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 ?
8001	2^338073-77971	101771	Stefano Morozzi	01/2022
8002	2^338074+55579	101771	Stefano Morozzi	01/2022
8003	2^338073-81813	101771	Stefano Morozzi	03/2022
8004	2^338073+138645	101771	Stefano Morozzi	05/2022
8005	2^338075+148043	101771	Stefano Morozzi	11/2022
8006	2^338070-152607	101770	Stefano Morozzi	01/2022
8007	2^338070+138787	101770	Stefano Morozzi	05/2022
8008	2^338071+165249	101770	Stefano Morozzi	06/2022
8009	2^338070+70359	101770	Stefano Morozzi	11/2022
8010	2^338071+98573	101770	Stefano Morozzi	11/2022
8011	2^338069+79365	101769	Stefano Morozzi	01/2022
8012	2^338069+107571	101769	Stefano Morozzi	02/2022
8013	2^338068+73035	101769	Stefano Morozzi	11/2022
8014	2^338064+100087	101768	Stefano Morozzi	11/2021
8015	2^338064-83793	101768	Stefano Morozzi	04/2022
8016	2^338064+193701	101768	Stefano Morozzi	09/2022
8017	2^338065+199947	101768	Stefano Morozzi	02/2023
8018	2^338060-151047	101767	Stefano Morozzi	12/2021
8019	2^338060-130805	101767	Stefano Morozzi	02/2022
8020	2^338060-136593	101767	Stefano Morozzi	12/2022
8021	2^338062-15725	101767	Stefano Morozzi	01/2023
8022	2^338058-76415	101766	Stefano Morozzi	12/2021
8023	2^338057+83865	101766	Stefano Morozzi	03/2022
8024	2^338057+86997	101766	Stefano Morozzi	04/2022
8025	2^338058+188589	101766	Stefano Morozzi	05/2022
8026	2^338058+68089	101766	Stefano Morozzi	09/2022
8027	2^338059+121803	101766	Stefano Morozzi	11/2022
8028	2^338057-39021	101766	Stefano Morozzi	01/2023
8029	2^338056+50605	101765	Stefano Morozzi	11/2021
8030	2^338053+53231	101765	Stefano Morozzi	01/2022
8031	2^338054-180497	101765	Stefano Morozzi	02/2022
8032	2^338053+59891	101765	Stefano Morozzi	03/2022
8033	2^338056+33987	101765	Stefano Morozzi	03/2022
8034	2^338055-157779	101765	Stefano Morozzi	03/2022
8035	2^338056+90307	101765	Stefano Morozzi	06/2022
8036	2^338055+124443	101765	Stefano Morozzi	02/2023
8037	2^338052-55373	101764	Stefano Morozzi	02/2022
8038	2^338050-138281	101764	Stefano Morozzi	12/2022
8039	2^338050+148959	101764	Stefano Morozzi	02/2023
8040	2^338051-118159	101764	Stefano Morozzi	02/2023
8041	2^338048+31185	101763	Stefano Morozzi	01/2022
8042	2^338047+31935	101763	Stefano Morozzi	02/2022
8043	2^338047+108011	101763	Stefano Morozzi	02/2022
8044	2^338049+56777	101763	Stefano Morozzi	02/2022
8045	2^338049-7531	101763	Stefano Morozzi	03/2022
8046	2^338048-304019	101763	Harrison Mesh	06/2022
8047	2^338049+191291	101763	Stefano Morozzi	06/2022
8048	2^338047-187699	101763	Stefano Morozzi	12/2022
8049	2^338047-66405	101763	Stefano Morozzi	01/2023
8050	2^338049-192633	101763	Stefano Morozzi	02/2023
8051	2^338046-25841	101762	Stefano Morozzi	12/2021
8052	2^338046-2285	101762	Stefano Morozzi	12/2021
8053	2^338046-177851	101762	Stefano Morozzi	01/2022
8054	2^338043+84045	101762	Stefano Morozzi	03/2022
8055	2^338046-57573	101762	Stefano Morozzi	03/2022
8056	2^338044-8177	101762	Stefano Morozzi	04/2022
8057	2^338045-58443	101762	Stefano Morozzi	04/2022
8058	2^338044+193497	101762	Stefano Morozzi	09/2022
8059	2^338043+45701	101762	Stefano Morozzi	11/2022
8060	2^338044-114197	101762	Stefano Morozzi	01/2023
8061	2^338042+194973	101761	Stefano Morozzi	11/2022
8062	2^338040-164483	101761	Stefano Morozzi	01/2023
8063	2^338038-57887	101760	Stefano Morozzi	04/2022
8064	2^338037+139169	101760	Stefano Morozzi	05/2022
8065	2^338037+188595	101760	Stefano Morozzi	05/2022
8066	2^338038-187241	101760	Stefano Morozzi	12/2022
8067	2^338039+124035	101760	Stefano Morozzi	02/2023
8068	2^338037-42523	101760	Stefano Morozzi	02/2023
8069	2^338034+125653	101759	Stefano Morozzi	11/2021
8070	2^338034-25211	101759	Stefano Morozzi	12/2021
8071	2^338033-154099	101759	Stefano Morozzi	02/2022
8072	2^338034-31803	101759	Stefano Morozzi	03/2022
8073	2^338033+162311	101759	Stefano Morozzi	04/2022
8074	2^338033-83071	101759	Stefano Morozzi	04/2022
8075	2^338035-158095	101759	Stefano Morozzi	04/2022
8076	2^338036-34193	101759	Stefano Morozzi	04/2022
8077	2^338036+42873	101759	Stefano Morozzi	09/2022
8078	2^338036+93373	101759	Stefano Morozzi	09/2022
8079	2^338035+146129	101759	Stefano Morozzi	11/2022
8080	2^338036+23983	101759	Stefano Morozzi	11/2022
8081	2^338036+170433	101759	Stefano Morozzi	11/2022
8082	2^338031+79989	101758	Stefano Morozzi	01/2022
8083	2^338032+158073	101758	Stefano Morozzi	02/2022
8084	2^338030-54371	101758	Stefano Morozzi	02/2022
8085	2^338032-180747	101758	Stefano Morozzi	02/2022
8086	2^338029-27909	101757	Stefano Morozzi	01/2022
8087	2^338027+70475	101757	Stefano Morozzi	11/2022
8088	2^338028-38705	101757	Stefano Morozzi	12/2022
8089	2^338028-140459	101757	Stefano Morozzi	01/2023
8090	2^338024-128495	101756	Stefano Morozzi	01/2022
8091	2^338025+34785	101756	Stefano Morozzi	03/2022
8092	2^338025-181765	101756	Stefano Morozzi	03/2022
8093	2^338024+63765	101756	Stefano Morozzi	05/2022
8094	2^338023-160621	101756	Stefano Morozzi	06/2022
8095	2^338026+117553	101756	Stefano Morozzi	09/2022
8096	2^338020-52437	101755	Stefano Morozzi	12/2021
8097	2^338021+160241	101755	Stefano Morozzi	03/2022
8098	2^338022+185845	101755	Stefano Morozzi	03/2022
8099	2^338021+189587	101755	Stefano Morozzi	05/2022
8100	2^338021-85891	101755	Stefano Morozzi	06/2022
8101	2^338020-87797	101755	Stefano Morozzi	12/2022
8102	2^338018-102741	101754	Stefano Morozzi	01/2022
8103	2^338018+29937	101754	Stefano Morozzi	01/2022
8104	2^338017-29505	101754	Stefano Morozzi	02/2022
8105	2^338018-30873	101754	Stefano Morozzi	02/2022
8106	2^338018-157013	101754	Stefano Morozzi	03/2022
8107	2^338019+168929	101754	Stefano Morozzi	09/2022
8108	2^338017+172721	101754	Stefano Morozzi	11/2022
8109	2^338018-136131	101754	Stefano Morozzi	12/2022
8110	2^338016+50797	101753	Stefano Morozzi	11/2021
8111	2^338016+26707	101753	Stefano Morozzi	12/2021
8112	2^338014+104677	101753	Stefano Morozzi	01/2022
8113	2^338013+145091	101753	Stefano Morozzi	11/2022
8114	2^338016-16335	101753	Stefano Morozzi	01/2023
8117	2^338010-19833	101752	Enzo Doria	06/2013
8115	2^338011+28665	101752	Stefano Morozzi	01/2022
8116	2^338010+89505	101752	Stefano Morozzi	05/2022
8118	2^338007+58985	101751	Stefano Morozzi	03/2022
8119	2^338008+109741	101751	Stefano Morozzi	03/2022
8120	2^338009+9527	101751	Stefano Morozzi	03/2022
8121	2^338007+14511	101751	Stefano Morozzi	05/2022
8122	2^338008+67957	101751	Stefano Morozzi	09/2022
8123	2^338009-11935	101751	Stefano Morozzi	12/2022
8124	2^338007-14199	101751	Stefano Morozzi	01/2023
8125	2^338005-75829	101750	Stefano Morozzi	12/2021
8126	2^338006-125055	101750	Stefano Morozzi	12/2021
8127	2^338006+5013	101750	Stefano Morozzi	01/2022
8128	2^338003+40269	101750	Stefano Morozzi	06/2022
8129	2^338006+166495	101750	Stefano Morozzi	06/2022
8130	2^338003-188551	101750	Stefano Morozzi	12/2022
8131	2^338006-118041	101750	Stefano Morozzi	02/2023
8132	2^338000+25113	101749	Stefano Morozzi	12/2021
8134	3^213215-76	101730	Lelio R Paula	09/2016
8133	23907^17998+17998^23907	101730	Hans Havermann	01/2019
8135	10^101728+154953	101729	Patrick De Geest	02/2020
8138	2^337930+63	101728	Lelio R Paula	07/2011
8136	10^101728-987654321	101728	Robert Price	12/2019
8137	10^101728-60741	101728	Patrick De Geest	02/2020
8139	2^337920+1869661	101725	Enzo Doria	05/2016
8140	2^337922+100280245065	101725	Paul Bourdelais	10/2021
8141	24116^16509+16509^24116	101715	Hans Havermann	01/2019
8142	(2^337875+3174)/2	101711	Stefano Morozzi	09/2020
8143	2^337859-19645	101706	Enzo Doria	05/2013
8144	2^337754+1869169	101675	Enzo Doria	05/2016
8145	3*10^101657-37	101658	Robert Price	07/2018
8146	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
8147	11^97605-24	101646	Lelio R Paula	10/2016
8148	(83*10^101636+133)/9	101637	Robert Price	08/2021
8149	(2^337624+3606)/2	101635	Stefano Morozzi	09/2020
8150	8^112539-112539	101633	Robert Price	01/2014
8151	(2^337575+1818)/2	101620	Stefano Morozzi	02/2021
8152	(11*10^101613+61)/9	101614	Tyler Busby	01/2023
8153	25694^9003+9003^25694	101605	Hans Havermann	12/2018
8154	2^337515-19869	101603	Enzo Doria	06/2013
8155	2^337473+719	101590	Lelio R Paula	08/2011
8156	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
8157	2^337452-108815	101584	Enzo Doria	03/2014
8158	2^337453+1185	101584	Lelio R Paula	09/2016
8159	(41*10^101583+319)/9	101584	Robert Price	06/2021
8160	2^337410-113561	101571	Enzo Doria	08/2014
8161	2^337387+855	101564	Lelio R Paula	09/2016
8162	2^337367-17295	101558	Lelio R Paula	09/2016
8163	2^337342-109035	101551	Enzo Doria	04/2014
8164	23703^19238+19238^23703	101548	Hans Havermann	12/2018
8165	(26*10^101537-167)/3	101538	Robert Price	10/2019
8166	2^337267-19	101528	Lelio R Paula	07/2011
8167	(2^337259+1766)/2	101525	Stefano Morozzi	09/2020
8168	(2^337257+2306)/2	101525	Stefano Morozzi	02/2021
8169	2^337222-340871	101514	Harrison Mesh	06/2022
8170	(2^337195+2646)/2	101506	Stefano Morozzi	09/2020
8171	2^337183-19989	101503	Enzo Doria	06/2013
8172	2^337149+72425	101492	Enzo Doria	04/2016
8173	24041^16642+16642^24041	101483	Hans Havermann	12/2018
8174	33982^969+969^33982	101482	Hans Havermann	12/2018
8175	2^337101-20241	101478	Enzo Doria	06/2013
8176	2^337035-20001	101458	Enzo Doria	06/2013
8177	(7*10^101456+89)/3	101457	Robert Price	08/2020
8178	2^337017-16995	101453	Lelio R Paula	09/2016
8179	(8677^25759-1)/8676	101445	Serge Batalov	06/2022
8180	2^336979-115315	101441	Enzo Doria	06/2015
8181	2^336970-20885	101439	Enzo Doria	06/2013
8182	2^336958+79	101435	Lelio R Paula	10/2009
8183	(1589^31687-1)/1588	101431	Serge Batalov	06/2022
8184	2^336942+169	101430	Lelio R Paula	10/2009
8185	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
8186	4*10^101415-89	101416	Robert Price	11/2018
8187	(14*10^101410-89)/3	101411	Robert Price	05/2020
8188	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
8189	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
8190	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
8191	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
8192	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
8193	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
8194	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
8195	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
8196	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
8197	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
8198	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
8199	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
8200	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
8201	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
8202	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
8203	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
8204	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
8205	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
8206	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
8207	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
8208	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
8209	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
8210	24097^16150+16150^24097	101405	Hans Havermann	12/2018
8211	2^336842+94065	101400	Lelio R Paula	09/2016
8212	(7*10^101395-1)/3	101396	Robert Price	08/2022
8213	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
8214	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
8215	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
8216	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
8217	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
8218	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
8219	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
8220	10^101369+203811	101370	Patrick De Geest	11/2016
8221	10^101369-99	101369	Lelio R Paula	09/2016
8222	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
8223	2^336701-113563	101358	Enzo Doria	08/2014
8224	89717!4-512	101351	Robert Price	11/2019
8225	2^336644-109023	101340	Enzo Doria	04/2014
8226	2^336601-21081	101327	Enzo Doria	06/2013
8227	(4*34^66153+227)/33	101312	Eric Chen	03/2023
8228	20^77869+63	101310	Lelio R Paula	09/2016
8229	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
8231	6^130179-137	101299	Lelio R Paula	10/2016
8230	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
8232	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
8233	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
8234	2^336369-19753	101258	Enzo Doria	05/2013
8235	23842^17653+17653^23842	101253	Hans Havermann	11/2018
8236	2^336350-344291	101252	Enzo Doria	07/2015
8237	(17*10^101251-161)/9	101252	Robert Price	02/2021
8238	(56*10^101222-47)/9	101223	Robert Price	02/2019
8239	2^336243-108777	101220	Enzo Doria	03/2014
8240	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
8241	23535^19954+19954^23535	101202	Hans Havermann	11/2018
8242	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
8243	2^336150-20393	101192	Enzo Doria	06/2013
8244	23996^16473+16473^23996	101186	Hans Havermann	11/2018
8245	2^336112-1865249	101180	Enzo Doria	03/2016
8246	2^336103-109015	101178	Enzo Doria	04/2014
8247	(2^336095+2078)/2	101175	Stefano Morozzi	09/2020
8248	2^336060+22201	101165	Enzo Doria	09/2023
8249	13^90809-96	101157	Lelio R Paula	10/2016
8250	26199^7258+7258^26199	101150	Hans Havermann	11/2018

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Probable Primes Top 10000

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