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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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 ?
8001	2^299868-109613	90270	Enzo Doria	04/2014
8002	10^90259+359299	90260	Patrick De Geest	07/2019
8003	10^90259-9443	90259	Patrick De Geest	09/2018
8004	(2^299831+3786)/2	90258	Stefano Morozzi	01/2020
8005	10^90252+102873	90253	Patrick De Geest	07/2019
8006	10^90252-8103	90252	Patrick De Geest	09/2018
8007	5*2^299799-3	90250	Lelio R Paula	08/2014
8008	(2^299803+3326)/2	90250	Stefano Morozzi	01/2020
8009	13^81008-2	90239	Lelio R Paula	09/2013
8010	80697!4-256	90234	Robert Price	11/2019
8012	64^49957-63^49957	90232	Robert Price	07/2013
8011	(2^299745+2994)/2	90232	Stefano Morozzi	01/2020
8013	10^90227+56281	90228	Patrick De Geest	06/2016
8016	2^299725+315	90227	Lelio R Paula	11/2013
8014	10^90227-1000000001	90227	Robert Price	05/2016
8015	10^90227-68763	90227	Patrick De Geest	06/2016
8017	5^129082+48	90225	Lelio R Paula	03/2016
8018	2^299699+195	90219	Lelio R Paula	10/2012
8019	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
8020	22131^11918+11918^22131	90211	Hans Havermann	08/2020
8021	10^90209+8971	90210	Patrick De Geest	09/2018
8022	10^90209-724797	90209	Patrick De Geest	07/2019
8023	10^90208+189531	90209	Patrick De Geest	07/2019
8024	10^90208-2247	90208	Patrick De Geest	09/2018
8025	(629^32233-1)/628	90207	Michael Stocker	05/2020
8026	116^43693-115	90203	Norbert Schneider	08/2018
8027	10^90202+3553	90203	Patrick De Geest	09/2018
8028	3^189053+280	90202	Lelio R Paula	04/2016
8029	10^90202-67793	90202	Patrick De Geest	07/2019
8030	2^299639-187	90201	Lelio R Paula	10/2012
8031	10^90199+254031	90200	Patrick De Geest	07/2019
8032	10^90199-2891	90199	Patrick De Geest	09/2018
8033	2^299631+183	90198	Lelio R Paula	10/2012
8034	21567^15212+15212^21567	90198	Hans Havermann	08/2020
8035	10^90196+187539	90197	Patrick De Geest	07/2019
8037	10^90196-9683	90196	Patrick De Geest	09/2018
8036	21708^14287+14287^21708	90196	Hans Havermann	08/2020
8038	10^90193+104973	90194	Patrick De Geest	07/2019
8039	10^90193-9809	90193	Patrick De Geest	09/2018
8040	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
8041	(2277^26863-1)/2276	90186	Serge Batalov	08/2020
8042	2^299567+113	90179	Lelio R Paula	10/2012
8043	2^299550+189	90174	Lelio R Paula	10/2012
8044	10^90170+376063	90171	Patrick De Geest	07/2019
8045	10^90170-6749	90170	Patrick De Geest	09/2018
8046	(2^299535+3)/29	90168	Lelio R Paula	01/2013
8047	(2^299521+13)/15	90164	Stefano Morozzi	03/2020
8048	22316^10971+10971^22316	90163	Hans Havermann	08/2020
8049	10^90160+271947	90161	Patrick De Geest	07/2019
8050	10^90160-5613	90160	Patrick De Geest	09/2018
8051	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
8052	(29*10^90153+583)/9	90154	Robert Price	06/2021
8054	3^188938+8680	90147	Lelio R Paula	04/2016
8053	10^90146+160209	90147	Patrick De Geest	07/2019
8055	10^90146-2027	90146	Patrick De Geest	09/2018
8056	6^115840-55	90142	Lelio R Paula	05/2016
8057	(5*10^90142-473)/9	90142	Robert Price	12/2017
8058	8*7^106659+5	90139	Lelio R Paula	10/2014
8059	2^299406-16653	90131	Enzo Doria	05/2013
8060	(317057^16384+1)/2	90131	Richard Fischer	10/2019
8061	(2^299409+834)/2	90131	Stefano Morozzi	01/2020
8062	10^90128+288673	90129	Patrick De Geest	07/2019
8064	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
8063	10^90128-8387	90128	Patrick De Geest	09/2018
8065	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
8066	6^115819-53	90125	Lelio R Paula	05/2016
8067	10^90123+6313	90124	Patrick De Geest	09/2018
8069	6^115816-16853	90123	Enzo Doria	02/2013
8068	10^90123-22617	90123	Patrick De Geest	07/2019
8070	6^115813-23	90121	Lelio R Paula	05/2016
8071	2^299351-933075	90114	Paul Bourdelais	04/2021
8072	(22*10^90110+161)/3	90111	Robert Price	02/2017
8073	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
8074	10^90105+915759	90106	Patrick De Geest	07/2019
8077	10^90105-767	90105	Patrick De Geest	09/2018
8075	10^90104+48189	90105	Patrick De Geest	07/2019
8076	(6050^23827-1)/6049	90105	Serge Batalov	08/2020
8078	10^90104-7703	90104	Patrick De Geest	09/2018
8079	10^90103+9159	90104	Patrick De Geest	09/2018
8080	(797*10^90102-23)/9	90104	Robert Price	01/2022
8081	10^90103-208457	90103	Patrick De Geest	07/2019
8082	10^90102+73011	90103	Patrick De Geest	07/2019
8083	10^90102-602433	90102	Patrick De Geest	07/2019
8084	10^90101+1225537	90102	Patrick De Geest	07/2019
8086	10^90101-3207	90101	Patrick De Geest	09/2018
8085	21730^14007+14007^21730	90101	Hans Havermann	08/2020
8087	(29*10^90096-17)/3	90097	Erik Branger	09/2014
8088	10^90089+143181	90090	Patrick De Geest	07/2019
8089	10^90089-3573	90089	Patrick De Geest	09/2018
8090	2^299247+1870529	90083	Enzo Doria	05/2016
8091	10^90079+1609	90080	Patrick De Geest	09/2018
8092	10^90079-230043	90079	Patrick De Geest	07/2019
8093	2^299229-2797783	90077	Enzo Doria	04/2016
8094	2^299220-16317	90075	Enzo Doria	04/2013
8095	11^86491-1350	90072	Enzo Doria	12/2012
8096	10^90071+52333	90072	Patrick De Geest	07/2019
8098	10^90071-1233	90071	Patrick De Geest	09/2018
8097	(314401^16384+1)/2	90071	Richard Fischer	10/2019
8099	10^90069+158527	90070	Patrick De Geest	07/2019
8100	10^90069-7841	90069	Patrick De Geest	09/2018
8101	(31*10^90064-1)/3	90066	Robert Price	03/2017
8102	10^90060+149431	90061	Patrick De Geest	07/2019
8103	10^90060-839	90060	Patrick De Geest	09/2018
8104	10^90052+2361	90053	Patrick De Geest	09/2018
8105	10^90052-90929	90052	Patrick De Geest	07/2019
8106	10^90047+619	90048	Patrick De Geest	09/2018
8107	10^90047-151071	90047	Patrick De Geest	07/2019
8108	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
8109	22996^8233+8233^22996	90043	Hans Havermann	08/2020
8110	2^299112+73951	90042	Enzo Doria	04/2016
8111	8^99702+7^(99702-1)	90040	Robert Price	02/2016
8112	10^90038+157803	90039	Patrick De Geest	07/2019
8113	10^90038-9687	90038	Patrick De Geest	09/2018
8114	5*10^90033+3	90034	Dmitry Domanov	11/2010
8115	(17574^21211-1)/17573	90034	Serge Batalov	08/2020
8116	10^90030+225813	90031	Patrick De Geest	07/2019
8117	10^90030-1461	90030	Patrick De Geest	09/2018
8118	243^37738+37738^243	90029	Norbert Schneider	01/2015
8119	10^90025+70569	90026	Patrick De Geest	07/2019
8120	10^90025-8703	90025	Patrick De Geest	09/2018
8121	2^299048-113297	90023	Enzo Doria	07/2014
8122	10^90015+849	90016	Patrick De Geest	09/2018
8123	10^90015-228387	90015	Patrick De Geest	07/2019
8124	10^90010+6811	90011	Patrick De Geest	09/2018
8125	10^90010-183597	90010	Patrick De Geest	11/2018
8126	10^90009+58321	90010	Patrick De Geest	11/2018
8127	10^90008+847	90009	Patrick De Geest	09/2018
8128	10^90009-356013	90009	Patrick De Geest	11/2018
8129	25696^3183+3183^25696	90009	Hans Havermann	08/2020
8131	3^188648+92	90008	Lelio R Paula	12/2015
8130	10^90008-706049	90008	Patrick De Geest	11/2018
8132	5*2^298991+7	90006	Lelio R Paula	08/2014
8133	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
8134	10^90000+8869	90001	Patrick De Geest	12/2009
8136	10^89999+82939	90000	Dirk Augustin	04/2007
8135	10^90000-140343	90000	Patrick De Geest	12/2009
8137	10^89999-194891	89999	Patrick De Geest	11/2009
8138	(2^298918+1798)/2	89983	Stefano Morozzi	01/2020
8139	19^70365-78	89980	Lelio R Paula	12/2015
8140	Phi(186062,10)/134609632483003347004451	89977	Makoto Kamada	04/2021
8141	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
8142	2^298852-64875	89964	Lelio R Paula	11/2013
8143	(2^298825+1010)/2	89955	Stefano Morozzi	01/2020
8144	18^71659+37	89952	Lelio R Paula	12/2015
8145	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
8146	(2^298769+1202)/2	89939	Stefano Morozzi	01/2020
8147	(5941^23827-1)/5940	89916	Serge Batalov	08/2020
8148	17^73067+20	89906	Lelio R Paula	11/2015
8149	2^298637-99	89899	Lelio R Paula	10/2012
8150	25513^3336+3336^25513	89889	Hans Havermann	08/2020
8151	29748^1051+1051^29748	89887	Hans Havermann	08/2020
8152	9*10^89882-91	89883	Robert Price	06/2021
8153	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
8154	2*10^89876+83	89877	Robert Price	12/2021
8155	(2^298558+3654)/2	89875	Stefano Morozzi	01/2020
8156	9*10^89858+19	89859	Robert Price	05/2016
8157	2^298501+1870067	89858	Enzo Doria	05/2016
8158	(286*10^89852-1)/3	89854	Robert Price	11/2020
8159	11^86280-98	89852	Lelio R Paula	11/2015
8160	2^298473-110059	89850	Enzo Doria	04/2014
8161	19^70263-32	89850	Lelio R Paula	12/2015
8162	21208^17221+17221^21208	89839	Hans Havermann	08/2020
8163	(299*10^89836-17)/3	89838	Robert Price	01/2017
8164	3^188286+14	89836	Robert Price	09/2013
8165	(2^298408+450)/2	89830	Stefano Morozzi	01/2020
8166	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
8167	2^298367+58905	89818	Lelio R Paula	11/2013
8168	21966^12269+12269^21966	89815	Hans Havermann	08/2020
8169	(2^298333+3126)/2	89807	Stefano Morozzi	01/2020
8170	2^298319-109657	89803	Enzo Doria	04/2014
8171	7*10^89801+13	89802	Robert Price	03/2021
8172	8*10^89800+81	89801	Robert Price	05/2017
8173	21354^16037+16037^21354	89797	Hans Havermann	08/2020
8174	(2^298249+714)/2	89782	Stefano Morozzi	01/2020
8175	21227^16954+16954^21227	89775	Hans Havermann	08/2020
8176	(733^31333-1)/732	89770	Serge Batalov	08/2020
8179	18^71505-91	89759	Lelio R Paula	12/2015
8177	(2^298171+1586)/2	89759	Stefano Morozzi	01/2020
8178	(4788^24391-1)/4787	89759	Serge Batalov	08/2020
8180	(2^298161+3530)/2	89756	Stefano Morozzi	01/2020
8181	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
8182	2^298079-109531	89731	Enzo Doria	04/2014
8183	(9255^22621-1)/9254	89720	Serge Batalov	08/2020
8184	117^43380+116	89718	Norbert Schneider	08/2018
8185	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
8186	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
8187	2^298003-66945	89708	Lelio R Paula	11/2013
8188	(23*10^89705-83)/3	89706	Robert Price	09/2017
8189	17^72900-54	89700	Lelio R Paula	11/2015
8190	(2^297968+2482)/2	89698	Stefano Morozzi	01/2020
8191	3*2^297956+5	89695	Lelio R Paula	08/2014
8192	(2^297952+3558)/2	89693	Stefano Morozzi	01/2020
8193	(3992^24907-1)/3991	89692	Serge Batalov	08/2020
8194	20^68938-11	89691	Lelio R Paula	01/2016
8195	89*10^89687-7	89689	Robert Price	03/2017
8196	(6882^23371-1)/6881	89688	Serge Batalov	08/2020
8197	(297847^16384+1)/2	89686	Richard Fischer	08/2019
8198	2^297923+77783	89684	Enzo Doria	05/2016
8199	(2^297893+1694)/2	89675	Stefano Morozzi	01/2020
8200	11^86107-24576000	89672	Enzo Doria	02/2013
8201	2^297878-111911	89671	Enzo Doria	05/2014
8202	20823^20236+20236^20823	89667	Hans Havermann	08/2020
8203	25708^3075+3075^25708	89666	Hans Havermann	08/2020
8204	21002^18585+18585^21002	89661	Hans Havermann	08/2020
8205	(2^297830+3670)/2	89656	Stefano Morozzi	01/2020
8206	7^106084+40	89652	Lelio R Paula	10/2015
8207	(2^297815+618)/2	89651	Stefano Morozzi	01/2020
8208	21223^16752+16752^21223	89648	Hans Havermann	08/2020
8210	(86*10^89640-311)/9	89641	Robert Price	10/2017
8209	(2^297781+2094)/2	89641	Stefano Morozzi	01/2020
8211	(2^297741+3326)/2	89629	Stefano Morozzi	01/2020
8212	(2^297724+3606)/2	89624	Stefano Morozzi	01/2020
8213	3*10^89608-59	89609	Robert Price	10/2017
8214	(2^297650+3250)/2	89602	Stefano Morozzi	01/2020
8215	(34*10^89599+191)/9	89600	Robert Price	08/2021
8216	3^187780-11038	89594	Enzo Doria	05/2014
8217	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
8218	5^128141-36	89567	Lelio R Paula	10/2015
8219	4*7^105951+9	89540	Lelio R Paula	10/2014
8220	(7*10^89539-439)/9	89539	Robert Price	09/2017
8221	(9772^22441-1)/9771	89536	Serge Batalov	08/2020
8222	22823^8374+8374^22823	89534	Hans Havermann	08/2020
8223	(2^297401+2954)/2	89527	Stefano Morozzi	01/2020
8224	(2^297403+1670)/2	89527	Stefano Morozzi	01/2020
8225	2^297397+177257	89526	Enzo Doria	05/2016
8226	(77*10^89518+247)/9	89519	Robert Price	03/2021
8227	2^297346-16241	89511	Enzo Doria	04/2013
8228	(5*10^89510+79)/3	89511	Robert Price	11/2017
8230	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
8229	2^297328-869688105	89505	Lelio R Paula	07/2016
8231	2^297325-459043	89504	Enzo Doria	05/2015
8232	2^297310-112391	89500	Enzo Doria	06/2014
8233	2^297296-112157	89496	Enzo Doria	06/2014
8234	57^50966-2	89490	Lelio R Paula	08/2013
8235	(266*10^89482+1)/3	89484	Robert Price	02/2016
8236	(14*10^89480-101)/3	89481	Robert Price	04/2017
8237	2618^26175+26175^2618	89466	Norbert Schneider	01/2020
8238	(2^297150+3922)/2	89451	Stefano Morozzi	01/2020
8239	(2^297141+1842)/2	89449	Stefano Morozzi	01/2020
8240	(2^297140+1458)/2	89448	Stefano Morozzi	01/2020
8241	(2^297129+726)/2	89445	Stefano Morozzi	01/2020
8242	2^297122+99	89443	Lelio R Paula	10/2012
8243	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
8244	(28*10^89425+101)/3	89426	Robert Price	09/2020
8245	(2^297037+3522)/2	89417	Stefano Morozzi	01/2020
8246	(25*10^89413+161)/3	89414	Robert Price	01/2017
8247	(89*10^89411-737)/9	89412	Robert Price	01/2022
8248	29080^1187+1187^29080	89406	Hans Havermann	08/2020
8249	2^296990+1870699	89403	Enzo Doria	05/2016
8250	2^296972-1017	89398	Lelio R Paula	11/2013

Find by discoverer :

PRP Records

Probable Primes Top 10000

(288949 PRPs in the top)