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 ?
7751	(14*10^107694-83)/3	107695	Robert Price	12/2018
7752	2^357688-1854269	107675	Enzo Doria	09/2015
7753	2^357671-112225	107670	Enzo Doria	06/2014
7754	34323^1370+1370^34323	107662	Hans Havermann	11/2020
7755	2^357618-21005	107654	Enzo Doria	06/2013
7756	2^357615-17505	107653	Enzo Doria	05/2013
7757	26350^12171+12171^26350	107649	Hans Havermann	11/2020
7759	(30^72871-1)/29	107638	Robert Price	12/2011
7758	Phi(72871,5#)	107638	Henri Lifchitz	12/2025
7760	25021^20026+20026^25021	107631	Hans Havermann	11/2020
7761	2^357521+1870217	107625	Enzo Doria	05/2016
7762	2^357477-1203	107612	Lelio R Paula	03/2017
7763	26008^13693+13693^26008	107583	Hans Havermann	10/2020
7764	25432^16991+16991^25432	107583	Hans Havermann	10/2020
7765	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
7766	5^153894-18	107568	Lelio R Paula	02/2017
7767	2^357324-69059	107566	Enzo Doria	11/2015
7768	467^40296+40296^467	107563	Norbert Schneider	03/2019
7769	29446^4495+4495^29446	107559	Hans Havermann	10/2020
7770	(8*10^107556-149)/3	107557	Robert Price	12/2021
7771	2^357283-869688105	107553	Lelio R Paula	01/2017
7772	2^357280-16805	107552	Enzo Doria	05/2013
7773	10^107547+481719	107548	Patrick De Geest	03/2017
7774	10^107547-47	107547	Lelio R Paula	02/2017
7775	(23*10^107540+37)/3	107541	Robert Price	02/2022
7776	17^87396-32	107537	Lelio R Paula	04/2017
7777	(746*10^107505+1)/9	107507	Robert Price	03/2020
7778	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
7779	2^357081+107	107493	Lelio R Paula	12/2011
7780	2^357058-3911	107486	Yves Minet	04/2017
7781	3^225274+64	107484	Lelio R Paula	03/2017
7782	5*10^107482-57	107483	Robert Price	03/2021
7783	18^85619-95	107476	Lelio R Paula	04/2017
7784	Phi(118283,10)/102584248160709208281690489429805181088536061161	107473	Anonymous	01/2026
7785	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
7786	3^225248-130	107471	Lelio R Paula	03/2017
7787	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
7788	27029^9448+9448^27029	107450	Hans Havermann	11/2020
7789	2^356935-18085	107449	Enzo Doria	05/2013
7790	55396^87+87^55396	107442	Hans Havermann	10/2020
7791	(14*10^107439-137)/3	107440	Robert Price	04/2021
7792	164^48505-48505^164	107432	Norman Luhn	09/2024
7793	10^107409+37	107410	Lelio R Paula	02/2017
7794	10^107409-329633	107409	Patrick De Geest	03/2017
7795	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
7796	2^356787-109027	107404	Enzo Doria	04/2014
7797	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
7798	3*10^107389+77	107390	Robert Price	09/2018
7799	(11*10^107385+61)/9	107386	Tyler Busby	01/2023
7800	5^153622-42	107378	Lelio R Paula	02/2017
7801	2^356699-97305	107378	Lelio R Paula	03/2017
7802	13129^26072-26072^13129	107371	Norbert Schneider	09/2022
7803	2^356654+85	107364	Lelio R Paula	11/2011
7804	2^356641-19921	107360	Enzo Doria	06/2013
7805	5*10^107355+11	107356	Robert Price	08/2019
7806	2^356623-465	107355	Lelio R Paula	03/2017
7807	19^83945-92	107345	Lelio R Paula	02/2017
7808	25491^16246+16246^25491	107337	Hans Havermann	11/2020
7809	10^107334+28149	107335	Patrick De Geest	03/2017
7810	10^107334-83	107334	Lelio R Paula	02/2017
7811	2^356518+885	107323	Lelio R Paula	03/2017
7812	(59*10^107322+391)/9	107323	Robert Price	03/2021
7813	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
7814	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
7815	2^356442-114713	107300	Enzo Doria	04/2015
7816	2^356425+72257	107295	Enzo Doria	04/2016
7817	2^356351-112237	107273	Enzo Doria	06/2014
7819	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
7818	2^356322+74539	107264	Enzo Doria	04/2016
7820	2^356274+1874479	107250	Enzo Doria	06/2016
7821	24606^22819+22819^24606	107241	Hans Havermann	10/2020
7822	(2^356243+3686)/2	107240	Stefano Morozzi	09/2020
7823	20^82422-93	107234	Lelio R Paula	02/2017
7824	2^356157-20365	107214	Enzo Doria	06/2013
7825	8*10^107209+99	107210	Robert Price	03/2021
7826	2^356129-18949	107206	Enzo Doria	05/2013
7827	(15^91163-1)/13873078234414574	107200	Paul Vanderveen	06/2025
7828	2^356100-109587	107197	Enzo Doria	04/2014
7829	2*10^107173-37	107174	Robert Price	11/2021
7830	(2^355978+3262)/2	107160	Stefano Morozzi	02/2021
7831	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
7832	2^355968-64875	107158	Lelio R Paula	01/2017
7833	2^355952+1870321	107153	Enzo Doria	05/2016
7834	27069^9088+9088^27069	107152	Hans Havermann	11/2020
7835	2^355915-117	107142	Lelio R Paula	11/2011
7836	(16*10^107140+77)/3	107141	Robert Price	03/2019
7837	24628^22369+22369^24628	107124	Hans Havermann	11/2020
7838	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
7840	3^224495-8	107112	Lelio R Paula	12/2013
7839	Phi(227687,3)	107112	Henri Lifchitz	12/2025
7841	3*10^107096+23	107097	Robert Price	03/2022
7842	25077^18632+18632^25077	107086	Hans Havermann	10/2020
7843	7^126691-44	107067	Lelio R Paula	03/2017
7844	4^177830-8243	107065	Mike Oakes	02/2011
7845	(509*10^107057+13)/9	107059	Robert Price	05/2022
7846	2^355604+214051	107048	Enzo Doria	10/2023
7847	(2^355562+1702)/2	107035	Stefano Morozzi	09/2020
7848	10^107028+3593037	107029	Paul Bourdelais	10/2021
7849	10^107028-43301	107028	Alfred Reich	08/2024
7850	2^355524-21237	107024	Enzo Doria	06/2013
7852	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
7851	24843^20320+20320^24843	107022	Hans Havermann	10/2020
7853	2^355494-19901	107015	Enzo Doria	06/2013
7854	2^355454-869688105	107003	Lelio R Paula	01/2017
7855	4*10^106997+13	106998	Robert Price	02/2021
7856	(8*10^106985-629)/9	106985	Robert Price	01/2022
7857	2^355366+54615	106976	Lelio R Paula	01/2017
7858	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
7859	2^355275-19861	106949	Enzo Doria	06/2013
7860	27503^7738+7738^27503	106949	Hans Havermann	11/2020
7861	(85*10^106943+77)/9	106944	Robert Price	07/2022
7862	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
7863	4*10^106914-93	106915	Robert Price	07/2020
7864	(151^49069-1)/90910031243271150	106904	Paul Vanderveen	06/2025
7865	4*10^106892-3	106893	Robert Price	10/2015
7866	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
7867	2^355001+335931	106866	Enzo Doria	08/2024
7868	2^354946-3	106850	M. Frind & P. Underwood	08/2002
7869	(2^354945+3134)/2	106849	Stefano Morozzi	09/2020
7870	(46^64384+1)/(46^128+1)	106843	Martin Hopf	12/2023
7871	2^354873-18693	106828	Enzo Doria	05/2013
7872	(2^354831+3186)/2	106815	Stefano Morozzi	09/2020
7874	2^354828+4257	106814	Lelio R Paula	01/2017
7873	25216^17217+17217^25216	106814	Hans Havermann	10/2020
7875	(2^354799+1218)/2	106805	Stefano Morozzi	09/2020
7876	436^40459+40459^436	106791	Norbert Schneider	03/2019
7877	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
7878	(115*10^106772-7)/9	106774	Robert Price	02/2020
7879	2^354640-354640+1	106758	Robert Price	10/2014
7880	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
7881	2^354585+95	106741	Lelio R Paula	10/2011
7882	(206*10^106737+1)/9	106739	Robert Price	04/2022
7883	2^354553+189	106732	Lelio R Paula	10/2011
7885	(2^354546+1338)/2	106729	Stefano Morozzi	02/2021
7884	(8*10^106729-71)/9	106729	Serge Batalov	11/2022
7886	2^354514-109031	106720	Enzo Doria	04/2014
7887	2^354509-109465	106718	Enzo Doria	04/2014
7888	fibonacci(510628)+2	106715	Jon Grantham	08/2023
7889	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
7890	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
7891	15^90710+28	106684	Lelio R Paula	04/2017
7892	7^126237+34	106683	Lelio R Paula	03/2017
7893	2^354385-115315	106681	Enzo Doria	06/2015
7894	2^354327-19305	106664	Enzo Doria	06/2013
7895	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
7896	10^106636+97	106637	Lelio R Paula	02/2017
7897	10^106636-22923	106636	Patrick De Geest	03/2017
7898	2^354220-57	106631	Lelio R Paula	10/2011
7899	(68*10^106628-329)/9	106629	Robert Price	03/2021
7900	(29*10^106620-77)/3	106621	Robert Price	02/2020
7901	(746*10^106618+1)/9	106620	Robert Price	03/2020
7902	2*10^106613+29	106614	Robert Price	02/2021
7903	2^354157-17041	106612	Enzo Doria	05/2013
7904	12^98778+73	106600	Lelio R Paula	02/2017
7905	Phi(447629,-2)	106594	Henri Lifchitz	12/2025
7906	33333^1576+1576^33333	106585	Hans Havermann	11/2020
7907	2^354064+1870651	106584	Enzo Doria	05/2016
7908	24568^21779+21779^24568	106577	Hans Havermann	11/2020
7909	2^353992-57	106563	Lelio R Paula	10/2011
7910	9*10^106559+59	106560	Robert Price	01/2020
7911	7*10^106553+27	106554	Robert Price	11/2020
7912	28847^4938+4938^28847	106548	Hans Havermann	10/2020
7913	(20^81901-1)/42030774209	106546	Paul Vanderveen	06/2025
7915	NSW(139160)	106535	Robert Price	12/2018
7914	f(278321)	106535	Robert Price	07/2023
7916	(7*10^106516+113)/3	106517	Robert Price	02/2018
7917	2^353832-1853849	106515	Enzo Doria	09/2015
7920	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
7918	Phi(126037,7)	106513	Henri Lifchitz	12/2025
7919	Phi(252074,-7)	106513	Henri Lifchitz	02/2026
7921	2^353794-18453	106503	Enzo Doria	05/2013
7922	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
7923	2^353728+7695	106483	Lelio R Paula	01/2017
7924	26476^10509+10509^26476	106475	Hans Havermann	10/2020
7925	2^353672-303	106466	Yves Minet	02/2012
7926	6^136811+101	106460	Lelio R Paula	02/2017
7927	2^353641+1871981	106457	Enzo Doria	05/2016
7928	(8*10^106454-29)/3	106455	Robert Price	07/2018
7929	27845^6654+6654^27845	106454	Hans Havermann	11/2020
7930	10^106449-700001	106449	Robert Price	08/2021
7931	25316^16017+16017^25316	106444	Hans Havermann	11/2020
7932	2^353553+54615	106431	Lelio R Paula	01/2017
7933	2^353544-18897	106428	Enzo Doria	05/2013
7934	28894^4823+4823^28894	106426	Hans Havermann	11/2020
7935	(19*10^106422+29)/3	106423	Robert Price	12/2021
7936	(694*10^106418+53)/9	106420	Robert Price	02/2022
7937	6*10^106412-13	106413	Robert Price	07/2022
7938	25696^13829+13829^25696	106402	Hans Havermann	11/2020
7939	6^136729-133	106396	Lelio R Paula	02/2017
7940	2^353418+1605	106390	Lelio R Paula	01/2017
7941	2^353387+65	106381	Lelio R Paula	10/2011
7942	2^353372+74311	106376	Enzo Doria	04/2016
7943	2^353344-3693	106368	Yves Minet	03/2017
7944	(772*10^106365-7)/9	106367	Robert Price	06/2022
7945	(56*10^106351+619)/9	106352	Robert Price	05/2021
7947	2^353277-20089	106347	Enzo Doria	06/2013
7946	2^353275+72173	106347	Enzo Doria	04/2016
7948	2^353268-17705	106345	Enzo Doria	05/2013
7949	2^353267-19857	106344	Enzo Doria	06/2013
7950	(46*10^106343+143)/9	106344	Robert Price	01/2019
7952	(2^353189+3054)/2	106321	Stefano Morozzi	09/2020
7951	35087^1072+1072^35087	106321	Hans Havermann	10/2020
7953	(2^353184+1290)/2	106319	Stefano Morozzi	01/2021
7954	F(508799)/24738824977/1990778864897	106310	Serge Batalov	07/2024
7955	26985^8684+8684^26985	106287	Hans Havermann	10/2020
7956	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
7958	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
7957	(46*10^106277+107)/9	106278	Robert Price	06/2022
7959	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
7960	2^353025+72257	106272	Enzo Doria	04/2016
7963	2^352932-20345	106244	Enzo Doria	06/2013
7961	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
7962	25628^13983+13983^25628	106244	Hans Havermann	10/2020
7964	2^352883-187	106229	Lelio R Paula	10/2011
7965	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
7966	(55*10^106222+377)/9	106223	Robert Price	02/2019
7967	2^352814-131	106208	Lelio R Paula	10/2011
7968	2^352752+73951	106189	Enzo Doria	04/2016
7969	11876*25^75945+357	106171	Eric Chen	10/2023
7970	6^136434+5	106167	Lelio R Paula	11/2014
7971	25296^15737+15737^25296	106166	Hans Havermann	09/2020
7972	8*10^106157-13	106158	Robert Price	08/2019
7973	2^352641+225677	106156	Enzo Doria	08/2024
7974	7*5^151872-8	106155	Lelio R Paula	11/2014
7975	105^52520-2	106153	Lelio R Paula	10/2017
7976	(23*10^106152-29)/3	106153	Robert Price	03/2022
7977	2^352601-1604809	106144	Enzo Doria	05/2015
7978	12^98353-43	106141	Lelio R Paula	02/2017
7979	2^352585-18901	106139	Enzo Doria	05/2013
7980	26363^10614+10614^26363	106135	Hans Havermann	09/2020
7981	(2^352554-3)/193	106128	Lelio R Paula	12/2013
7982	2^352540+15015	106126	Lelio R Paula	01/2017
7983	25068^17119+17119^25068	106125	Hans Havermann	09/2020
7984	2^352524-3149	106121	Yves Minet	10/2014
7985	(7*10^106119-67)/3	106120	Robert Price	10/2021
7986	2^352486-1858781	106109	Enzo Doria	04/2016
7987	2^352444+12705	106097	Lelio R Paula	01/2017
7988	28561^5182+5182^28561	106090	Hans Havermann	10/2020
7989	(182*10^106083+43)/9	106085	Robert Price	02/2020
7990	(266*10^106066+1)/3	106068	Robert Price	04/2020
7991	(7*10^106066-187)/9	106066	Tyler Busby	01/2023
7992	2^352228-18953	106032	Enzo Doria	05/2013
7993	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
7994	(2^352212+2250)/2	106027	Stefano Morozzi	01/2021
7995	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
7996	2^352107+1872533	105995	Enzo Doria	05/2016
7997	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
7998	2^352066-2591	105983	Yves Minet	07/2014
7999	2^352030+715	105972	Lelio R Paula	10/2011
8000	9*6^136176-5	105967	Lelio R Paula	11/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(302587 PRPs in the top)