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	10^90358+104641	90359	Patrick De Geest	07/2019
6004	2*6^116118+7	90358	Lelio R Paula	10/2014
6003	10^90358-4979	90358	Patrick De Geest	11/2018
6002	10^90357+112837	90358	Patrick De Geest	07/2019
6005	10^90357-189593	90357	Patrick De Geest	07/2019
6006	10^90356+53113	90357	Patrick De Geest	07/2019
6007	10^90356-7197	90356	Patrick De Geest	11/2018
6008	10^90353+603211	90354	Patrick De Geest	07/2019
6009	10^90353-1089	90353	Patrick De Geest	11/2018
6010	(24737*2^300101+1)/25	90343	Lelio R Paula	06/2014
6011	4*10^90334-21	90335	Robert Price	04/2016
6012	(4546^24697-1)/4545	90329	Serge Batalov	08/2020
6013	10^90322+137691	90323	Patrick De Geest	07/2019
6014	10^90322-9551	90322	Patrick De Geest	11/2018
6015	10^90316+9991	90317	Patrick De Geest	11/2018
6016	(4550^24691-1)/4549	90317	Serge Batalov	08/2020
6017	10^90316-45627	90316	Patrick De Geest	07/2019
6018	10^90315+32889	90316	Patrick De Geest	07/2019
6020	2^300019-110335	90315	Enzo Doria	05/2014
6019	10^90315-8561	90315	Patrick De Geest	11/2018
6021	FAB2(300001,5032)	90310	Robert Price	05/2019
6022	FAB2(300001,29405)	90310	Robert Price	05/2019
6023	(2^299965+2774)/2	90299	Stefano Morozzi	01/2020
6024	23679^6506+6506^23679	90296	Hans Havermann	08/2020
6025	2^299949-1005	90294	Lelio R Paula	11/2013
6026	(2^299947+2054)/2	90293	Stefano Morozzi	01/2020
6027	21740^14229+14229^21740	90291	Hans Havermann	08/2020
6028	10^90279+62457	90280	Patrick De Geest	07/2019
6029	10^90279-1551	90279	Patrick De Geest	09/2018
6030	(2^299892+1986)/2	90277	Stefano Morozzi	01/2020
6031	(2^299893+3866)/2	90277	Stefano Morozzi	01/2020
6032	2^299868-109613	90270	Enzo Doria	04/2014
6033	10^90259+359299	90260	Patrick De Geest	07/2019
6034	10^90259-9443	90259	Patrick De Geest	09/2018
6035	(2^299831+3786)/2	90258	Stefano Morozzi	01/2020
6036	10^90252+102873	90253	Patrick De Geest	07/2019
6037	10^90252-8103	90252	Patrick De Geest	09/2018
6039	5*2^299799-3	90250	Lelio R Paula	08/2014
6038	(2^299803+3326)/2	90250	Stefano Morozzi	01/2020
6040	13^81008-2	90239	Lelio R Paula	09/2013
6041	80697!4-256	90234	Robert Price	11/2019
6043	64^49957-63^49957	90232	Robert Price	07/2013
6042	(2^299745+2994)/2	90232	Stefano Morozzi	01/2020
6044	10^90227+56281	90228	Patrick De Geest	06/2016
6047	2^299725+315	90227	Lelio R Paula	11/2013
6045	10^90227-1000000001	90227	Robert Price	05/2016
6046	10^90227-68763	90227	Patrick De Geest	06/2016
6048	5^129082+48	90225	Lelio R Paula	03/2016
6049	2^299699+195	90219	Lelio R Paula	10/2012
6050	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
6051	22131^11918+11918^22131	90211	Hans Havermann	08/2020
6052	10^90209+8971	90210	Patrick De Geest	09/2018
6053	10^90209-724797	90209	Patrick De Geest	07/2019
6054	10^90208+189531	90209	Patrick De Geest	07/2019
6055	10^90208-2247	90208	Patrick De Geest	09/2018
6056	(629^32233-1)/628	90207	Michael Stocker	05/2020
6057	116^43693-115	90203	Norbert Schneider	08/2018
6058	10^90202+3553	90203	Patrick De Geest	09/2018
6060	3^189053+280	90202	Lelio R Paula	04/2016
6059	10^90202-67793	90202	Patrick De Geest	07/2019
6061	2^299639-187	90201	Lelio R Paula	10/2012
6062	10^90199+254031	90200	Patrick De Geest	07/2019
6063	10^90199-2891	90199	Patrick De Geest	09/2018
6065	2^299631+183	90198	Lelio R Paula	10/2012
6064	21567^15212+15212^21567	90198	Hans Havermann	08/2020
6066	10^90196+187539	90197	Patrick De Geest	07/2019
6068	10^90196-9683	90196	Patrick De Geest	09/2018
6067	21708^14287+14287^21708	90196	Hans Havermann	08/2020
6069	10^90193+104973	90194	Patrick De Geest	07/2019
6070	10^90193-9809	90193	Patrick De Geest	09/2018
6071	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
6072	(2277^26863-1)/2276	90186	Serge Batalov	08/2020
6073	2^299567+113	90179	Lelio R Paula	10/2012
6074	2^299550+189	90174	Lelio R Paula	10/2012
6075	10^90170+376063	90171	Patrick De Geest	07/2019
6076	10^90170-6749	90170	Patrick De Geest	09/2018
6077	(2^299535+3)/29	90168	Lelio R Paula	01/2013
6078	(2^299521+13)/15	90164	Stefano Morozzi	03/2020
6079	22316^10971+10971^22316	90163	Hans Havermann	08/2020
6080	10^90160+271947	90161	Patrick De Geest	07/2019
6081	10^90160-5613	90160	Patrick De Geest	09/2018
6082	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
6084	3^188938+8680	90147	Lelio R Paula	04/2016
6083	10^90146+160209	90147	Patrick De Geest	07/2019
6085	10^90146-2027	90146	Patrick De Geest	09/2018
6086	6^115840-55	90142	Lelio R Paula	05/2016
6087	(5*10^90142-473)/9	90142	Robert Price	12/2017
6088	8*7^106659+5	90139	Lelio R Paula	10/2014
6091	2^299406-16653	90131	Enzo Doria	05/2013
6089	(317057^16384+1)/2	90131	Richard Fischer	10/2019
6090	(2^299409+834)/2	90131	Stefano Morozzi	01/2020
6092	10^90128+288673	90129	Patrick De Geest	07/2019
6094	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
6093	10^90128-8387	90128	Patrick De Geest	09/2018
6095	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
6096	6^115819-53	90125	Lelio R Paula	05/2016
6097	10^90123+6313	90124	Patrick De Geest	09/2018
6099	6^115816-16853	90123	Enzo Doria	02/2013
6098	10^90123-22617	90123	Patrick De Geest	07/2019
6100	6^115813-23	90121	Lelio R Paula	05/2016
6101	(22*10^90110+161)/3	90111	Robert Price	02/2017
6103	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
6102	10^90105+915759	90106	Patrick De Geest	07/2019
6105	10^90105-767	90105	Patrick De Geest	09/2018
6104	10^90104+48189	90105	Patrick De Geest	07/2019
6106	(6050^23827-1)/6049	90105	Serge Batalov	08/2020
6107	10^90104-7703	90104	Patrick De Geest	09/2018
6108	10^90103+9159	90104	Patrick De Geest	09/2018
6109	10^90103-208457	90103	Patrick De Geest	07/2019
6110	10^90102+73011	90103	Patrick De Geest	07/2019
6111	10^90102-602433	90102	Patrick De Geest	07/2019
6112	10^90101+1225537	90102	Patrick De Geest	07/2019
6113	10^90101-3207	90101	Patrick De Geest	09/2018
6114	21730^14007+14007^21730	90101	Hans Havermann	08/2020
6115	(29*10^90096-17)/3	90097	Erik Branger	09/2014
6116	10^90089+143181	90090	Patrick De Geest	07/2019
6117	10^90089-3573	90089	Patrick De Geest	09/2018
6118	2^299247+1870529	90083	Enzo Doria	05/2016
6119	10^90079+1609	90080	Patrick De Geest	09/2018
6120	10^90079-230043	90079	Patrick De Geest	07/2019
6121	2^299229-2797783	90077	Enzo Doria	04/2016
6122	2^299220-16317	90075	Enzo Doria	04/2013
6123	11^86491-1350	90072	Enzo Doria	12/2012
6124	10^90071+52333	90072	Patrick De Geest	07/2019
6126	10^90071-1233	90071	Patrick De Geest	09/2018
6125	(314401^16384+1)/2	90071	Richard Fischer	10/2019
6127	10^90069+158527	90070	Patrick De Geest	07/2019
6128	10^90069-7841	90069	Patrick De Geest	09/2018
6129	(31*10^90064-1)/3	90066	Robert Price	03/2017
6130	10^90060+149431	90061	Patrick De Geest	07/2019
6131	10^90060-839	90060	Patrick De Geest	09/2018
6132	10^90052+2361	90053	Patrick De Geest	09/2018
6133	10^90052-90929	90052	Patrick De Geest	07/2019
6134	10^90047+619	90048	Patrick De Geest	09/2018
6135	10^90047-151071	90047	Patrick De Geest	07/2019
6136	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
6137	22996^8233+8233^22996	90043	Hans Havermann	08/2020
6138	2^299112+73951	90042	Enzo Doria	04/2016
6139	8^99702+7^(99702-1)	90040	Robert Price	02/2016
6140	10^90038+157803	90039	Patrick De Geest	07/2019
6141	10^90038-9687	90038	Patrick De Geest	09/2018
6143	5*10^90033+3	90034	Dmitry Domanov	11/2010
6142	(17574^21211-1)/17573	90034	Serge Batalov	08/2020
6144	10^90030+225813	90031	Patrick De Geest	07/2019
6145	10^90030-1461	90030	Patrick De Geest	09/2018
6146	243^37738+37738^243	90029	Norbert Schneider	01/2015
6147	10^90025+70569	90026	Patrick De Geest	07/2019
6148	10^90025-8703	90025	Patrick De Geest	09/2018
6149	2^299048-113297	90023	Enzo Doria	07/2014
6150	10^90015+849	90016	Patrick De Geest	09/2018
6151	10^90015-228387	90015	Patrick De Geest	07/2019
6152	10^90010+6811	90011	Patrick De Geest	09/2018
6153	10^90010-183597	90010	Patrick De Geest	11/2018
6154	10^90009+58321	90010	Patrick De Geest	11/2018
6155	10^90008+847	90009	Patrick De Geest	09/2018
6156	10^90009-356013	90009	Patrick De Geest	11/2018
6157	25696^3183+3183^25696	90009	Hans Havermann	08/2020
6158	3^188648+92	90008	Lelio R Paula	12/2015
6159	10^90008-706049	90008	Patrick De Geest	11/2018
6160	5*2^298991+7	90006	Lelio R Paula	08/2014
6161	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
6162	10^90000+8869	90001	Patrick De Geest	12/2009
6164	10^89999+82939	90000	Dirk Augustin	04/2007
6163	10^90000-140343	90000	Patrick De Geest	12/2009
6165	10^89999-194891	89999	Patrick De Geest	11/2009
6166	(2^298918+1798)/2	89983	Stefano Morozzi	01/2020
6167	19^70365-78	89980	Lelio R Paula	12/2015
6168	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
6169	2^298852-64875	89964	Lelio R Paula	11/2013
6170	(2^298825+1010)/2	89955	Stefano Morozzi	01/2020
6171	18^71659+37	89952	Lelio R Paula	12/2015
6172	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
6173	(2^298769+1202)/2	89939	Stefano Morozzi	01/2020
6174	(5941^23827-1)/5940	89916	Serge Batalov	08/2020
6175	17^73067+20	89906	Lelio R Paula	11/2015
6176	2^298637-99	89899	Lelio R Paula	10/2012
6177	25513^3336+3336^25513	89889	Hans Havermann	08/2020
6178	29748^1051+1051^29748	89887	Hans Havermann	08/2020
6179	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
6180	(2^298558+3654)/2	89875	Stefano Morozzi	01/2020
6181	9*10^89858+19	89859	Robert Price	05/2016
6182	2^298501+1870067	89858	Enzo Doria	05/2016
6183	11^86280-98	89852	Lelio R Paula	11/2015
6184	2^298473-110059	89850	Enzo Doria	04/2014
6185	19^70263-32	89850	Lelio R Paula	12/2015
6186	21208^17221+17221^21208	89839	Hans Havermann	08/2020
6187	(299*10^89836-17)/3	89838	Robert Price	01/2017
6188	3^188286+14	89836	Robert Price	09/2013
6189	(2^298408+450)/2	89830	Stefano Morozzi	01/2020
6190	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
6191	2^298367+58905	89818	Lelio R Paula	11/2013
6192	21966^12269+12269^21966	89815	Hans Havermann	08/2020
6193	(2^298333+3126)/2	89807	Stefano Morozzi	01/2020
6194	2^298319-109657	89803	Enzo Doria	04/2014
6195	8*10^89800+81	89801	Robert Price	05/2017
6196	21354^16037+16037^21354	89797	Hans Havermann	08/2020
6197	(2^298249+714)/2	89782	Stefano Morozzi	01/2020
6198	21227^16954+16954^21227	89775	Hans Havermann	08/2020
6199	(733^31333-1)/732	89770	Serge Batalov	08/2020
6202	18^71505-91	89759	Lelio R Paula	12/2015
6200	(2^298171+1586)/2	89759	Stefano Morozzi	01/2020
6201	(4788^24391-1)/4787	89759	Serge Batalov	08/2020
6203	(2^298161+3530)/2	89756	Stefano Morozzi	01/2020
6204	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
6205	2^298079-109531	89731	Enzo Doria	04/2014
6206	(9255^22621-1)/9254	89720	Serge Batalov	08/2020
6207	117^43380+116	89718	Norbert Schneider	08/2018
6208	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
6209	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
6210	2^298003-66945	89708	Lelio R Paula	11/2013
6211	(23*10^89705-83)/3	89706	Robert Price	09/2017
6212	17^72900-54	89700	Lelio R Paula	11/2015
6213	(2^297968+2482)/2	89698	Stefano Morozzi	01/2020
6214	3*2^297956+5	89695	Lelio R Paula	08/2014
6215	(2^297952+3558)/2	89693	Stefano Morozzi	01/2020
6216	(3992^24907-1)/3991	89692	Serge Batalov	08/2020
6217	20^68938-11	89691	Lelio R Paula	01/2016
6218	89*10^89687-7	89689	Robert Price	03/2017
6219	(6882^23371-1)/6881	89688	Serge Batalov	08/2020
6220	(297847^16384+1)/2	89686	Richard Fischer	08/2019
6221	2^297923+77783	89684	Enzo Doria	05/2016
6222	(2^297893+1694)/2	89675	Stefano Morozzi	01/2020
6223	11^86107-24576000	89672	Enzo Doria	02/2013
6224	2^297878-111911	89671	Enzo Doria	05/2014
6225	20823^20236+20236^20823	89667	Hans Havermann	08/2020
6226	25708^3075+3075^25708	89666	Hans Havermann	08/2020
6227	21002^18585+18585^21002	89661	Hans Havermann	08/2020
6228	(2^297830+3670)/2	89656	Stefano Morozzi	01/2020
6229	7^106084+40	89652	Lelio R Paula	10/2015
6230	(2^297815+618)/2	89651	Stefano Morozzi	01/2020
6231	21223^16752+16752^21223	89648	Hans Havermann	08/2020
6233	(86*10^89640-311)/9	89641	Robert Price	10/2017
6232	(2^297781+2094)/2	89641	Stefano Morozzi	01/2020
6234	(2^297741+3326)/2	89629	Stefano Morozzi	01/2020
6235	(2^297724+3606)/2	89624	Stefano Morozzi	01/2020
6236	3*10^89608-59	89609	Robert Price	10/2017
6237	(2^297650+3250)/2	89602	Stefano Morozzi	01/2020
6238	3^187780-11038	89594	Enzo Doria	05/2014
6239	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
6240	5^128141-36	89567	Lelio R Paula	10/2015
6241	4*7^105951+9	89540	Lelio R Paula	10/2014
6242	(7*10^89539-439)/9	89539	Robert Price	09/2017
6243	(9772^22441-1)/9771	89536	Serge Batalov	08/2020
6244	22823^8374+8374^22823	89534	Hans Havermann	08/2020
6245	(2^297401+2954)/2	89527	Stefano Morozzi	01/2020
6246	(2^297403+1670)/2	89527	Stefano Morozzi	01/2020
6247	2^297397+177257	89526	Enzo Doria	05/2016
6249	2^297346-16241	89511	Enzo Doria	04/2013
6248	(5*10^89510+79)/3	89511	Robert Price	11/2017
6250	4^148663-3^148663	89505	Jean-Louis Charton	11/2005

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Probable Primes Top 10000

(271000 PRPs in the top)