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	50^56543-49	96065	Norbert Schneider	09/2018
7002	2^319107-109555	96061	Enzo Doria	04/2014
7003	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
7004	2^319098-112157	96059	Enzo Doria	06/2014
7005	15^81673+94	96055	Lelio R Paula	07/2016
7006	2^319074+1871749	96051	Enzo Doria	05/2016
7007	25670^5517+5517^25670	96050	Hans Havermann	06/2020
7008	6*10^96037+19	96038	Robert Price	11/2021
7009	2^319007-112111	96031	Enzo Doria	06/2014
7010	2^318946-1421	96013	Yves Minet	01/2013
7011	22830^16003+16003^22830	95982	Hans Havermann	02/2020
7012	2^318834-110411	95979	Enzo Doria	05/2014
7013	2^318831-1965	95978	Lelio R Paula	03/2016
7014	(5*10^95976+7)/3	95977	Erik Branger	03/2014
7015	22871^15696+15696^22871	95962	Hans Havermann	01/2020
7016	(2^318760+858)/2	95957	Stefano Morozzi	02/2021
7017	23167^13860+13860^23167	95953	Hans Havermann	01/2020
7018	5*3^201089-8	95945	Lelio R Paula	08/2014
7019	2^318711-139	95942	Lelio R Paula	11/2012
7020	2^318635-1167	95919	Lelio R Paula	03/2016
7021	15^81555+16	95917	Lelio R Paula	07/2016
7022	(37*10^95895+377)/9	95896	Robert Price	10/2017
7023	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
7024	2^318496-97305	95877	Lelio R Paula	03/2016
7025	22129^21496+21496^22129	95871	Hans Havermann	07/2020
7027	2^318466+15015	95868	Lelio R Paula	03/2016
7026	24847^7216+7216^24847	95868	Hans Havermann	07/2020
7028	23706^11065+11065^23706	95866	Hans Havermann	07/2020
7029	6^123187-173129	95859	Mike Oakes	04/2011
7030	2^318423-487	95855	Yves Minet	03/2012
7031	(2^318359+678)/2	95836	Stefano Morozzi	09/2020
7032	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
7033	(2^318267+2550)/2	95808	Stefano Morozzi	09/2020
7034	4*10^95799+13	95800	Robert Price	02/2021
7035	45369!2+1024	95787	Robert Price	02/2015
7036	3^200758-86	95786	Lelio R Paula	05/2016
7037	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
7038	(2^318171+2030)/2	95779	Stefano Morozzi	09/2020
7039	3*10^95776-59	95777	Robert Price	10/2017
7040	193^41901-2	95768	Lelio R Paula	10/2017
7041	(2^318124+2502)/2	95765	Stefano Morozzi	09/2020
7042	4*10^95752-71	95753	Robert Price	11/2017
7043	23640^11197+11197^23640	95721	Hans Havermann	12/2019
7044	10^95712-4000001	95712	Robert Price	07/2021
7045	((10^47850-1)10000/9+6421)10^47850+(10^47850-1)/9	95704	Hans Havermann	05/2019
7046	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
7047	(2^317853+1086)/2	95683	Stefano Morozzi	09/2020
7048	4*10^95672+91	95673	Robert Price	11/2017
7049	6*10^95665+43	95666	Robert Price	07/2020
7050	(11*10^95641-113)/3	95642	Robert Price	01/2017
7051	(13*10^95588+11)/3	95589	Robert Price	05/2015
7052	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
7053	3^200325+70	95580	Lelio R Paula	05/2016
7054	(25*10^95574-7)/9	95575	Robert Price	12/2014
7055	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
7056	2^317464+31	95567	Lelio R Paula	11/2012
7057	(2^317451+2114)/2	95562	Stefano Morozzi	09/2020
7058	7^113073+82	95558	Lelio R Paula	04/2016
7059	2^317251+465	95503	Lelio R Paula	03/2016
7060	19^74684+58	95503	Lelio R Paula	06/2016
7061	(2^317250-7)/339	95500	Lelio R Paula	07/2013
7062	5*10^95498-21	95499	Robert Price	12/2021
7063	6^122718-79	95494	Lelio R Paula	05/2016
7064	22168^20291+20291^22168	95485	Hans Havermann	10/2019
7065	2^317141-110491	95469	Enzo Doria	05/2014
7066	(2^317097+3014)/2	95456	Stefano Morozzi	09/2020
7067	2^317094+76309	95455	Enzo Doria	05/2016
7068	2^317085+95	95453	Lelio R Paula	11/2012
7069	(17*10^95451-377)/9	95452	Robert Price	11/2017
7070	2^317057-109551	95444	Enzo Doria	04/2014
7071	3^200026+28	95437	Lelio R Paula	05/2016
7072	2^317024+93	95434	Donovan Johnson	06/2008
7073	(86*10^95428-437)/9	95429	Robert Price	03/2021
7074	10^95427+192591	95428	Patrick De Geest	05/2021
7077	2^316999+1605	95427	Lelio R Paula	03/2016
7076	(2^317000+3210)/2	95427	Stefano Morozzi	09/2020
7075	10^95427-10001	95427	Robert Price	02/2021
7078	2^316995-110427	95426	Enzo Doria	05/2014
7079	22300^18987+18987^22300	95410	Hans Havermann	06/2020
7081	2^316937+177	95408	Lelio R Paula	11/2012
7080	4*10^95407+91	95408	Robert Price	11/2017
7082	2^316908+1915	95399	Lelio R Paula	03/2016
7083	2^316894+99	95395	Lelio R Paula	11/2012
7084	(2^316887+2546)/2	95393	Stefano Morozzi	09/2020
7085	2*10^95374-21	95375	Robert Price	09/2020
7086	6^122547+11	95361	Lelio R Paula	05/2016
7087	2^316771+82875	95358	Lelio R Paula	03/2016
7088	(2^316765+3102)/2	95356	Stefano Morozzi	09/2020
7089	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
7090	1*10^95326+57	95327	Robert Price	03/2011
7091	10^95326-393687	95326	Patrick De Geest	09/2013
7092	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
7093	2^316654-109481	95323	Enzo Doria	04/2014
7094	8*10^95316+51	95317	Robert Price	05/2017
7095	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
7096	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
7098	(71*10^95277-539)/9	95278	Robert Price	11/2017
7097	23422^11691+11691^23422	95278	Hans Havermann	10/2019
7099	19^74503-56	95271	Lelio R Paula	06/2016
7100	11^91475-4380	95262	Enzo Doria	01/2013
7101	(62*10^95251-611)/9	95252	Robert Price	05/2017
7102	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
7103	26541^3868+3868^26541	95216	Hans Havermann	07/2020
7104	(79*10^95214-43)/9	95215	Erik Branger	11/2013
7105	(7176^24691-1)/7175	95202	Anonymous	11/2020
7106	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
7107	5*2^316213+9	95191	Lelio R Paula	08/2014
7108	2*10^95188-91	95189	Robert Price	04/2020
7109	2^316205-1848163	95188	Enzo Doria	07/2015
7110	2^316185-2787913	95182	Enzo Doria	04/2016
7111	(2^316174+3538)/2	95178	Stefano Morozzi	09/2020
7112	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
7113	2^316140-5	95168	Henri Lifchitz	02/2006
7114	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
7115	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
7116	2^316069+76817	95147	Enzo Doria	05/2016
7117	(199*10^95134-7)/3	95136	Robert Price	02/2017
7118	2^316027-97305	95134	Lelio R Paula	03/2016
7119	2^316006-2798051	95128	Enzo Doria	04/2016
7120	24994^6397+6397^24994	95127	Hans Havermann	02/2020
7122	2^315921-2797603	95102	Enzo Doria	04/2016
7121	(2^315921+1314)/2	95102	Stefano Morozzi	02/2021
7123	2*10^95095+63	95096	Robert Price	10/2017
7124	2^315857+1299	95083	Lelio R Paula	03/2016
7125	(2^315858+2598)/2	95083	Stefano Morozzi	09/2020
7127	14^82955-43	95078	Lelio R Paula	06/2016
7126	(8*10^95078-269)/9	95078	Robert Price	09/2021
7128	(23*10^95074-101)/3	95075	Robert Price	04/2021
7129	2^315827-933075	95074	Paul Bourdelais	04/2021
7130	(2*10^95072-17)/3	95072	Robert Price	08/2014
7131	(286*10^95059-1)/3	95061	Robert Price	11/2020
7132	(2^315779+1610)/2	95059	Stefano Morozzi	09/2020
7133	2^315775-111546435	95058	Paul Bourdelais	10/2021
7134	21938^21513+21513^21938	95051	Hans Havermann	09/2020
7135	2^315727+65	95044	Lelio R Paula	11/2012
7136	2^315725+1885757	95043	Enzo Doria	03/2017
7137	23277^12058+12058^23277	95000	Hans Havermann	09/2020
7138	1*10^94983+21	94984	Robert Price	03/2011
7139	10^94983-717	94983	Patrick De Geest	08/2013
7140	17^77187-82	94975	Lelio R Paula	07/2016
7141	3*10^94964+37	94965	Robert Price	10/2017
7142	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
7143	2^315423-110329	94952	Enzo Doria	05/2014
7144	11^91169-7230	94943	Enzo Doria	02/2013
7145	7*10^94938+61	94939	Robert Price	02/2017
7146	2^315351+1025	94931	Lelio R Paula	03/2016
7147	2^315350-112253	94930	Enzo Doria	06/2014
7148	(2^315343+1766)/2	94928	Stefano Morozzi	09/2020
7149	(2^315343+3066)/2	94928	Stefano Morozzi	09/2020
7152	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
7151	2^315268+7	94906	Lelio R Paula	10/2012
7150	11^91133+62	94906	Lelio R Paula	05/2016
7153	(2^315264+1558)/2	94904	Stefano Morozzi	09/2020
7154	30^64244+41	94897	Lelio R Paula	08/2012
7155	(151*10^94885-7)/9	94887	Robert Price	07/2017
7156	4^157583+22147	94875	Mike Oakes	01/2011
7157	2^315098+123	94854	Lelio R Paula	11/2012
7158	3^198791-34	94848	Robert Price	11/2013
7159	3*2^315067+7	94846	Lelio R Paula	08/2014
7160	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
7161	22576^15875+15875^22576	94836	Hans Havermann	09/2020
7162	(16*10^94822+53)/3	94823	Robert Price	12/2016
7163	8*6^121849-7	94818	Lelio R Paula	10/2014
7164	(85*10^94802+473)/9	94803	Robert Price	03/2017
7165	21767^21852-21852^21767	94790	Norbert Schneider	06/2020
7166	2^314870-108761	94786	Enzo Doria	03/2014
7167	5*2^314841-3	94778	Lelio R Paula	08/2014
7168	(2^314842+550)/2	94777	Stefano Morozzi	09/2020
7169	(2^314787+2630)/2	94761	Stefano Morozzi	09/2020
7170	6^121772+113	94758	Lelio R Paula	05/2016
7171	(2^314740+3642)/2	94746	Stefano Morozzi	09/2020
7172	6^121756-16253	94745	Enzo Doria	02/2013
7173	2^314718-112793	94740	Enzo Doria	06/2014
7174	2^314697-1847293	94734	Enzo Doria	07/2015
7175	22836^14065+14065^22836	94727	Hans Havermann	09/2020
7177	2^314548-249	94689	Yves Minet	02/2012
7176	5^135469+42	94689	Lelio R Paula	04/2016
7178	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
7179	25773^4712+4712^25773	94670	Hans Havermann	08/2020
7180	(2^314485+3614)/2	94670	Stefano Morozzi	09/2020
7181	(2*10^94604+547)/9	94604	Robert Price	10/2017
7182	(2^314164+2562)/2	94573	Stefano Morozzi	09/2020
7183	3*2^314152+5	94570	Lelio R Paula	08/2014
7184	2*6^121530-5	94570	Lelio R Paula	10/2014
7185	7*10^94563+87	94564	Robert Price	11/2016
7186	2^314114-109677	94558	Enzo Doria	04/2014
7187	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
7188	2^314059+76583	94542	Enzo Doria	05/2016
7189	2^314041-4035	94536	Lelio R Paula	03/2016
7190	(2^314028+3102)/2	94532	Stefano Morozzi	09/2020
7191	(2^314012+618)/2	94527	Stefano Morozzi	09/2020
7192	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
7193	11^90760-4710	94517	Enzo Doria	01/2013
7194	21675^21796+21796^21675	94507	Norbert Schneider	04/2020
7195	2^313942+100280245065	94506	Paul Bourdelais	10/2021
7196	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
7197	94*10^94493-3	94495	Robert Price	11/2016
7198	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
7199	(2^313859+2706)/2	94481	Stefano Morozzi	09/2020
7200	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
7201	7^111792-32	94476	Lelio R Paula	04/2016
7202	(2^313800+822)/2	94463	Stefano Morozzi	01/2021
7203	9*10^94462-47	94463	Robert Price	11/2021
7204	11*10^94460+3	94462	Robert Price	07/2021
7205	(202*10^94441-1)/3	94443	Robert Price	05/2020
7206	11^90680-5850	94434	Enzo Doria	01/2013
7207	(752^32833-1)/751	94432	Michael Stocker	05/2020
7208	2^313675-110125	94426	Enzo Doria	04/2014
7209	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
7210	2^313609-112225	94406	Enzo Doria	06/2014
7211	2^313584+72901	94399	Enzo Doria	04/2016
7212	(2^313567+1310)/2	94393	Stefano Morozzi	02/2021
7213	(2^313562+730)/2	94392	Stefano Morozzi	09/2020
7214	2^313510-112865	94376	Enzo Doria	06/2014
7215	7*10^94373+87	94374	Robert Price	11/2016
7216	(9^98897+8^98897)/17	94371	Robert Price	12/2012
7217	2^313453-114703	94359	Enzo Doria	04/2015
7218	8*10^94357-51	94358	Robert Price	10/2017
7219	25903^4392+4392^25903	94356	Hans Havermann	09/2020
7220	31706^945+945^31706	94340	Hans Havermann	09/2020
7221	(379*10^94337-1)/9	94339	Robert Price	08/2017
7222	2^313344-313344+1	94326	Robert Price	10/2014
7223	(2^313313+3662)/2	94317	Stefano Morozzi	09/2020
7224	20^72481-49	94300	Lelio R Paula	05/2016
7225	(34*10^94293-259)/9	94294	Robert Price	12/2021
7226	44725!2+128	94289	Robert Price	03/2015
7227	4*10^94286+9	94287	Robert Price	05/2015
7228	17^76621+24	94279	Lelio R Paula	07/2016
7229	26274^3875+3875^26274	94279	Hans Havermann	09/2020
7230	4*10^94270-33	94271	Robert Price	04/2021
7231	2^313156-112859	94270	Enzo Doria	06/2014
7232	6^121130-59	94258	Lelio R Paula	05/2016
7233	3^197542+28	94252	Robert Price	11/2013
7234	(2^313076+3550)/2	94245	Stefano Morozzi	09/2020
7235	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
7236	2^313045-5955	94236	Lelio R Paula	03/2016
7237	22099^18358+18358^22099	94227	Hans Havermann	08/2020
7238	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
7239	2^312909-1865203	94195	Enzo Doria	03/2016
7240	25013^5830+5830^25013	94191	Hans Havermann	09/2020
7241	2^312848-149	94177	Lelio R Paula	11/2012
7242	(2^312819+3278)/2	94168	Stefano Morozzi	02/2021
7243	4^156403-77597	94164	Mike Oakes	04/2011
7244	18^75004-85	94151	Lelio R Paula	06/2016
7245	19^73622-48	94145	Lelio R Paula	06/2016
7246	(11^90397-3^90397)/8	94138	Robert Price	04/2011
7247	(3^197287+5)/16	94129	Lelio R Paula	04/2013
7248	24220^7691+7691^24220	94119	Hans Havermann	09/2020
7249	12^87212-37	94118	Lelio R Paula	06/2016
7250	11^90376+76	94117	Lelio R Paula	05/2016

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Probable Primes Top 10000

(288949 PRPs in the top)