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 ?
6001	2^338156-151247	101796	Stefano Morozzi	12/2021
6002	2^338156+103273	101796	Stefano Morozzi	01/2022
6003	2^338152-25767	101794	Stefano Morozzi	12/2021
6004	2^338147+29343	101793	Stefano Morozzi	01/2022
6005	2^338141-77301	101791	Stefano Morozzi	12/2021
6006	2^338133+1445	101789	Stefano Morozzi	12/2021
6007	2^338128+128953	101787	Stefano Morozzi	01/2022
6008	2^338123-25959	101786	Stefano Morozzi	12/2021
6009	2^338122-20117	101785	Enzo Doria	06/2013
6010	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
6011	2^338117+103761	101784	Stefano Morozzi	01/2022
6012	2^338118+53817	101784	Stefano Morozzi	01/2022
6013	2^338110-175365	101782	Stefano Morozzi	12/2021
6014	2^338110-3963	101782	Stefano Morozzi	01/2022
6016	35^65917-7092	101781	Enzo Doria	03/2013
6015	2^338107-1221	101781	Stefano Morozzi	12/2021
6017	2^338100-100389	101779	Stefano Morozzi	12/2021
6018	2^338100+27595	101779	Stefano Morozzi	12/2021
6019	2^338101+101139	101779	Stefano Morozzi	12/2021
6020	2^338097+100229	101778	Stefano Morozzi	11/2021
6021	2^338097-25695	101778	Stefano Morozzi	12/2021
6022	2^338093-128403	101777	Stefano Morozzi	01/2022
6023	2^338090-175353	101776	Stefano Morozzi	12/2021
6024	2^338086+177643	101775	Stefano Morozzi	12/2021
6025	2^338085-3301	101774	Stefano Morozzi	01/2022
6026	2^338073-77971	101771	Stefano Morozzi	01/2022
6027	2^338070-152607	101770	Stefano Morozzi	01/2022
6028	2^338069+79365	101769	Stefano Morozzi	01/2022
6029	2^338064+100087	101768	Stefano Morozzi	11/2021
6030	2^338060-151047	101767	Stefano Morozzi	12/2021
6031	2^338058-76415	101766	Stefano Morozzi	12/2021
6032	2^338056+50605	101765	Stefano Morozzi	11/2021
6033	2^338053+53231	101765	Stefano Morozzi	01/2022
6034	2^338046-25841	101762	Stefano Morozzi	12/2021
6035	2^338046-2285	101762	Stefano Morozzi	12/2021
6036	2^338046-177851	101762	Stefano Morozzi	01/2022
6037	2^338034+125653	101759	Stefano Morozzi	11/2021
6038	2^338034-25211	101759	Stefano Morozzi	12/2021
6039	2^338029-27909	101757	Stefano Morozzi	01/2022
6040	2^338024-128495	101756	Stefano Morozzi	01/2022
6041	2^338020-52437	101755	Stefano Morozzi	12/2021
6042	2^338018-102741	101754	Stefano Morozzi	01/2022
6043	2^338016+50797	101753	Stefano Morozzi	11/2021
6044	2^338016+26707	101753	Stefano Morozzi	12/2021
6046	2^338010-19833	101752	Enzo Doria	06/2013
6045	2^338011+28665	101752	Stefano Morozzi	01/2022
6047	2^338005-75829	101750	Stefano Morozzi	12/2021
6048	2^338006-125055	101750	Stefano Morozzi	12/2021
6049	2^338006+5013	101750	Stefano Morozzi	01/2022
6050	2^338000+25113	101749	Stefano Morozzi	12/2021
6052	3^213215-76	101730	Lelio R Paula	09/2016
6051	23907^17998+17998^23907	101730	Hans Havermann	01/2019
6053	10^101728+154953	101729	Patrick De Geest	02/2020
6056	2^337930+63	101728	Lelio R Paula	07/2011
6054	10^101728-987654321	101728	Robert Price	12/2019
6055	10^101728-60741	101728	Patrick De Geest	02/2020
6057	2^337920+1869661	101725	Enzo Doria	05/2016
6058	2^337922+100280245065	101725	Paul Bourdelais	10/2021
6059	24116^16509+16509^24116	101715	Hans Havermann	01/2019
6060	(2^337875+3174)/2	101711	Stefano Morozzi	09/2020
6061	2^337859-19645	101706	Enzo Doria	05/2013
6062	2^337754+1869169	101675	Enzo Doria	05/2016
6063	3*10^101657-37	101658	Robert Price	07/2018
6064	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
6065	11^97605-24	101646	Lelio R Paula	10/2016
6066	(83*10^101636+133)/9	101637	Robert Price	08/2021
6067	(2^337624+3606)/2	101635	Stefano Morozzi	09/2020
6068	8^112539-112539	101633	Robert Price	01/2014
6069	(2^337575+1818)/2	101620	Stefano Morozzi	02/2021
6070	25694^9003+9003^25694	101605	Hans Havermann	12/2018
6071	2^337515-19869	101603	Enzo Doria	06/2013
6072	2^337473+719	101590	Lelio R Paula	08/2011
6073	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
6074	2^337452-108815	101584	Enzo Doria	03/2014
6075	2^337453+1185	101584	Lelio R Paula	09/2016
6076	(41*10^101583+319)/9	101584	Robert Price	06/2021
6077	2^337410-113561	101571	Enzo Doria	08/2014
6078	2^337387+855	101564	Lelio R Paula	09/2016
6079	2^337367-17295	101558	Lelio R Paula	09/2016
6080	2^337342-109035	101551	Enzo Doria	04/2014
6081	23703^19238+19238^23703	101548	Hans Havermann	12/2018
6082	(26*10^101537-167)/3	101538	Robert Price	10/2019
6083	2^337267-19	101528	Lelio R Paula	07/2011
6084	(2^337259+1766)/2	101525	Stefano Morozzi	09/2020
6085	(2^337257+2306)/2	101525	Stefano Morozzi	02/2021
6086	(2^337195+2646)/2	101506	Stefano Morozzi	09/2020
6087	2^337183-19989	101503	Enzo Doria	06/2013
6088	2^337149+72425	101492	Enzo Doria	04/2016
6089	24041^16642+16642^24041	101483	Hans Havermann	12/2018
6090	33982^969+969^33982	101482	Hans Havermann	12/2018
6091	2^337101-20241	101478	Enzo Doria	06/2013
6092	2^337035-20001	101458	Enzo Doria	06/2013
6093	(7*10^101456+89)/3	101457	Robert Price	08/2020
6094	2^337017-16995	101453	Lelio R Paula	09/2016
6095	2^336979-115315	101441	Enzo Doria	06/2015
6096	2^336970-20885	101439	Enzo Doria	06/2013
6097	2^336958+79	101435	Lelio R Paula	10/2009
6098	2^336942+169	101430	Lelio R Paula	10/2009
6099	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
6100	4*10^101415-89	101416	Robert Price	11/2018
6101	(14*10^101410-89)/3	101411	Robert Price	05/2020
6102	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
6103	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
6104	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
6105	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
6106	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
6107	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
6108	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
6109	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
6110	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
6111	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
6112	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
6113	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
6114	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
6115	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
6116	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
6117	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
6118	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
6119	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
6120	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
6121	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
6122	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
6123	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
6124	24097^16150+16150^24097	101405	Hans Havermann	12/2018
6125	2^336842+94065	101400	Lelio R Paula	09/2016
6126	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
6127	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
6128	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
6129	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
6130	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
6131	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
6132	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
6133	10^101369+203811	101370	Patrick De Geest	11/2016
6134	10^101369-99	101369	Lelio R Paula	09/2016
6135	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
6136	2^336701-113563	101358	Enzo Doria	08/2014
6137	89717!4-512	101351	Robert Price	11/2019
6138	2^336644-109023	101340	Enzo Doria	04/2014
6139	2^336601-21081	101327	Enzo Doria	06/2013
6140	20^77869+63	101310	Lelio R Paula	09/2016
6141	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
6143	6^130179-137	101299	Lelio R Paula	10/2016
6142	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
6144	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
6145	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
6146	2^336369-19753	101258	Enzo Doria	05/2013
6147	23842^17653+17653^23842	101253	Hans Havermann	11/2018
6148	2^336350-344291	101252	Enzo Doria	07/2015
6149	(17*10^101251-161)/9	101252	Robert Price	02/2021
6150	(56*10^101222-47)/9	101223	Robert Price	02/2019
6151	2^336243-108777	101220	Enzo Doria	03/2014
6152	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
6153	23535^19954+19954^23535	101202	Hans Havermann	11/2018
6154	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
6155	2^336150-20393	101192	Enzo Doria	06/2013
6156	23996^16473+16473^23996	101186	Hans Havermann	11/2018
6157	2^336112-1865249	101180	Enzo Doria	03/2016
6158	2^336103-109015	101178	Enzo Doria	04/2014
6159	(2^336095+2078)/2	101175	Stefano Morozzi	09/2020
6160	13^90809-96	101157	Lelio R Paula	10/2016
6161	26199^7258+7258^26199	101150	Hans Havermann	11/2018
6162	19^79098-30	101147	Lelio R Paula	10/2016
6163	19^79095+88	101144	Lelio R Paula	10/2016
6164	15^85976+32	101116	Lelio R Paula	10/2016
6165	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
6166	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
6167	(4^167933+17)/3	101106	Robert Price	02/2017
6168	2^335858+153	101104	Lelio R Paula	10/2009
6169	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
6170	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
6171	(2^335839+2114)/2	101098	Stefano Morozzi	09/2020
6172	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
6174	6^129918-35	101096	Lelio R Paula	10/2016
6173	(2*10^101096-107)/3	101096	Robert Price	11/2020
6175	3^211885-70	101095	Lelio R Paula	09/2016
6176	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
6177	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
6178	2^335818-20033	101092	Enzo Doria	06/2013
6179	2^335813-110083	101090	Enzo Doria	04/2014
6180	2^335804+2155	101088	Lelio R Paula	09/2016
6181	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
6182	2^335784-16145	101082	Enzo Doria	04/2013
6183	11^97051+62	101069	Lelio R Paula	10/2016
6184	3*10^101065+11	101066	Robert Price	07/2018
6185	27820^4293+4293^27820	101064	Hans Havermann	10/2018
6186	(2^335714+3750)/2	101060	Stefano Morozzi	01/2021
6187	(2^335690+1038)/2	101053	Stefano Morozzi	09/2020
6188	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
6189	2^335658-94395	101044	Lelio R Paula	09/2016
6190	24514^13215+13215^24514	101024	Hans Havermann	11/2018
6191	2^335586+169	101022	Lelio R Paula	10/2009
6192	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
6193	(2^335562+1258)/2	101014	Stefano Morozzi	09/2020
6194	(38*10^100999+169)/9	101000	Robert Price	11/2021
6195	(19*10^100997+737)/9	100998	Robert Price	07/2018
6196	47599!2+1024	100991	Robert Price	02/2015
6197	2^335468-18629	100986	Enzo Doria	05/2013
6198	2^335454-20961	100982	Enzo Doria	06/2013
6199	(2^335454+3258)/2	100982	Stefano Morozzi	02/2021
6200	10^100978+61	100979	Lelio R Paula	09/2016
6201	10^100978-156437	100978	Patrick De Geest	11/2016
6202	(2^335422+3114)/2	100972	Stefano Morozzi	09/2020
6203	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
6204	2^335403-1859167	100967	Enzo Doria	03/2016
6205	23599^18976+18976^23599	100962	Hans Havermann	10/2018
6206	6*10^100958+43	100959	Robert Price	07/2020
6207	9*2^335364-5	100956	Lelio R Paula	08/2014
6208	2^335349+72287	100951	Enzo Doria	04/2016
6209	2^335329+16095	100945	Lelio R Paula	09/2016
6210	232823#+233663	100937	Makoto Morimoto	10/2017
6211	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
6212	2^335237-20893	100917	Enzo Doria	06/2013
6213	2^335222-19337	100912	Enzo Doria	05/2013
6214	2^335222-109985	100912	Enzo Doria	04/2014
6215	2^335182-17237	100900	Enzo Doria	05/2013
6216	(2^335107+1634)/2	100877	Stefano Morozzi	09/2020
6217	2^335043-16737	100858	Enzo Doria	05/2013
6218	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
6219	2^335038-20633	100857	Enzo Doria	06/2013
6220	2^335031+1873373	100855	Enzo Doria	06/2016
6221	23489^19650+19650^23489	100847	Hans Havermann	10/2018
6222	3^211354-8816	100842	Enzo Doria	05/2014
6223	2^334984-112757	100841	Enzo Doria	06/2014
6224	(746*10^100827+1)/9	100829	Robert Price	03/2020
6225	29451^2648+2648^29451	100809	Hans Havermann	09/2018
6226	25583^8716+8716^25583	100806	Hans Havermann	08/2018
6228	2^334857+48527	100803	Lelio R Paula	08/2011
6227	12^93406+29	100803	Lelio R Paula	10/2016
6229	28780^3179+3179^28780	100796	Hans Havermann	09/2018
6230	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
6231	2^334809-13	100788	Lelio R Paula	04/2011
6232	(82*10^100780-1)/9	100781	Robert Price	12/2014
6233	31395^1622+1622^31395	100780	Hans Havermann	09/2018
6234	(2^334779+47)/5	100778	Lelio R Paula	12/2013
6235	2^334751+2049	100771	Lelio R Paula	09/2016
6236	13^90443-98	100749	Lelio R Paula	10/2016
6237	(2^334674+3190)/2	100747	Stefano Morozzi	09/2020
6238	(2^334651+1050)/2	100740	Stefano Morozzi	09/2020
6239	(7*10^100737+71)/3	100738	Robert Price	05/2018
6240	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
6241	15^85639-28	100720	Lelio R Paula	10/2016
6242	27068^5259+5259^27068	100718	Hans Havermann	08/2018
6243	2^334562+577294575	100711	Lelio R Paula	09/2016
6244	4*3^211077-5	100710	Lelio R Paula	08/2014
6245	2^334524+145	100702	Lelio R Paula	07/2009
6246	(2^334451+714)/2	100680	Stefano Morozzi	09/2020
6247	27648^4375+4375^27648	100666	Hans Havermann	09/2018
6248	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
6249	(2^334309+3122)/2	100637	Stefano Morozzi	09/2020
6250	2^334294-113111	100633	Enzo Doria	07/2014

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PRP Records

Probable Primes Top 10000

(288949 PRPs in the top)