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 ?
9001	2^299949-1005	90294	Lelio R Paula	11/2013
9002	(2^299947+2054)/2	90293	Stefano Morozzi	01/2020
9003	21740^14229+14229^21740	90291	Hans Havermann	08/2020
9004	10^90279+62457	90280	Patrick De Geest	07/2019
9005	10^90279-1551	90279	Patrick De Geest	09/2018
9006	(2^299892+1986)/2	90277	Stefano Morozzi	01/2020
9007	(2^299893+3866)/2	90277	Stefano Morozzi	01/2020
9008	2^299868-109613	90270	Enzo Doria	04/2014
9009	10^90259+359299	90260	Patrick De Geest	07/2019
9010	10^90259-9443	90259	Patrick De Geest	09/2018
9011	(2^299831+3786)/2	90258	Stefano Morozzi	01/2020
9012	10^90252+102873	90253	Patrick De Geest	07/2019
9013	10^90252-8103	90252	Patrick De Geest	09/2018
9014	5*2^299799-3	90250	Lelio R Paula	08/2014
9015	(2^299803+3326)/2	90250	Stefano Morozzi	01/2020
9016	13^81008-2	90239	Lelio R Paula	09/2013
9017	80697!4-256	90234	Robert Price	11/2019
9019	64^49957-63^49957	90232	Robert Price	07/2013
9018	(2^299745+2994)/2	90232	Stefano Morozzi	01/2020
9020	10^90227+56281	90228	Patrick De Geest	06/2016
9024	2^299725+315	90227	Lelio R Paula	11/2013
9021	10^90227-1000000001	90227	Robert Price	05/2016
9022	10^90227-68763	90227	Patrick De Geest	06/2016
9023	9*10^90226+29	90227	Robert Price	03/2022
9025	5^129082+48	90225	Lelio R Paula	03/2016
9026	2^299699+195	90219	Lelio R Paula	10/2012
9027	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
9028	22131^11918+11918^22131	90211	Hans Havermann	08/2020
9029	10^90209+8971	90210	Patrick De Geest	09/2018
9030	10^90209-724797	90209	Patrick De Geest	07/2019
9031	10^90208+189531	90209	Patrick De Geest	07/2019
9032	10^90208-2247	90208	Patrick De Geest	09/2018
9033	(629^32233-1)/628	90207	Michael Stocker	05/2020
9034	116^43693-115	90203	Norbert Schneider	08/2018
9035	10^90202+3553	90203	Patrick De Geest	09/2018
9036	3^189053+280	90202	Lelio R Paula	04/2016
9037	10^90202-67793	90202	Patrick De Geest	07/2019
9038	2^299639-187	90201	Lelio R Paula	10/2012
9039	10^90199+254031	90200	Patrick De Geest	07/2019
9040	10^90199-2891	90199	Patrick De Geest	09/2018
9042	2^299631+183	90198	Lelio R Paula	10/2012
9041	21567^15212+15212^21567	90198	Hans Havermann	08/2020
9043	10^90196+187539	90197	Patrick De Geest	07/2019
9045	10^90196-9683	90196	Patrick De Geest	09/2018
9044	21708^14287+14287^21708	90196	Hans Havermann	08/2020
9046	10^90193+104973	90194	Patrick De Geest	07/2019
9047	10^90193-9809	90193	Patrick De Geest	09/2018
9048	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
9049	(2277^26863-1)/2276	90186	Serge Batalov	08/2020
9050	2^299567+113	90179	Lelio R Paula	10/2012
9051	2^299550+189	90174	Lelio R Paula	10/2012
9052	10^90170+376063	90171	Patrick De Geest	07/2019
9053	10^90170-6749	90170	Patrick De Geest	09/2018
9054	(2^299535+3)/29	90168	Lelio R Paula	01/2013
9055	(2^299521+13)/15	90164	Stefano Morozzi	03/2020
9056	22316^10971+10971^22316	90163	Hans Havermann	08/2020
9057	10^90160+271947	90161	Patrick De Geest	07/2019
9058	10^90160-5613	90160	Patrick De Geest	09/2018
9059	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
9060	(29*10^90153+583)/9	90154	Robert Price	06/2021
9062	3^188938+8680	90147	Lelio R Paula	04/2016
9061	10^90146+160209	90147	Patrick De Geest	07/2019
9063	10^90146-2027	90146	Patrick De Geest	09/2018
9064	6^115840-55	90142	Lelio R Paula	05/2016
9065	(5*10^90142-473)/9	90142	Robert Price	12/2017
9066	8*7^106659+5	90139	Lelio R Paula	10/2014
9067	2^299406-16653	90131	Enzo Doria	05/2013
9068	(317057^16384+1)/2	90131	Richard Fischer	10/2019
9069	(2^299409+834)/2	90131	Stefano Morozzi	01/2020
9070	10^90128+288673	90129	Patrick De Geest	07/2019
9072	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
9071	10^90128-8387	90128	Patrick De Geest	09/2018
9074	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
9073	(5^128941-3^128941)/2	90126	Kellen Shenton	05/2022
9075	6^115819-53	90125	Lelio R Paula	05/2016
9076	10^90123+6313	90124	Patrick De Geest	09/2018
9077	6^115816-16853	90123	Enzo Doria	02/2013
9078	10^90123-22617	90123	Patrick De Geest	07/2019
9079	6^115813-23	90121	Lelio R Paula	05/2016
9080	2^299351-933075	90114	Paul Bourdelais	04/2021
9081	(22*10^90110+161)/3	90111	Robert Price	02/2017
9083	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
9082	10^90105+915759	90106	Patrick De Geest	07/2019
9084	10^90105-767	90105	Patrick De Geest	09/2018
9085	10^90104+48189	90105	Patrick De Geest	07/2019
9086	(6050^23827-1)/6049	90105	Serge Batalov	08/2020
9088	10^90104-7703	90104	Patrick De Geest	09/2018
9089	10^90103+9159	90104	Patrick De Geest	09/2018
9087	(797*10^90102-23)/9	90104	Robert Price	01/2022
9090	10^90103-208457	90103	Patrick De Geest	07/2019
9091	10^90102+73011	90103	Patrick De Geest	07/2019
9092	10^90102-602433	90102	Patrick De Geest	07/2019
9093	10^90101+1225537	90102	Patrick De Geest	07/2019
9095	10^90101-3207	90101	Patrick De Geest	09/2018
9094	21730^14007+14007^21730	90101	Hans Havermann	08/2020
9096	(29*10^90096-17)/3	90097	Erik Branger	09/2014
9097	(49*10^90094+221)/9	90095	Robert Price	02/2022
9098	10^90089+143181	90090	Patrick De Geest	07/2019
9099	10^90089-3573	90089	Patrick De Geest	09/2018
9100	2^299247+1870529	90083	Enzo Doria	05/2016
9101	10^90079+1609	90080	Patrick De Geest	09/2018
9102	10^90079-230043	90079	Patrick De Geest	07/2019
9103	2^299229-2797783	90077	Enzo Doria	04/2016
9104	2^299220-16317	90075	Enzo Doria	04/2013
9105	11^86491-1350	90072	Enzo Doria	12/2012
9106	10^90071+52333	90072	Patrick De Geest	07/2019
9108	10^90071-1233	90071	Patrick De Geest	09/2018
9107	(314401^16384+1)/2	90071	Richard Fischer	10/2019
9109	10^90069+158527	90070	Patrick De Geest	07/2019
9110	10^90069-7841	90069	Patrick De Geest	09/2018
9111	(31*10^90064-1)/3	90066	Robert Price	03/2017
9112	10^90060+149431	90061	Patrick De Geest	07/2019
9113	10^90060-839	90060	Patrick De Geest	09/2018
9114	10^90052+2361	90053	Patrick De Geest	09/2018
9115	10^90052-90929	90052	Patrick De Geest	07/2019
9116	10^90047+619	90048	Patrick De Geest	09/2018
9117	10^90047-151071	90047	Patrick De Geest	07/2019
9118	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
9119	22996^8233+8233^22996	90043	Hans Havermann	08/2020
9120	2^299112+73951	90042	Enzo Doria	04/2016
9121	8^99702+7^(99702-1)	90040	Robert Price	02/2016
9122	10^90038+157803	90039	Patrick De Geest	07/2019
9123	10^90038-9687	90038	Patrick De Geest	09/2018
9125	5*10^90033+3	90034	Dmitry Domanov	11/2010
9124	(17574^21211-1)/17573	90034	Serge Batalov	08/2020
9126	10^90030+225813	90031	Patrick De Geest	07/2019
9127	10^90030-1461	90030	Patrick De Geest	09/2018
9128	243^37738+37738^243	90029	Norbert Schneider	01/2015
9129	10^90025+70569	90026	Patrick De Geest	07/2019
9130	10^90025-8703	90025	Patrick De Geest	09/2018
9131	2^299048-113297	90023	Enzo Doria	07/2014
9132	10^90015+849	90016	Patrick De Geest	09/2018
9133	10^90015-228387	90015	Patrick De Geest	07/2019
9134	10^90010+6811	90011	Patrick De Geest	09/2018
9135	10^90010-183597	90010	Patrick De Geest	11/2018
9136	10^90009+58321	90010	Patrick De Geest	11/2018
9137	10^90008+847	90009	Patrick De Geest	09/2018
9138	10^90009-356013	90009	Patrick De Geest	11/2018
9139	25696^3183+3183^25696	90009	Hans Havermann	08/2020
9141	3^188648+92	90008	Lelio R Paula	12/2015
9140	10^90008-706049	90008	Patrick De Geest	11/2018
9142	5*2^298991+7	90006	Lelio R Paula	08/2014
9143	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
9144	10^90000+8869	90001	Patrick De Geest	12/2009
9146	10^89999+82939	90000	Dirk Augustin	04/2007
9145	10^90000-140343	90000	Patrick De Geest	12/2009
9147	10^89999-194891	89999	Patrick De Geest	11/2009
9148	(2^298918+1798)/2	89983	Stefano Morozzi	01/2020
9149	19^70365-78	89980	Lelio R Paula	12/2015
9150	Phi(186062,10)/134609632483003347004451	89977	Makoto Kamada	04/2021
9151	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
9152	2^298852-64875	89964	Lelio R Paula	11/2013
9153	(2^298825+1010)/2	89955	Stefano Morozzi	01/2020
9154	18^71659+37	89952	Lelio R Paula	12/2015
9155	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
9156	(2^298769+1202)/2	89939	Stefano Morozzi	01/2020
9157	(5941^23827-1)/5940	89916	Serge Batalov	08/2020
9158	17^73067+20	89906	Lelio R Paula	11/2015
9159	2^298637-99	89899	Lelio R Paula	10/2012
9160	25513^3336+3336^25513	89889	Hans Havermann	08/2020
9161	29748^1051+1051^29748	89887	Hans Havermann	08/2020
9162	9*10^89882-91	89883	Robert Price	06/2021
9163	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
9164	2*10^89876+83	89877	Robert Price	12/2021
9165	(2^298558+3654)/2	89875	Stefano Morozzi	01/2020
9166	9*10^89858+19	89859	Robert Price	05/2016
9167	2^298501+1870067	89858	Enzo Doria	05/2016
9168	(286*10^89852-1)/3	89854	Robert Price	11/2020
9169	11^86280-98	89852	Lelio R Paula	11/2015
9170	2^298473-110059	89850	Enzo Doria	04/2014
9171	19^70263-32	89850	Lelio R Paula	12/2015
9172	21208^17221+17221^21208	89839	Hans Havermann	08/2020
9173	(299*10^89836-17)/3	89838	Robert Price	01/2017
9174	3^188286+14	89836	Robert Price	09/2013
9175	(2^298408+450)/2	89830	Stefano Morozzi	01/2020
9176	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
9177	2^298367+58905	89818	Lelio R Paula	11/2013
9178	21966^12269+12269^21966	89815	Hans Havermann	08/2020
9179	(2^298333+3126)/2	89807	Stefano Morozzi	01/2020
9180	2^298319-109657	89803	Enzo Doria	04/2014
9181	7*10^89801+13	89802	Robert Price	03/2021
9182	8*10^89800+81	89801	Robert Price	05/2017
9183	21354^16037+16037^21354	89797	Hans Havermann	08/2020
9184	(2^298249+714)/2	89782	Stefano Morozzi	01/2020
9185	21227^16954+16954^21227	89775	Hans Havermann	08/2020
9186	(733^31333-1)/732	89770	Serge Batalov	08/2020
9189	18^71505-91	89759	Lelio R Paula	12/2015
9187	(2^298171+1586)/2	89759	Stefano Morozzi	01/2020
9188	(4788^24391-1)/4787	89759	Serge Batalov	08/2020
9190	(2^298161+3530)/2	89756	Stefano Morozzi	01/2020
9191	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
9192	2^298079-109531	89731	Enzo Doria	04/2014
9193	(9255^22621-1)/9254	89720	Serge Batalov	08/2020
9194	117^43380+116	89718	Norbert Schneider	08/2018
9195	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
9196	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
9197	2^298003-66945	89708	Lelio R Paula	11/2013
9198	(23*10^89705-83)/3	89706	Robert Price	09/2017
9199	17^72900-54	89700	Lelio R Paula	11/2015
9200	(2^297968+2482)/2	89698	Stefano Morozzi	01/2020
9201	3*2^297956+5	89695	Lelio R Paula	08/2014
9202	(2^297952+3558)/2	89693	Stefano Morozzi	01/2020
9203	(3992^24907-1)/3991	89692	Serge Batalov	08/2020
9204	20^68938-11	89691	Lelio R Paula	01/2016
9205	89*10^89687-7	89689	Robert Price	03/2017
9206	(6882^23371-1)/6881	89688	Serge Batalov	08/2020
9207	(297847^16384+1)/2	89686	Richard Fischer	08/2019
9208	2^297923+77783	89684	Enzo Doria	05/2016
9209	(2^297893+1694)/2	89675	Stefano Morozzi	01/2020
9210	11^86107-24576000	89672	Enzo Doria	02/2013
9211	2^297878-111911	89671	Enzo Doria	05/2014
9212	20823^20236+20236^20823	89667	Hans Havermann	08/2020
9213	25708^3075+3075^25708	89666	Hans Havermann	08/2020
9214	21002^18585+18585^21002	89661	Hans Havermann	08/2020
9215	(2^297830+3670)/2	89656	Stefano Morozzi	01/2020
9216	7^106084+40	89652	Lelio R Paula	10/2015
9217	(2^297815+618)/2	89651	Stefano Morozzi	01/2020
9218	21223^16752+16752^21223	89648	Hans Havermann	08/2020
9220	(86*10^89640-311)/9	89641	Robert Price	10/2017
9219	(2^297781+2094)/2	89641	Stefano Morozzi	01/2020
9221	(2^297741+3326)/2	89629	Stefano Morozzi	01/2020
9222	(2^297724+3606)/2	89624	Stefano Morozzi	01/2020
9223	3*10^89608-59	89609	Robert Price	10/2017
9224	(2^297650+3250)/2	89602	Stefano Morozzi	01/2020
9225	(34*10^89599+191)/9	89600	Robert Price	08/2021
9226	3^187780-11038	89594	Enzo Doria	05/2014
9227	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
9228	5^128141-36	89567	Lelio R Paula	10/2015
9229	4*7^105951+9	89540	Lelio R Paula	10/2014
9230	(7*10^89539-439)/9	89539	Robert Price	09/2017
9231	(9772^22441-1)/9771	89536	Serge Batalov	08/2020
9232	22823^8374+8374^22823	89534	Hans Havermann	08/2020
9233	(2^297401+2954)/2	89527	Stefano Morozzi	01/2020
9234	(2^297403+1670)/2	89527	Stefano Morozzi	01/2020
9235	2^297397+177257	89526	Enzo Doria	05/2016
9236	(77*10^89518+247)/9	89519	Robert Price	03/2021
9237	2^297346-16241	89511	Enzo Doria	04/2013
9238	(5*10^89510+79)/3	89511	Robert Price	11/2017
9240	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
9239	2^297328-869688105	89505	Lelio R Paula	07/2016
9241	2^297325-459043	89504	Enzo Doria	05/2015
9242	2^297310-112391	89500	Enzo Doria	06/2014
9243	2^297296-112157	89496	Enzo Doria	06/2014
9244	57^50966-2	89490	Lelio R Paula	08/2013
9245	(266*10^89482+1)/3	89484	Robert Price	02/2016
9246	(14*10^89480-101)/3	89481	Robert Price	04/2017
9247	2618^26175+26175^2618	89466	Norbert Schneider	01/2020
9248	(2^297150+3922)/2	89451	Stefano Morozzi	01/2020
9249	(2^297141+1842)/2	89449	Stefano Morozzi	01/2020
9250	(2^297140+1458)/2	89448	Stefano Morozzi	01/2020

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Probable Primes Top 10000

(290751 PRPs in the top)