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 ?
7001	2^338111-85627	101782	Stefano Morozzi	06/2022
7009	35^65917-7092	101781	Enzo Doria	03/2013
7002	2^338107-1221	101781	Stefano Morozzi	12/2021
7003	2^338109+108539	101781	Stefano Morozzi	03/2022
7004	2^338109-7261	101781	Stefano Morozzi	03/2022
7005	2^338109-131961	101781	Stefano Morozzi	03/2022
7006	2^338108+39585	101781	Stefano Morozzi	05/2022
7007	2^338109+38147	101781	Stefano Morozzi	05/2022
7008	2^338108+17301	101781	Stefano Morozzi	09/2022
7010	2^338105+79599	101780	Stefano Morozzi	01/2022
7011	2^338103-180675	101780	Stefano Morozzi	02/2022
7012	2^338103+19499	101780	Stefano Morozzi	09/2022
7013	2^338100-100389	101779	Stefano Morozzi	12/2021
7014	2^338100+27595	101779	Stefano Morozzi	12/2021
7015	2^338101+101139	101779	Stefano Morozzi	12/2021
7016	2^338101+134985	101779	Stefano Morozzi	03/2022
7017	2^338102+186135	101779	Stefano Morozzi	03/2022
7018	2^338100+36885	101779	Stefano Morozzi	04/2022
7019	2^338102-8151	101779	Stefano Morozzi	04/2022
7020	2^338100+90637	101779	Stefano Morozzi	06/2022
7021	2^338101+68505	101779	Stefano Morozzi	09/2022
7022	2^338097+100229	101778	Stefano Morozzi	11/2021
7023	2^338097-25695	101778	Stefano Morozzi	12/2021
7024	2^338098-110043	101778	Stefano Morozzi	06/2022
7025	2^338093-128403	101777	Stefano Morozzi	01/2022
7026	2^338093+33051	101777	Stefano Morozzi	02/2022
7027	2^338094+135555	101777	Stefano Morozzi	03/2022
7028	2^338095-32395	101777	Stefano Morozzi	03/2022
7029	2^338090-175353	101776	Stefano Morozzi	12/2021
7030	2^338090+33277	101776	Stefano Morozzi	02/2022
7031	2^338091-105601	101776	Stefano Morozzi	02/2022
7032	2^338091-32127	101776	Stefano Morozzi	03/2022
7033	2^338092+12873	101776	Stefano Morozzi	04/2022
7034	2^338091-58485	101776	Stefano Morozzi	04/2022
7035	2^338086+177643	101775	Stefano Morozzi	12/2021
7036	2^338089+82905	101775	Stefano Morozzi	02/2022
7037	2^338088+87565	101775	Stefano Morozzi	04/2022
7038	2^338085-3301	101774	Stefano Morozzi	01/2022
7039	2^338084+108691	101774	Stefano Morozzi	03/2022
7040	2^338083+164369	101774	Stefano Morozzi	05/2022
7041	2^338080+107521	101773	Stefano Morozzi	02/2022
7042	2^338080-156917	101773	Stefano Morozzi	03/2022
7043	2^338076+62311	101772	Stefano Morozzi	04/2022
7044	2^338079+161745	101772	Stefano Morozzi	04/2022
7045	2^338078-60075	101772	Stefano Morozzi	06/2022
7046	2^338079+167079	101772	Stefano Morozzi	09/2022
7047	2^338073-77971	101771	Stefano Morozzi	01/2022
7048	2^338074+55579	101771	Stefano Morozzi	01/2022
7049	2^338073-81813	101771	Stefano Morozzi	03/2022
7050	2^338073+138645	101771	Stefano Morozzi	05/2022
7051	2^338070-152607	101770	Stefano Morozzi	01/2022
7052	2^338070+138787	101770	Stefano Morozzi	05/2022
7053	2^338071+165249	101770	Stefano Morozzi	06/2022
7054	2^338069+79365	101769	Stefano Morozzi	01/2022
7055	2^338069+107571	101769	Stefano Morozzi	02/2022
7056	2^338064+100087	101768	Stefano Morozzi	11/2021
7057	2^338064-83793	101768	Stefano Morozzi	04/2022
7058	2^338064+193701	101768	Stefano Morozzi	09/2022
7059	2^338060-151047	101767	Stefano Morozzi	12/2021
7060	2^338060-130805	101767	Stefano Morozzi	02/2022
7061	2^338058-76415	101766	Stefano Morozzi	12/2021
7062	2^338057+83865	101766	Stefano Morozzi	03/2022
7063	2^338057+86997	101766	Stefano Morozzi	04/2022
7064	2^338058+188589	101766	Stefano Morozzi	05/2022
7065	2^338058+68089	101766	Stefano Morozzi	09/2022
7066	2^338056+50605	101765	Stefano Morozzi	11/2021
7067	2^338053+53231	101765	Stefano Morozzi	01/2022
7068	2^338054-180497	101765	Stefano Morozzi	02/2022
7069	2^338053+59891	101765	Stefano Morozzi	03/2022
7070	2^338056+33987	101765	Stefano Morozzi	03/2022
7071	2^338055-157779	101765	Stefano Morozzi	03/2022
7072	2^338056+90307	101765	Stefano Morozzi	06/2022
7073	2^338052-55373	101764	Stefano Morozzi	02/2022
7074	2^338048+31185	101763	Stefano Morozzi	01/2022
7075	2^338047+31935	101763	Stefano Morozzi	02/2022
7076	2^338047+108011	101763	Stefano Morozzi	02/2022
7077	2^338049+56777	101763	Stefano Morozzi	02/2022
7078	2^338049-7531	101763	Stefano Morozzi	03/2022
7079	2^338048-304019	101763	Harrison Mesh	06/2022
7080	2^338049+191291	101763	Stefano Morozzi	06/2022
7081	2^338046-25841	101762	Stefano Morozzi	12/2021
7082	2^338046-2285	101762	Stefano Morozzi	12/2021
7083	2^338046-177851	101762	Stefano Morozzi	01/2022
7084	2^338043+84045	101762	Stefano Morozzi	03/2022
7085	2^338046-57573	101762	Stefano Morozzi	03/2022
7086	2^338044-8177	101762	Stefano Morozzi	04/2022
7087	2^338045-58443	101762	Stefano Morozzi	04/2022
7088	2^338044+193497	101762	Stefano Morozzi	09/2022
7089	2^338038-57887	101760	Stefano Morozzi	04/2022
7090	2^338037+139169	101760	Stefano Morozzi	05/2022
7091	2^338037+188595	101760	Stefano Morozzi	05/2022
7092	2^338034+125653	101759	Stefano Morozzi	11/2021
7093	2^338034-25211	101759	Stefano Morozzi	12/2021
7094	2^338033-154099	101759	Stefano Morozzi	02/2022
7095	2^338034-31803	101759	Stefano Morozzi	03/2022
7096	2^338033+162311	101759	Stefano Morozzi	04/2022
7097	2^338033-83071	101759	Stefano Morozzi	04/2022
7098	2^338035-158095	101759	Stefano Morozzi	04/2022
7099	2^338036-34193	101759	Stefano Morozzi	04/2022
7100	2^338036+42873	101759	Stefano Morozzi	09/2022
7101	2^338036+93373	101759	Stefano Morozzi	09/2022
7102	2^338031+79989	101758	Stefano Morozzi	01/2022
7103	2^338032+158073	101758	Stefano Morozzi	02/2022
7104	2^338030-54371	101758	Stefano Morozzi	02/2022
7105	2^338032-180747	101758	Stefano Morozzi	02/2022
7106	2^338029-27909	101757	Stefano Morozzi	01/2022
7107	2^338024-128495	101756	Stefano Morozzi	01/2022
7108	2^338025+34785	101756	Stefano Morozzi	03/2022
7109	2^338025-181765	101756	Stefano Morozzi	03/2022
7110	2^338024+63765	101756	Stefano Morozzi	05/2022
7111	2^338023-160621	101756	Stefano Morozzi	06/2022
7112	2^338026+117553	101756	Stefano Morozzi	09/2022
7113	2^338020-52437	101755	Stefano Morozzi	12/2021
7114	2^338021+160241	101755	Stefano Morozzi	03/2022
7115	2^338022+185845	101755	Stefano Morozzi	03/2022
7116	2^338021+189587	101755	Stefano Morozzi	05/2022
7117	2^338021-85891	101755	Stefano Morozzi	06/2022
7118	2^338018-102741	101754	Stefano Morozzi	01/2022
7119	2^338018+29937	101754	Stefano Morozzi	01/2022
7120	2^338017-29505	101754	Stefano Morozzi	02/2022
7121	2^338018-30873	101754	Stefano Morozzi	02/2022
7122	2^338018-157013	101754	Stefano Morozzi	03/2022
7123	2^338019+168929	101754	Stefano Morozzi	09/2022
7124	2^338016+50797	101753	Stefano Morozzi	11/2021
7125	2^338016+26707	101753	Stefano Morozzi	12/2021
7126	2^338014+104677	101753	Stefano Morozzi	01/2022
7129	2^338010-19833	101752	Enzo Doria	06/2013
7127	2^338011+28665	101752	Stefano Morozzi	01/2022
7128	2^338010+89505	101752	Stefano Morozzi	05/2022
7130	2^338007+58985	101751	Stefano Morozzi	03/2022
7131	2^338008+109741	101751	Stefano Morozzi	03/2022
7132	2^338009+9527	101751	Stefano Morozzi	03/2022
7133	2^338007+14511	101751	Stefano Morozzi	05/2022
7134	2^338008+67957	101751	Stefano Morozzi	09/2022
7135	2^338005-75829	101750	Stefano Morozzi	12/2021
7136	2^338006-125055	101750	Stefano Morozzi	12/2021
7137	2^338006+5013	101750	Stefano Morozzi	01/2022
7138	2^338003+40269	101750	Stefano Morozzi	06/2022
7139	2^338006+166495	101750	Stefano Morozzi	06/2022
7140	2^338000+25113	101749	Stefano Morozzi	12/2021
7142	3^213215-76	101730	Lelio R Paula	09/2016
7141	23907^17998+17998^23907	101730	Hans Havermann	01/2019
7143	10^101728+154953	101729	Patrick De Geest	02/2020
7146	2^337930+63	101728	Lelio R Paula	07/2011
7144	10^101728-987654321	101728	Robert Price	12/2019
7145	10^101728-60741	101728	Patrick De Geest	02/2020
7147	2^337920+1869661	101725	Enzo Doria	05/2016
7148	2^337922+100280245065	101725	Paul Bourdelais	10/2021
7149	24116^16509+16509^24116	101715	Hans Havermann	01/2019
7150	(2^337875+3174)/2	101711	Stefano Morozzi	09/2020
7151	2^337859-19645	101706	Enzo Doria	05/2013
7152	2^337754+1869169	101675	Enzo Doria	05/2016
7153	3*10^101657-37	101658	Robert Price	07/2018
7154	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
7155	11^97605-24	101646	Lelio R Paula	10/2016
7156	(83*10^101636+133)/9	101637	Robert Price	08/2021
7157	(2^337624+3606)/2	101635	Stefano Morozzi	09/2020
7158	8^112539-112539	101633	Robert Price	01/2014
7159	(2^337575+1818)/2	101620	Stefano Morozzi	02/2021
7160	25694^9003+9003^25694	101605	Hans Havermann	12/2018
7161	2^337515-19869	101603	Enzo Doria	06/2013
7162	2^337473+719	101590	Lelio R Paula	08/2011
7163	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
7164	2^337452-108815	101584	Enzo Doria	03/2014
7165	2^337453+1185	101584	Lelio R Paula	09/2016
7166	(41*10^101583+319)/9	101584	Robert Price	06/2021
7167	2^337410-113561	101571	Enzo Doria	08/2014
7168	2^337387+855	101564	Lelio R Paula	09/2016
7169	2^337367-17295	101558	Lelio R Paula	09/2016
7170	2^337342-109035	101551	Enzo Doria	04/2014
7171	23703^19238+19238^23703	101548	Hans Havermann	12/2018
7172	(26*10^101537-167)/3	101538	Robert Price	10/2019
7173	2^337267-19	101528	Lelio R Paula	07/2011
7174	(2^337259+1766)/2	101525	Stefano Morozzi	09/2020
7175	(2^337257+2306)/2	101525	Stefano Morozzi	02/2021
7176	2^337222-340871	101514	Harrison Mesh	06/2022
7177	(2^337195+2646)/2	101506	Stefano Morozzi	09/2020
7178	2^337183-19989	101503	Enzo Doria	06/2013
7179	2^337149+72425	101492	Enzo Doria	04/2016
7180	24041^16642+16642^24041	101483	Hans Havermann	12/2018
7181	33982^969+969^33982	101482	Hans Havermann	12/2018
7182	2^337101-20241	101478	Enzo Doria	06/2013
7183	2^337035-20001	101458	Enzo Doria	06/2013
7184	(7*10^101456+89)/3	101457	Robert Price	08/2020
7185	2^337017-16995	101453	Lelio R Paula	09/2016
7186	(8677^25759-1)/8676	101445	Serge Batalov	06/2022
7187	2^336979-115315	101441	Enzo Doria	06/2015
7188	2^336970-20885	101439	Enzo Doria	06/2013
7189	2^336958+79	101435	Lelio R Paula	10/2009
7190	(1589^31687-1)/1588	101431	Serge Batalov	06/2022
7191	2^336942+169	101430	Lelio R Paula	10/2009
7192	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
7193	4*10^101415-89	101416	Robert Price	11/2018
7194	(14*10^101410-89)/3	101411	Robert Price	05/2020
7195	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
7196	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
7197	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
7198	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
7199	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
7200	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
7201	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
7202	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
7203	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
7204	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
7205	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
7206	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
7207	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
7208	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
7209	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
7210	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
7211	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
7212	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
7213	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
7214	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
7215	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
7216	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
7217	24097^16150+16150^24097	101405	Hans Havermann	12/2018
7218	2^336842+94065	101400	Lelio R Paula	09/2016
7219	(7*10^101395-1)/3	101396	Robert Price	08/2022
7220	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
7221	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
7222	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
7223	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
7224	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
7225	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
7226	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
7227	10^101369+203811	101370	Patrick De Geest	11/2016
7228	10^101369-99	101369	Lelio R Paula	09/2016
7229	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
7230	2^336701-113563	101358	Enzo Doria	08/2014
7231	89717!4-512	101351	Robert Price	11/2019
7232	2^336644-109023	101340	Enzo Doria	04/2014
7233	2^336601-21081	101327	Enzo Doria	06/2013
7234	20^77869+63	101310	Lelio R Paula	09/2016
7235	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
7237	6^130179-137	101299	Lelio R Paula	10/2016
7236	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
7238	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
7239	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
7240	2^336369-19753	101258	Enzo Doria	05/2013
7241	23842^17653+17653^23842	101253	Hans Havermann	11/2018
7242	2^336350-344291	101252	Enzo Doria	07/2015
7243	(17*10^101251-161)/9	101252	Robert Price	02/2021
7244	(56*10^101222-47)/9	101223	Robert Price	02/2019
7245	2^336243-108777	101220	Enzo Doria	03/2014
7246	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
7247	23535^19954+19954^23535	101202	Hans Havermann	11/2018
7248	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
7249	2^336150-20393	101192	Enzo Doria	06/2013
7250	23996^16473+16473^23996	101186	Hans Havermann	11/2018

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Probable Primes Top 10000

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