813	101771	Stefano Morozzi	03/2022
6771	2^338073+138645	101771	Stefano Morozzi	05/2022
6772	2^338070-152607	101770	Stefano Morozzi	01/2022
6773	2^338070+138787	101770	Stefano Morozzi	05/2022
6774	2^338069+79365	101769	Stefano Morozzi	01/2022
6775	2^338069+107571	101769	Stefano Morozzi	02/2022
6776	2^338064+100087	101768	Stefano Morozzi	11/2021
6777	2^338064-83793	101768	Stefano Morozzi	04/2022
6778	2^338060-151047	101767	Stefano Morozzi	12/2021
6779	2^338060-130805	101767	Stefano Morozzi	02/2022
6780	2^338058-76415	101766	Stefano Morozzi	12/2021
6781	2^338057+83865	101766	Stefano Morozzi	03/2022
6782	2^338057+86997	101766	Stefano Morozzi	04/2022
6783	2^338058+188589	101766	Stefano Morozzi	05/2022
6784	2^338056+50605	101765	Stefano Morozzi	11/2021
6785	2^338053+53231	101765	Stefano Morozzi	01/2022
6786	2^338054-180497	101765	Stefano Morozzi	02/2022
6787	2^338053+59891	101765	Stefano Morozzi	03/2022
6788	2^338056+33987	101765	Stefano Morozzi	03/2022
6789	2^338055-157779	101765	Stefano Morozzi	03/2022
6790	2^338052-55373	101764	Stefano Morozzi	02/2022
6791	2^338048+31185	101763	Stefano Morozzi	01/2022
6792	2^338047+31935	101763	Stefano Morozzi	02/2022
6793	2^338047+108011	101763	Stefano Morozzi	02/2022
6794	2^338049+56777	101763	Stefano Morozzi	02/2022
6795	2^338049-7531	101763	Stefano Morozzi	03/2022
6796	2^338048-304019	101763	Harrison Mesh	06/2022
6797	2^338046-25841	101762	Stefano Morozzi	12/2021
6798	2^338046-2285	101762	Stefano Morozzi	12/2021
6799	2^338046-177851	101762	Stefano Morozzi	01/2022
6800	2^338043+84045	101762	Stefano Morozzi	03/2022
6801	2^338046-57573	101762	Stefano Morozzi	03/2022
6802	2^338044-8177	101762	Stefano Morozzi	04/2022
6803	2^338045-58443	101762	Stefano Morozzi	04/2022
6804	2^338038-57887	101760	Stefano Morozzi	04/2022
6805	2^338037+139169	101760	Stefano Morozzi	05/2022
6806	2^338037+188595	101760	Stefano Morozzi	05/2022
6807	2^338034+125653	101759	Stefano Morozzi	11/2021
6808	2^338034-25211	101759	Stefano Morozzi	12/2021
6809	2^338033-154099	101759	Stefano Morozzi	02/2022
6810	2^338034-31803	101759	Stefano Morozzi	03/2022
6811	2^338033+162311	101759	Stefano Morozzi	04/2022
6812	2^338033-83071	101759	Stefano Morozzi	04/2022
6813	2^338035-158095	101759	Stefano Morozzi	04/2022
6814	2^338036-34193	101759	Stefano Morozzi	04/2022
6815	2^338031+79989	101758	Stefano Morozzi	01/2022
6816	2^338032+158073	101758	Stefano Morozzi	02/2022
6817	2^338030-54371	101758	Stefano Morozzi	02/2022
6818	2^338032-180747	101758	Stefano Morozzi	02/2022
6819	2^338029-27909	101757	Stefano Morozzi	01/2022
6820	2^338024-128495	101756	Stefano Morozzi	01/2022
6821	2^338025+34785	101756	Stefano Morozzi	03/2022
6822	2^338025-181765	101756	Stefano Morozzi	03/2022
6823	2^338024+63765	101756	Stefano Morozzi	05/2022
6824	2^338020-52437	101755	Stefano Morozzi	12/2021
6825	2^338021+160241	101755	Stefano Morozzi	03/2022
6826	2^338022+185845	101755	Stefano Morozzi	03/2022
6827	2^338021+189587	101755	Stefano Morozzi	05/2022
6828	2^338018-102741	101754	Stefano Morozzi	01/2022
6829	2^338018+29937	101754	Stefano Morozzi	01/2022
6830	2^338017-29505	101754	Stefano Morozzi	02/2022
6831	2^338018-30873	101754	Stefano Morozzi	02/2022
6832	2^338018-157013	101754	Stefano Morozzi	03/2022
6833	2^338016+50797	101753	Stefano Morozzi	11/2021
6834	2^338016+26707	101753	Stefano Morozzi	12/2021
6835	2^338014+104677	101753	Stefano Morozzi	01/2022
6838	2^338010-19833	101752	Enzo Doria	06/2013
6836	2^338011+28665	101752	Stefano Morozzi	01/2022
6837	2^338010+89505	101752	Stefano Morozzi	05/2022
6839	2^338007+58985	101751	Stefano Morozzi	03/2022
6840	2^338008+109741	101751	Stefano Morozzi	03/2022
6841	2^338009+9527	101751	Stefano Morozzi	03/2022
6842	2^338007+14511	101751	Stefano Morozzi	05/2022
6843	2^338005-75829	101750	Stefano Morozzi	12/2021
6844	2^338006-125055	101750	Stefano Morozzi	12/2021
6845	2^338006+5013	101750	Stefano Morozzi	01/2022
6846	2^338000+25113	101749	Stefano Morozzi	12/2021
6848	3^213215-76	101730	Lelio R Paula	09/2016
6847	23907^17998+17998^23907	101730	Hans Havermann	01/2019
6849	10^101728+154953	101729	Patrick De Geest	02/2020
6852	2^337930+63	101728	Lelio R Paula	07/2011
6850	10^101728-987654321	101728	Robert Price	12/2019
6851	10^101728-60741	101728	Patrick De Geest	02/2020
6853	2^337920+1869661	101725	Enzo Doria	05/2016
6854	2^337922+100280245065	101725	Paul Bourdelais	10/2021
6855	24116^16509+16509^24116	101715	Hans Havermann	01/2019
6856	(2^337875+3174)/2	101711	Stefano Morozzi	09/2020
6857	2^337859-19645	101706	Enzo Doria	05/2013
6858	2^337754+1869169	101675	Enzo Doria	05/2016
6859	3*10^101657-37	101658	Robert Price	07/2018
6860	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
6861	11^97605-24	101646	Lelio R Paula	10/2016
6862	(83*10^101636+133)/9	101637	Robert Price	08/2021
6863	(2^337624+3606)/2	101635	Stefano Morozzi	09/2020
6864	8^112539-112539	101633	Robert Price	01/2014
6865	(2^337575+1818)/2	101620	Stefano Morozzi	02/2021
6866	25694^9003+9003^25694	101605	Hans Havermann	12/2018
6867	2^337515-19869	101603	Enzo Doria	06/2013
6868	2^337473+719	101590	Lelio R Paula	08/2011
6869	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
6870	2^337452-108815	101584	Enzo Doria	03/2014
6871	2^337453+1185	101584	Lelio R Paula	09/2016
6872	(41*10^101583+319)/9	101584	Robert Price	06/2021
6873	2^337410-113561	101571	Enzo Doria	08/2014
6874	2^337387+855	101564	Lelio R Paula	09/2016
6875	2^337367-17295	101558	Lelio R Paula	09/2016
6876	2^337342-109035	101551	Enzo Doria	04/2014
6877	23703^19238+19238^23703	101548	Hans Havermann	12/2018
6878	(26*10^101537-167)/3	101538	Robert Price	10/2019
6879	2^337267-19	101528	Lelio R Paula	07/2011
6880	(2^337259+1766)/2	101525	Stefano Morozzi	09/2020
6881	(2^337257+2306)/2	101525	Stefano Morozzi	02/2021
6882	2^337222-340871	101514	Harrison Mesh	06/2022
6883	(2^337195+2646)/2	101506	Stefano Morozzi	09/2020
6884	2^337183-19989	101503	Enzo Doria	06/2013
6885	2^337149+72425	101492	Enzo Doria	04/2016
6886	24041^16642+16642^24041	101483	Hans Havermann	12/2018
6887	33982^969+969^33982	101482	Hans Havermann	12/2018
6888	2^337101-20241	101478	Enzo Doria	06/2013
6889	2^337035-20001	101458	Enzo Doria	06/2013
6890	(7*10^101456+89)/3	101457	Robert Price	08/2020
6891	2^337017-16995	101453	Lelio R Paula	09/2016
6892	(8677^25759-1)/8676	101445	Serge Batalov	06/2022
6893	2^336979-115315	101441	Enzo Doria	06/2015
6894	2^336970-20885	101439	Enzo Doria	06/2013
6895	2^336958+79	101435	Lelio R Paula	10/2009
6896	(1589^31687-1)/1588	101431	Serge Batalov	06/2022
6897	2^336942+169	101430	Lelio R Paula	10/2009
6898	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
6899	4*10^101415-89	101416	Robert Price	11/2018
6900	(14*10^101410-89)/3	101411	Robert Price	05/2020
6901	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
6902	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
6903	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
6904	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
6905	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
6906	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
6907	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
6908	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
6909	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
6910	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
6911	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
6912	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
6913	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
6914	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
6915	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
6916	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
6917	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
6918	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
6919	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
6920	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
6921	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
6922	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
6923	24097^16150+16150^24097	101405	Hans Havermann	12/2018
6924	2^336842+94065	101400	Lelio R Paula	09/2016
6925	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
6926	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
6927	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
6928	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
6929	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
6930	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
6931	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
6932	10^101369+203811	101370	Patrick De Geest	11/2016
6933	10^101369-99	101369	Lelio R Paula	09/2016
6934	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
6935	2^336701-113563	101358	Enzo Doria	08/2014
6936	89717!4-512	101351	Robert Price	11/2019
6937	2^336644-109023	101340	Enzo Doria	04/2014
6938	2^336601-21081	101327	Enzo Doria	06/2013
6939	20^77869+63	101310	Lelio R Paula	09/2016
6940	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
6942	6^130179-137	101299	Lelio R Paula	10/2016
6941	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
6943	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
6944	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
6945	2^336369-19753	101258	Enzo Doria	05/2013
6946	23842^17653+17653^23842	101253	Hans Havermann	11/2018
6947	2^336350-344291	101252	Enzo Doria	07/2015
6948	(17*10^101251-161)/9	101252	Robert Price	02/2021
6949	(56*10^101222-47)/9	101223	Robert Price	02/2019
6950	2^336243-108777	101220	Enzo Doria	03/2014
6951	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
6952	23535^19954+19954^23535	101202	Hans Havermann	11/2018
6953	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
6954	2^336150-20393	101192	Enzo Doria	06/2013
6955	23996^16473+16473^23996	101186	Hans Havermann	11/2018
6956	2^336112-1865249	101180	Enzo Doria	03/2016
6957	2^336103-109015	101178	Enzo Doria	04/2014
6958	(2^336095+2078)/2	101175	Stefano Morozzi	09/2020
6959	13^90809-96	101157	Lelio R Paula	10/2016
6960	26199^7258+7258^26199	101150	Hans Havermann	11/2018
6961	19^79098-30	101147	Lelio R Paula	10/2016
6962	19^79095+88	101144	Lelio R Paula	10/2016
6963	15^85976+32	101116	Lelio R Paula	10/2016
6964	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
6965	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
6966	(4^167933+17)/3	101106	Robert Price	02/2017
6967	2^335858+153	101104	Lelio R Paula	10/2009
6968	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
6969	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
6970	(2^335839+2114)/2	101098	Stefano Morozzi	09/2020
6971	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
6973	6^129918-35	101096	Lelio R Paula	10/2016
6972	(2*10^101096-107)/3	101096	Robert Price	11/2020
6974	3^211885-70	101095	Lelio R Paula	09/2016
6975	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
6976	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
6977	2^335818-20033	101092	Enzo Doria	06/2013
6978	2^335813-110083	101090	Enzo Doria	04/2014
6979	2^335804+2155	101088	Lelio R Paula	09/2016
6980	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
6981	2^335784-16145	101082	Enzo Doria	04/2013
6982	11^97051+62	101069	Lelio R Paula	10/2016
6983	3*10^101065+11	101066	Robert Price	07/2018
6984	27820^4293+4293^27820	101064	Hans Havermann	10/2018
6985	(2^335714+3750)/2	101060	Stefano Morozzi	01/2021
6986	(2^335690+1038)/2	101053	Stefano Morozzi	09/2020
6987	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
6988	2^335658-94395	101044	Lelio R Paula	09/2016
6989	24514^13215+13215^24514	101024	Hans Havermann	11/2018
6990	2^335586+169	101022	Lelio R Paula	10/2009
6991	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
6992	(2^335562+1258)/2	101014	Stefano Morozzi	09/2020
6993	2^335541+4849845	101008	Paul Bourdelais	04/2022
6994	(38*10^100999+169)/9	101000	Robert Price	11/2021
6995	(19*10^100997+737)/9	100998	Robert Price	07/2018
6996	47599!2+1024	100991	Robert Price	02/2015
6997	2^335468-18629	100986	Enzo Doria	05/2013
6998	2^335454-20961	100982	Enzo Doria	06/2013
6999	(2^335454+3258)/2	100982	Stefano Morozzi	02/2021
7000	10^100978+61	100979	Lelio R Paula	09/2016

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Probable Primes Top 10000

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