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	14^76677+69	87882	Lelio R Paula	11/2015
7002	(22*10^87863-1)/3	87864	Robert Price	12/2014
7003	2^291822-2797811	87848	Enzo Doria	04/2016
7004	(2^291730+1614)/2	87820	Stefano Morozzi	01/2020
7005	2^291716-111389	87816	Enzo Doria	05/2014
7006	(782*10^87809-71)/9	87811	Robert Price	06/2017
7007	3^184039+1820	87809	Lelio R Paula	12/2015
7008	12^81356+41	87798	Lelio R Paula	11/2015
7009	21307^13188+13188^21307	87789	Hans Havermann	08/2020
7010	(2527^25801-1)/2526	87788	Serge Batalov	08/2020
7011	(2^291596+1986)/2	87779	Stefano Morozzi	01/2020
7013	6^112792-18983	87770	Enzo Doria	03/2013
7012	(3123^25117-1)/3122	87770	Serge Batalov	08/2020
7014	3*6^112787-5	87766	Lelio R Paula	10/2014
7015	7^103848+82	87762	Lelio R Paula	10/2015
7016	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
7017	(2^291506+918)/2	87752	Stefano Morozzi	01/2020
7018	24411^3932+3932^24411	87749	Hans Havermann	08/2020
7019	(3^183915+5)/128	87748	Lelio R Paula	01/2013
7020	19^68619+24	87747	Lelio R Paula	12/2015
7022	2^291480+1185	87745	Lelio R Paula	10/2013
7021	2^291482+1867369	87745	Enzo Doria	03/2016
7023	2^291467-937	87741	Yves Minet	05/2013
7024	(25*10^87726+161)/3	87727	Robert Price	01/2017
7025	11^84239-2850	87726	Enzo Doria	12/2012
7026	10^87720+215541	87721	Patrick De Geest	01/2011
7027	10^87720-3	87720	Markus Tervooren	07/2010
7028	(2^291383+3078)/2	87715	Stefano Morozzi	01/2020
7030	(5*10^87712-473)/9	87712	Robert Price	12/2017
7029	(2^291373+2946)/2	87712	Stefano Morozzi	01/2020
7031	22591^7630+7630^22591	87711	Hans Havermann	08/2020
7032	22081^9378+9378^22081	87709	Hans Havermann	08/2020
7033	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
7034	(2^291280+462)/2	87684	Stefano Morozzi	01/2020
7035	20749^16816+16816^20749	87680	Hans Havermann	08/2020
7037	93^44541-2	87679	Lelio R Paula	09/2013
7036	2^291261-109561	87679	Enzo Doria	04/2014
7038	(4*10^87669+149)/9	87669	Robert Price	03/2017
7039	2^291217+4257	87666	Lelio R Paula	10/2013
7040	22748^7137+7137^22748	87660	Hans Havermann	08/2020
7041	2*12^81214-5^81214	87645	Mike Oakes	12/2010
7042	(5005^23689-1)/5004	87632	Serge Batalov	08/2020
7043	(5*10^87622-473)/9	87622	Robert Price	12/2017
7044	12^81188+85	87617	Lelio R Paula	11/2015
7045	(2^291030+3462)/2	87609	Stefano Morozzi	01/2020
7046	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
7047	(2^290980+1150)/2	87594	Stefano Morozzi	01/2020
7048	2^290958+127	87588	Lelio R Paula	09/2012
7049	78531!4-8	87580	Robert Price	11/2019
7050	2^290923-67	87577	Lelio R Paula	09/2012
7051	3*10^87573-97	87574	Robert Price	08/2017
7052	(13*10^87565+11)/3	87566	Robert Price	05/2015
7053	(2^290881+1022)/2	87564	Stefano Morozzi	01/2020
7054	(2^290857-7)/55	87555	Lelio R Paula	01/2013
7055	(2^290808+1498)/2	87542	Stefano Morozzi	01/2020
7056	2^290802+82875	87541	Lelio R Paula	10/2013
7057	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
7058	3^183441+236	87524	Lelio R Paula	12/2015
7059	2^290618-33	87485	Lelio R Paula	09/2012
7060	(184*10^87473-1)/3	87475	Robert Price	02/2017
7061	2^290534-115151	87460	Enzo Doria	06/2015
7062	2^290512-109757	87453	Enzo Doria	04/2014
7063	(32*10^87448-41)/9	87449	Robert Price	05/2015
7064	(2^290493+3074)/2	87447	Stefano Morozzi	01/2020
7065	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
7066	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
7067	2^290426+82875	87427	Lelio R Paula	11/2013
7068	3*2^290415-7	87425	Lelio R Paula	08/2014
7071	10^87408+57	87409	Robert Price	03/2011
7070	2^290366+74779	87409	Enzo Doria	04/2016
7069	22284^8365+8365^22284	87409	Hans Havermann	08/2020
7072	10^87408-123569	87408	Patrick De Geest	07/2013
7073	21517^11536+11536^21517	87404	Hans Havermann	08/2020
7074	6*10^87396+77	87397	Robert Price	06/2020
7075	(2^290268+3882)/2	87380	Stefano Morozzi	01/2020
7076	2^290265+58905	87379	Lelio R Paula	10/2013
7077	7^103391+16	87376	Lelio R Paula	10/2015
7078	(115*10^87368-7)/9	87370	Robert Price	11/2017
7079	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
7080	8*7^103379+3	87367	Lelio R Paula	10/2014
7081	(2^290226+7)/71	87365	Lelio R Paula	01/2013
7082	(3216^24907-1)/3215	87354	Serge Batalov	08/2020
7083	(2^290160+2686)/2	87347	Stefano Morozzi	01/2020
7084	13^78407-30	87341	Lelio R Paula	11/2015
7085	4*10^87337-99	87338	Robert Price	12/2016
7086	7*10^87319+39	87320	Robert Price	07/2016
7087	3*5^124921+2	87317	Lelio R Paula	10/2014
7088	78315!4-16	87316	Robert Price	11/2019
7089	3^182984+88	87306	Lelio R Paula	12/2015
7090	(10^87323-1)/(9*33909262597306826117)	87303	Alfred Reich	02/2019
7091	(10^87323-1)/305183363375761435053	87303	Anonymous	10/2020
7092	(2^290008+958)/2	87301	Stefano Morozzi	01/2020
7093	(10536^21701-1)/10535	87293	Serge Batalov	08/2020
7094	4*10^87287-99	87288	Robert Price	12/2016
7096	11^83813-1860	87283	Enzo Doria	12/2012
7095	(3068^25033-1)/3067	87283	Serge Batalov	08/2020
7097	734^30453+30453^734	87270	Norbert Schneider	04/2017
7098	12^80855+29	87258	Lelio R Paula	11/2015
7099	22209^8482+8482^22209	87249	Hans Havermann	08/2020
7100	3*6^112119-5	87247	Lelio R Paula	10/2014
7101	12^80806+79	87205	Lelio R Paula	11/2015
7102	91382^9+9^91382	87201	Andrey Kulsha	11/2004
7103	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
7104	6^112054-47	87195	Lelio R Paula	12/2015
7105	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
7106	15^74131-68	87185	Lelio R Paula	11/2015
7107	2^289583-741	87174	Lelio R Paula	10/2013
7108	7^103146+12	87169	Lelio R Paula	10/2015
7109	(2^289562+2182)/2	87167	Stefano Morozzi	01/2020
7110	5*2^289556-3	87166	Lelio R Paula	08/2014
7111	2^289543-112735	87162	Enzo Doria	06/2014
7112	20204^20243-20243^20204	87155	Norbert Schneider	04/2020
7113	8*3^182655-7	87150	Lelio R Paula	08/2014
7114	2*10^87144+81	87145	Robert Price	01/2017
7115	20541^17468+17468^20541	87140	Hans Havermann	07/2020
7117	7^103106+2*3^103106	87135	Mike Oakes	08/2010
7116	(65*10^87134-29)/9	87135	Robert Price	01/2021
7118	8*3^182614+7	87130	Lelio R Paula	08/2014
7119	(4982^23563-1)/4981	87119	Serge Batalov	08/2020
7120	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
7121	3^182566+14	87107	Robert Price	09/2013
7122	1738^26881+26881^1738	87096	Norbert Schneider	04/2020
7123	24290^3849+3849^24290	87089	Hans Havermann	08/2020
7124	(3^182385-5)/2	87020	Lelio R Paula	01/2013
7125	11^83534-8	86992	Lelio R Paula	11/2015
7126	4^144479-14267	86986	Mike Oakes	03/2011
7127	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
7129	(151*10^86963-1)/3	86965	Robert Price	04/2017
7128	(2^288892+826)/2	86965	Stefano Morozzi	01/2020
7130	15^73940-58	86961	Lelio R Paula	11/2015
7131	2^288761-113143	86926	Enzo Doria	07/2014
7132	24440^3603+3603^24440	86925	Hans Havermann	08/2020
7134	2^288747+3083	86922	Yves Minet	03/2011
7133	(2^288749+3102)/2	86922	Stefano Morozzi	01/2020
7135	30^58842+29	86917	Norbert Schneider	03/2017
7136	(2^288705+2186)/2	86909	Stefano Morozzi	01/2020
7137	(10^86906-13)/3	86906	Robert Price	02/2017
7138	2^288692-110027	86905	Enzo Doria	04/2014
7139	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
7140	(26*10^86885+79)/3	86886	Robert Price	09/2020
7141	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
7142	3^182089-34	86879	Robert Price	11/2013
7143	(2^288571+1698)/2	86869	Stefano Morozzi	01/2020
7144	2^288543-109801	86861	Enzo Doria	04/2014
7145	60^48847-59	86858	Norbert Schneider	10/2014
7146	(2^288484+3186)/2	86843	Stefano Morozzi	01/2020
7147	2^288470-64875	86839	Lelio R Paula	10/2013
7148	10^86816+32997	86817	Patrick De Geest	07/2013
7149	10^86816-99	86816	Robert Price	05/2011
7150	(89*10^86802-539)/9	86803	Robert Price	11/2017
7151	20272^19123+19123^20272	86796	Hans Havermann	07/2020
7152	(2^288316+1530)/2	86792	Stefano Morozzi	01/2020
7153	(2^288316+2218)/2	86792	Stefano Morozzi	01/2020
7154	41487!2+256	86786	Robert Price	01/2015
7155	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
7156	(2^288278+1750)/2	86781	Stefano Morozzi	01/2020
7157	2^288243+76043	86770	Enzo Doria	04/2016
7158	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
7159	9*6^111495+5	86761	Lelio R Paula	10/2014
7160	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
7161	9*7^102654-2	86754	Lelio R Paula	10/2014
7162	(2^288155+1154)/2	86743	Stefano Morozzi	01/2020
7163	2^288122-112841	86734	Enzo Doria	06/2014
7164	5^124062-68	86716	Lelio R Paula	10/2015
7165	(2^288007-3)/125	86697	Lelio R Paula	01/2013
7166	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
7167	7^102555+48	86670	Lelio R Paula	10/2015
7168	2^287902-4961	86668	Yves Minet	05/2019
7169	77779!4+2	86660	Robert Price	08/2017
7170	(2^287842+3250)/2	86649	Stefano Morozzi	01/2020
7171	2^287809-111355	86640	Enzo Doria	05/2014
7172	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
7173	9*7^102504+8	86627	Lelio R Paula	10/2014
7174	3^181551+32	86622	Robert Price	11/2013
7175	2^287735-521347	86617	Paul Bourdelais	05/2013
7176	21912^8953+8953^21912	86596	Hans Havermann	08/2020
7177	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
7178	(2^287552+1302)/2	86562	Stefano Morozzi	01/2020
7179	2^287540-112967	86559	Enzo Doria	06/2014
7180	3^181407+20	86554	Robert Price	10/2013
7181	(28*10^86550+101)/3	86551	Robert Price	09/2020
7183	(13*10^86546+83)/3	86547	Robert Price	09/2016
7182	(2^287502+2238)/2	86547	Stefano Morozzi	01/2020
7184	2^287482-4715	86541	Yves Minet	05/2019
7185	3^181378-2^(181378-1)	86540	Robert Price	01/2016
7186	24588^3305+3305^24588	86530	Hans Havermann	08/2020
7187	83^45080-2	86513	Lelio R Paula	08/2013
7188	(2^287367+2570)/2	86506	Stefano Morozzi	01/2020
7190	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
7189	(2^287360+1006)/2	86504	Stefano Morozzi	01/2020
7191	25*29^59147+20936	86498	Curtis Bright	05/2015
7192	2^287298+1871359	86486	Enzo Doria	05/2016
7193	118^41740-117	86481	Norbert Schneider	08/2018
7194	3*10^86478+89	86479	Robert Price	03/2017
7195	2^287272-79049	86478	Paul Bourdelais	02/2012
7196	(2^287259+2846)/2	86474	Stefano Morozzi	01/2020
7197	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7198	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7199	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7200	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7201	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7202	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
7203	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
7204	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
7205	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
7206	(10^86453-1)/9	86453	Lew Baxter	10/2000
7207	(2^287172+658)/2	86448	Stefano Morozzi	01/2020
7208	(2^287146+2542)/2	86440	Stefano Morozzi	01/2020
7209	(2^287136+1726)/2	86437	Stefano Morozzi	01/2020
7210	(2^287128+958)/2	86434	Stefano Morozzi	01/2020
7211	87^44563-86^44563	86431	Robert Price	05/2015
7212	6^111057+61	86420	Lelio R Paula	12/2015
7213	2^287057-109909	86413	Enzo Doria	04/2014
7214	5^123608+22	86399	Lelio R Paula	10/2015
7215	(2^286970+618)/2	86387	Stefano Morozzi	01/2020
7216	(2^286916+2646)/2	86371	Stefano Morozzi	01/2020
7217	(2^286907+3690)/2	86368	Stefano Morozzi	01/2020
7218	(31*10^86364-121)/9	86365	Robert Price	06/2016
7219	(2^286868+2686)/2	86356	Stefano Morozzi	01/2020
7220	2^286859+71663	86354	Enzo Doria	04/2016
7221	(2^286845+1866)/2	86349	Stefano Morozzi	01/2020
7222	2^286740+29835	86318	Lelio R Paula	10/2013
7223	2*10^86310+9^86310	86311	Mike Oakes	05/2011
7224	11^82878-1860	86309	Enzo Doria	12/2012
7225	2223^25780+25780^2223	86285	Norbert Schneider	12/2019
7226	2^286547+16095	86260	Lelio R Paula	10/2013
7227	(58*10^86242+329)/9	86243	Robert Price	11/2017
7228	2^286455-110427	86232	Enzo Doria	05/2014
7229	(37*10^86230+53)/9	86231	Robert Price	05/2015
7230	8*3^180700+5	86217	Lelio R Paula	08/2014
7231	3^180697-40	86215	Lelio R Paula	12/2015
7232	(2^286383+3386)/2	86210	Stefano Morozzi	01/2020
7233	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
7234	(2^286295+1934)/2	86184	Stefano Morozzi	01/2020
7235	(2^286251+3974)/2	86170	Stefano Morozzi	01/2020
7236	2^286165+77	86145	Lelio R Paula	08/2012
7237	9*2^286140+7	86138	Lelio R Paula	08/2014
7238	(2^286128+1762)/2	86133	Stefano Morozzi	01/2020
7239	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
7240	(2^286077+1122)/2	86118	Stefano Morozzi	01/2020
7241	10^86110+161113	86111	Patrick De Geest	07/2013
7242	10^86110-69	86110	Robert Price	05/2011
7243	2^286036-869688105	86106	Lelio R Paula	07/2016
7244	(2^285946+2358)/2	86079	Stefano Morozzi	01/2020
7246	(77*10^86072+31)/9	86073	Robert Price	10/2015
7245	(2^285926+3382)/2	86073	Stefano Morozzi	01/2020
7247	2^285923+345	86072	Lelio R Paula	09/2013
7248	13^77266-90	86070	Lelio R Paula	11/2015
7249	2^285910-458903	86068	Enzo Doria	04/2015
7250	2^285904-125	86066	Lelio R Paula	08/2012

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