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	10^90202+3553	90203	Patrick De Geest	09/2018
7003	3^189053+280	90202	Lelio R Paula	04/2016
7002	10^90202-67793	90202	Patrick De Geest	07/2019
7004	2^299639-187	90201	Lelio R Paula	10/2012
7005	10^90199+254031	90200	Patrick De Geest	07/2019
7006	10^90199-2891	90199	Patrick De Geest	09/2018
7008	2^299631+183	90198	Lelio R Paula	10/2012
7007	21567^15212+15212^21567	90198	Hans Havermann	08/2020
7009	10^90196+187539	90197	Patrick De Geest	07/2019
7011	10^90196-9683	90196	Patrick De Geest	09/2018
7010	21708^14287+14287^21708	90196	Hans Havermann	08/2020
7012	10^90193+104973	90194	Patrick De Geest	07/2019
7013	10^90193-9809	90193	Patrick De Geest	09/2018
7014	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
7015	(2277^26863-1)/2276	90186	Serge Batalov	08/2020
7016	2^299567+113	90179	Lelio R Paula	10/2012
7017	2^299550+189	90174	Lelio R Paula	10/2012
7018	10^90170+376063	90171	Patrick De Geest	07/2019
7019	10^90170-6749	90170	Patrick De Geest	09/2018
7020	(2^299535+3)/29	90168	Lelio R Paula	01/2013
7021	(2^299521+13)/15	90164	Stefano Morozzi	03/2020
7022	22316^10971+10971^22316	90163	Hans Havermann	08/2020
7023	10^90160+271947	90161	Patrick De Geest	07/2019
7024	10^90160-5613	90160	Patrick De Geest	09/2018
7025	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
7027	3^188938+8680	90147	Lelio R Paula	04/2016
7026	10^90146+160209	90147	Patrick De Geest	07/2019
7028	10^90146-2027	90146	Patrick De Geest	09/2018
7029	6^115840-55	90142	Lelio R Paula	05/2016
7030	(5*10^90142-473)/9	90142	Robert Price	12/2017
7031	8*7^106659+5	90139	Lelio R Paula	10/2014
7034	2^299406-16653	90131	Enzo Doria	05/2013
7032	(317057^16384+1)/2	90131	Richard Fischer	10/2019
7033	(2^299409+834)/2	90131	Stefano Morozzi	01/2020
7035	10^90128+288673	90129	Patrick De Geest	07/2019
7037	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
7036	10^90128-8387	90128	Patrick De Geest	09/2018
7038	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
7039	6^115819-53	90125	Lelio R Paula	05/2016
7040	10^90123+6313	90124	Patrick De Geest	09/2018
7042	6^115816-16853	90123	Enzo Doria	02/2013
7041	10^90123-22617	90123	Patrick De Geest	07/2019
7043	6^115813-23	90121	Lelio R Paula	05/2016
7044	(22*10^90110+161)/3	90111	Robert Price	02/2017
7046	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
7045	10^90105+915759	90106	Patrick De Geest	07/2019
7048	10^90105-767	90105	Patrick De Geest	09/2018
7047	10^90104+48189	90105	Patrick De Geest	07/2019
7049	(6050^23827-1)/6049	90105	Serge Batalov	08/2020
7050	10^90104-7703	90104	Patrick De Geest	09/2018
7051	10^90103+9159	90104	Patrick De Geest	09/2018
7052	10^90103-208457	90103	Patrick De Geest	07/2019
7053	10^90102+73011	90103	Patrick De Geest	07/2019
7054	10^90102-602433	90102	Patrick De Geest	07/2019
7055	10^90101+1225537	90102	Patrick De Geest	07/2019
7056	10^90101-3207	90101	Patrick De Geest	09/2018
7057	21730^14007+14007^21730	90101	Hans Havermann	08/2020
7058	(29*10^90096-17)/3	90097	Erik Branger	09/2014
7059	10^90089+143181	90090	Patrick De Geest	07/2019
7060	10^90089-3573	90089	Patrick De Geest	09/2018
7061	2^299247+1870529	90083	Enzo Doria	05/2016
7062	10^90079+1609	90080	Patrick De Geest	09/2018
7063	10^90079-230043	90079	Patrick De Geest	07/2019
7064	2^299229-2797783	90077	Enzo Doria	04/2016
7065	2^299220-16317	90075	Enzo Doria	04/2013
7066	11^86491-1350	90072	Enzo Doria	12/2012
7067	10^90071+52333	90072	Patrick De Geest	07/2019
7069	10^90071-1233	90071	Patrick De Geest	09/2018
7068	(314401^16384+1)/2	90071	Richard Fischer	10/2019
7070	10^90069+158527	90070	Patrick De Geest	07/2019
7071	10^90069-7841	90069	Patrick De Geest	09/2018
7072	(31*10^90064-1)/3	90066	Robert Price	03/2017
7073	10^90060+149431	90061	Patrick De Geest	07/2019
7074	10^90060-839	90060	Patrick De Geest	09/2018
7075	10^90052+2361	90053	Patrick De Geest	09/2018
7076	10^90052-90929	90052	Patrick De Geest	07/2019
7077	10^90047+619	90048	Patrick De Geest	09/2018
7078	10^90047-151071	90047	Patrick De Geest	07/2019
7079	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
7080	22996^8233+8233^22996	90043	Hans Havermann	08/2020
7081	2^299112+73951	90042	Enzo Doria	04/2016
7082	8^99702+7^(99702-1)	90040	Robert Price	02/2016
7083	10^90038+157803	90039	Patrick De Geest	07/2019
7084	10^90038-9687	90038	Patrick De Geest	09/2018
7086	5*10^90033+3	90034	Dmitry Domanov	11/2010
7085	(17574^21211-1)/17573	90034	Serge Batalov	08/2020
7087	10^90030+225813	90031	Patrick De Geest	07/2019
7088	10^90030-1461	90030	Patrick De Geest	09/2018
7089	243^37738+37738^243	90029	Norbert Schneider	01/2015
7090	10^90025+70569	90026	Patrick De Geest	07/2019
7091	10^90025-8703	90025	Patrick De Geest	09/2018
7092	2^299048-113297	90023	Enzo Doria	07/2014
7093	10^90015+849	90016	Patrick De Geest	09/2018
7094	10^90015-228387	90015	Patrick De Geest	07/2019
7095	10^90010+6811	90011	Patrick De Geest	09/2018
7096	10^90010-183597	90010	Patrick De Geest	11/2018
7097	10^90009+58321	90010	Patrick De Geest	11/2018
7098	10^90008+847	90009	Patrick De Geest	09/2018
7099	10^90009-356013	90009	Patrick De Geest	11/2018
7100	25696^3183+3183^25696	90009	Hans Havermann	08/2020
7102	3^188648+92	90008	Lelio R Paula	12/2015
7101	10^90008-706049	90008	Patrick De Geest	11/2018
7103	5*2^298991+7	90006	Lelio R Paula	08/2014
7104	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
7105	10^90000+8869	90001	Patrick De Geest	12/2009
7107	10^89999+82939	90000	Dirk Augustin	04/2007
7106	10^90000-140343	90000	Patrick De Geest	12/2009
7108	10^89999-194891	89999	Patrick De Geest	11/2009
7109	(2^298918+1798)/2	89983	Stefano Morozzi	01/2020
7110	19^70365-78	89980	Lelio R Paula	12/2015
7111	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
7112	2^298852-64875	89964	Lelio R Paula	11/2013
7113	(2^298825+1010)/2	89955	Stefano Morozzi	01/2020
7114	18^71659+37	89952	Lelio R Paula	12/2015
7115	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
7116	(2^298769+1202)/2	89939	Stefano Morozzi	01/2020
7117	(5941^23827-1)/5940	89916	Serge Batalov	08/2020
7118	17^73067+20	89906	Lelio R Paula	11/2015
7119	2^298637-99	89899	Lelio R Paula	10/2012
7120	25513^3336+3336^25513	89889	Hans Havermann	08/2020
7121	29748^1051+1051^29748	89887	Hans Havermann	08/2020
7122	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
7123	(2^298558+3654)/2	89875	Stefano Morozzi	01/2020
7124	9*10^89858+19	89859	Robert Price	05/2016
7125	2^298501+1870067	89858	Enzo Doria	05/2016
7126	(286*10^89852-1)/3	89854	Robert Price	11/2020
7127	11^86280-98	89852	Lelio R Paula	11/2015
7128	2^298473-110059	89850	Enzo Doria	04/2014
7129	19^70263-32	89850	Lelio R Paula	12/2015
7130	21208^17221+17221^21208	89839	Hans Havermann	08/2020
7131	(299*10^89836-17)/3	89838	Robert Price	01/2017
7132	3^188286+14	89836	Robert Price	09/2013
7133	(2^298408+450)/2	89830	Stefano Morozzi	01/2020
7134	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
7135	2^298367+58905	89818	Lelio R Paula	11/2013
7136	21966^12269+12269^21966	89815	Hans Havermann	08/2020
7137	(2^298333+3126)/2	89807	Stefano Morozzi	01/2020
7138	2^298319-109657	89803	Enzo Doria	04/2014
7139	7*10^89801+13	89802	Robert Price	03/2021
7140	8*10^89800+81	89801	Robert Price	05/2017
7141	21354^16037+16037^21354	89797	Hans Havermann	08/2020
7142	(2^298249+714)/2	89782	Stefano Morozzi	01/2020
7143	21227^16954+16954^21227	89775	Hans Havermann	08/2020
7144	(733^31333-1)/732	89770	Serge Batalov	08/2020
7147	18^71505-91	89759	Lelio R Paula	12/2015
7145	(2^298171+1586)/2	89759	Stefano Morozzi	01/2020
7146	(4788^24391-1)/4787	89759	Serge Batalov	08/2020
7148	(2^298161+3530)/2	89756	Stefano Morozzi	01/2020
7149	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
7150	2^298079-109531	89731	Enzo Doria	04/2014
7151	(9255^22621-1)/9254	89720	Serge Batalov	08/2020
7152	117^43380+116	89718	Norbert Schneider	08/2018
7153	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
7154	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
7155	2^298003-66945	89708	Lelio R Paula	11/2013
7156	(23*10^89705-83)/3	89706	Robert Price	09/2017
7157	17^72900-54	89700	Lelio R Paula	11/2015
7158	(2^297968+2482)/2	89698	Stefano Morozzi	01/2020
7159	3*2^297956+5	89695	Lelio R Paula	08/2014
7160	(2^297952+3558)/2	89693	Stefano Morozzi	01/2020
7161	(3992^24907-1)/3991	89692	Serge Batalov	08/2020
7162	20^68938-11	89691	Lelio R Paula	01/2016
7163	89*10^89687-7	89689	Robert Price	03/2017
7164	(6882^23371-1)/6881	89688	Serge Batalov	08/2020
7165	(297847^16384+1)/2	89686	Richard Fischer	08/2019
7166	2^297923+77783	89684	Enzo Doria	05/2016
7167	(2^297893+1694)/2	89675	Stefano Morozzi	01/2020
7168	11^86107-24576000	89672	Enzo Doria	02/2013
7169	2^297878-111911	89671	Enzo Doria	05/2014
7170	20823^20236+20236^20823	89667	Hans Havermann	08/2020
7171	25708^3075+3075^25708	89666	Hans Havermann	08/2020
7172	21002^18585+18585^21002	89661	Hans Havermann	08/2020
7173	(2^297830+3670)/2	89656	Stefano Morozzi	01/2020
7174	7^106084+40	89652	Lelio R Paula	10/2015
7175	(2^297815+618)/2	89651	Stefano Morozzi	01/2020
7176	21223^16752+16752^21223	89648	Hans Havermann	08/2020
7178	(86*10^89640-311)/9	89641	Robert Price	10/2017
7177	(2^297781+2094)/2	89641	Stefano Morozzi	01/2020
7179	(2^297741+3326)/2	89629	Stefano Morozzi	01/2020
7180	(2^297724+3606)/2	89624	Stefano Morozzi	01/2020
7181	3*10^89608-59	89609	Robert Price	10/2017
7182	(2^297650+3250)/2	89602	Stefano Morozzi	01/2020
7183	3^187780-11038	89594	Enzo Doria	05/2014
7184	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
7185	5^128141-36	89567	Lelio R Paula	10/2015
7186	4*7^105951+9	89540	Lelio R Paula	10/2014
7187	(7*10^89539-439)/9	89539	Robert Price	09/2017
7188	(9772^22441-1)/9771	89536	Serge Batalov	08/2020
7189	22823^8374+8374^22823	89534	Hans Havermann	08/2020
7190	(2^297401+2954)/2	89527	Stefano Morozzi	01/2020
7191	(2^297403+1670)/2	89527	Stefano Morozzi	01/2020
7192	2^297397+177257	89526	Enzo Doria	05/2016
7193	(77*10^89518+247)/9	89519	Robert Price	03/2021
7195	2^297346-16241	89511	Enzo Doria	04/2013
7194	(5*10^89510+79)/3	89511	Robert Price	11/2017
7196	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
7197	2^297328-869688105	89505	Lelio R Paula	07/2016
7198	2^297325-459043	89504	Enzo Doria	05/2015
7199	2^297310-112391	89500	Enzo Doria	06/2014
7200	2^297296-112157	89496	Enzo Doria	06/2014
7201	57^50966-2	89490	Lelio R Paula	08/2013
7202	(266*10^89482+1)/3	89484	Robert Price	02/2016
7203	(14*10^89480-101)/3	89481	Robert Price	04/2017
7204	2618^26175+26175^2618	89466	Norbert Schneider	01/2020
7205	(2^297150+3922)/2	89451	Stefano Morozzi	01/2020
7206	(2^297141+1842)/2	89449	Stefano Morozzi	01/2020
7207	(2^297140+1458)/2	89448	Stefano Morozzi	01/2020
7208	(2^297129+726)/2	89445	Stefano Morozzi	01/2020
7209	2^297122+99	89443	Lelio R Paula	10/2012
7210	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
7211	(28*10^89425+101)/3	89426	Robert Price	09/2020
7212	(2^297037+3522)/2	89417	Stefano Morozzi	01/2020
7213	(25*10^89413+161)/3	89414	Robert Price	01/2017
7214	29080^1187+1187^29080	89406	Hans Havermann	08/2020
7215	2^296990+1870699	89403	Enzo Doria	05/2016
7216	2^296972-1017	89398	Lelio R Paula	11/2013
7217	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
7218	(85*10^89375-31)/9	89376	Robert Price	11/2015
7219	9*2^296870+7	89368	Lelio R Paula	08/2014
7220	100^44683-99^44683	89366	Robert Price	07/2013
7221	2^296810+76519	89349	Enzo Doria	05/2016
7222	(2747^25981-1)/2746	89342	Serge Batalov	08/2020
7223	8^98928+7^(98928+1)	89341	Robert Price	06/2016
7225	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
7224	21832^12359+12359^21832	89337	Hans Havermann	08/2020
7226	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
7227	2^296736-432149	89327	Paul Bourdelais	05/2013
7228	2^296737-112519	89327	Enzo Doria	06/2014
7229	2^296718-3645	89322	Lelio R Paula	11/2013
7230	(2^296702+2338)/2	89316	Stefano Morozzi	01/2020
7231	2^296681-16221	89310	Enzo Doria	04/2013
7232	2^296669-16513	89307	Enzo Doria	04/2013
7233	(2^296626+1282)/2	89294	Stefano Morozzi	01/2020
7234	2^296619-16357	89292	Enzo Doria	04/2013
7235	2^296614-110051	89290	Enzo Doria	04/2014
7236	(2^296601+1730)/2	89286	Stefano Morozzi	01/2020
7237	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
7238	(2*10^89279+457)/9	89279	Robert Price	01/2017
7239	(2^296568+1222)/2	89276	Stefano Morozzi	01/2020
7240	15^75907-28	89274	Lelio R Paula	11/2015
7241	2^296547-37	89270	Yves Minet	01/2012
7242	2^296485+191	89251	Lelio R Paula	10/2012
7243	2^296467-75	89246	Lelio R Paula	10/2012
7244	(2^296462+1674)/2	89244	Stefano Morozzi	01/2020
7245	2^296416-109535	89231	Enzo Doria	04/2014
7246	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
7247	66^49037-65	89225	Norbert Schneider	11/2014
7248	2^296377-16245	89219	Enzo Doria	04/2013
7249	2^296372-64875	89217	Lelio R Paula	11/2013
7250	5*6^114648-7	89215	Lelio R Paula	10/2014

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PRP Records

Probable Primes Top 10000

(280932 PRPs in the top)