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 ?
7501	2^354585+95	106741	Lelio R Paula	10/2011
7502	(206*10^106737+1)/9	106739	Robert Price	04/2022
7503	2^354553+189	106732	Lelio R Paula	10/2011
7505	(2^354546+1338)/2	106729	Stefano Morozzi	02/2021
7504	(8*10^106729-71)/9	106729	Serge Batalov	11/2022
7506	2^354514-109031	106720	Enzo Doria	04/2014
7507	2^354509-109465	106718	Enzo Doria	04/2014
7508	fibonacci(510628)+2	106715	Jon Grantham	08/2023
7509	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
7510	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
7511	15^90710+28	106684	Lelio R Paula	04/2017
7512	7^126237+34	106683	Lelio R Paula	03/2017
7513	2^354385-115315	106681	Enzo Doria	06/2015
7514	2^354327-19305	106664	Enzo Doria	06/2013
7515	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
7516	10^106636+97	106637	Lelio R Paula	02/2017
7517	10^106636-22923	106636	Patrick De Geest	03/2017
7518	2^354220-57	106631	Lelio R Paula	10/2011
7519	(68*10^106628-329)/9	106629	Robert Price	03/2021
7520	(29*10^106620-77)/3	106621	Robert Price	02/2020
7521	(746*10^106618+1)/9	106620	Robert Price	03/2020
7522	2*10^106613+29	106614	Robert Price	02/2021
7523	2^354157-17041	106612	Enzo Doria	05/2013
7524	12^98778+73	106600	Lelio R Paula	02/2017
7525	33333^1576+1576^33333	106585	Hans Havermann	11/2020
7526	2^354064+1870651	106584	Enzo Doria	05/2016
7527	24568^21779+21779^24568	106577	Hans Havermann	11/2020
7528	2^353992-57	106563	Lelio R Paula	10/2011
7529	9*10^106559+59	106560	Robert Price	01/2020
7530	7*10^106553+27	106554	Robert Price	11/2020
7531	28847^4938+4938^28847	106548	Hans Havermann	10/2020
7532	(20^81901-1)/42030774209	106546	Paul Vanderveen	06/2025
7534	NSW(139160)	106535	Robert Price	12/2018
7533	f(278321)	106535	Robert Price	07/2023
7535	(7*10^106516+113)/3	106517	Robert Price	02/2018
7536	2^353832-1853849	106515	Enzo Doria	09/2015
7537	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
7538	2^353794-18453	106503	Enzo Doria	05/2013
7539	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
7540	2^353728+7695	106483	Lelio R Paula	01/2017
7541	26476^10509+10509^26476	106475	Hans Havermann	10/2020
7542	2^353672-303	106466	Yves Minet	02/2012
7543	6^136811+101	106460	Lelio R Paula	02/2017
7544	2^353641+1871981	106457	Enzo Doria	05/2016
7545	(8*10^106454-29)/3	106455	Robert Price	07/2018
7546	27845^6654+6654^27845	106454	Hans Havermann	11/2020
7547	10^106449-700001	106449	Robert Price	08/2021
7548	25316^16017+16017^25316	106444	Hans Havermann	11/2020
7549	2^353553+54615	106431	Lelio R Paula	01/2017
7550	2^353544-18897	106428	Enzo Doria	05/2013
7551	28894^4823+4823^28894	106426	Hans Havermann	11/2020
7552	(19*10^106422+29)/3	106423	Robert Price	12/2021
7553	(694*10^106418+53)/9	106420	Robert Price	02/2022
7554	6*10^106412-13	106413	Robert Price	07/2022
7555	25696^13829+13829^25696	106402	Hans Havermann	11/2020
7556	6^136729-133	106396	Lelio R Paula	02/2017
7557	2^353418+1605	106390	Lelio R Paula	01/2017
7558	2^353387+65	106381	Lelio R Paula	10/2011
7559	2^353372+74311	106376	Enzo Doria	04/2016
7560	2^353344-3693	106368	Yves Minet	03/2017
7561	(772*10^106365-7)/9	106367	Robert Price	06/2022
7562	(56*10^106351+619)/9	106352	Robert Price	05/2021
7563	2^353277-20089	106347	Enzo Doria	06/2013
7564	2^353275+72173	106347	Enzo Doria	04/2016
7565	2^353268-17705	106345	Enzo Doria	05/2013
7566	2^353267-19857	106344	Enzo Doria	06/2013
7567	(46*10^106343+143)/9	106344	Robert Price	01/2019
7569	(2^353189+3054)/2	106321	Stefano Morozzi	09/2020
7568	35087^1072+1072^35087	106321	Hans Havermann	10/2020
7570	(2^353184+1290)/2	106319	Stefano Morozzi	01/2021
7571	F(508799)/24738824977/1990778864897	106310	Serge Batalov	07/2024
7572	26985^8684+8684^26985	106287	Hans Havermann	10/2020
7573	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
7575	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
7574	(46*10^106277+107)/9	106278	Robert Price	06/2022
7576	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
7577	2^353025+72257	106272	Enzo Doria	04/2016
7580	2^352932-20345	106244	Enzo Doria	06/2013
7578	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
7579	25628^13983+13983^25628	106244	Hans Havermann	10/2020
7581	2^352883-187	106229	Lelio R Paula	10/2011
7582	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
7583	(55*10^106222+377)/9	106223	Robert Price	02/2019
7584	2^352814-131	106208	Lelio R Paula	10/2011
7585	2^352752+73951	106189	Enzo Doria	04/2016
7586	11876*25^75945+357	106171	Eric Chen	10/2023
7587	6^136434+5	106167	Lelio R Paula	11/2014
7588	25296^15737+15737^25296	106166	Hans Havermann	09/2020
7589	8*10^106157-13	106158	Robert Price	08/2019
7590	2^352641+225677	106156	Enzo Doria	08/2024
7591	7*5^151872-8	106155	Lelio R Paula	11/2014
7592	105^52520-2	106153	Lelio R Paula	10/2017
7593	(23*10^106152-29)/3	106153	Robert Price	03/2022
7594	2^352601-1604809	106144	Enzo Doria	05/2015
7595	12^98353-43	106141	Lelio R Paula	02/2017
7596	2^352585-18901	106139	Enzo Doria	05/2013
7597	26363^10614+10614^26363	106135	Hans Havermann	09/2020
7598	(2^352554-3)/193	106128	Lelio R Paula	12/2013
7599	2^352540+15015	106126	Lelio R Paula	01/2017
7600	25068^17119+17119^25068	106125	Hans Havermann	09/2020
7601	2^352524-3149	106121	Yves Minet	10/2014
7602	(7*10^106119-67)/3	106120	Robert Price	10/2021
7603	2^352486-1858781	106109	Enzo Doria	04/2016
7604	2^352444+12705	106097	Lelio R Paula	01/2017
7605	28561^5182+5182^28561	106090	Hans Havermann	10/2020
7606	(182*10^106083+43)/9	106085	Robert Price	02/2020
7607	(266*10^106066+1)/3	106068	Robert Price	04/2020
7608	(7*10^106066-187)/9	106066	Tyler Busby	01/2023
7609	2^352228-18953	106032	Enzo Doria	05/2013
7610	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
7611	(2^352212+2250)/2	106027	Stefano Morozzi	01/2021
7612	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
7613	2^352107+1872533	105995	Enzo Doria	05/2016
7614	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
7615	2^352066-2591	105983	Yves Minet	07/2014
7616	2^352030+715	105972	Lelio R Paula	10/2011
7617	9*6^136176-5	105967	Lelio R Paula	11/2014
7618	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
7619	122^50789-50789^122	105965	Norman Luhn	09/2024
7620	28582^5097+5097^28582	105963	Hans Havermann	09/2020
7621	155^48377+2	105962	Lelio R Paula	08/2013
7622	(23*10^105944-119)/3	105945	Robert Price	07/2021
7623	2^351865+1869707	105922	Enzo Doria	05/2016
7624	24974^17427+17427^24974	105921	Hans Havermann	09/2020
7625	25163^16194+16194^25163	105920	Hans Havermann	09/2020
7626	2^351831+23	105912	Lelio R Paula	10/2011
7627	(2^351818+3798)/2	105908	Stefano Morozzi	02/2021
7628	9*2^351784-5	105899	Lelio R Paula	09/2014
7629	(2^351776+2766)/2	105895	Stefano Morozzi	01/2021
7630	(85*10^105881+203)/9	105882	Robert Price	09/2020
7631	2^351671-112387	105864	Enzo Doria	06/2014
7632	2^351669-109501	105863	Enzo Doria	04/2014
7633	2^351644+74731	105856	Enzo Doria	04/2016
7634	13^95025-42	105853	Lelio R Paula	12/2016
7635	2^351599+15015	105842	Lelio R Paula	01/2017
7636	19^82763+90	105834	Lelio R Paula	01/2017
7637	(205*10^105831-1)/3	105833	Robert Price	11/2021
7638	26050^11551+11551^26050	105832	Hans Havermann	09/2020
7639	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
7640	20^81329-51	105812	Lelio R Paula	01/2017
7641	(5*10^105811+211)/9	105811	Robert Price	02/2018
7642	2^351483+28425	105807	Lelio R Paula	01/2017
7643	25231^15610+15610^25231	105804	Hans Havermann	09/2020
7644	15^89960+86	105802	Lelio R Paula	02/2017
7645	2^351460-17289	105801	Enzo Doria	05/2013
7646	19^82735+22	105798	Lelio R Paula	01/2017
7647	2^351435-109077	105793	Enzo Doria	04/2014
7648	2^351393+1089	105780	Lelio R Paula	01/2017
7649	2^351364+72631	105772	Enzo Doria	04/2016
7650	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
7651	26818^8783+8783^26818	105761	Hans Havermann	09/2020
7654	2^351305+1872467	105754	Enzo Doria	05/2016
7653	3^221649+16	105754	Lelio R Paula	11/2016
7652	32511^1790+1790^32511	105754	Hans Havermann	09/2020
7655	8*3^221637-5	105749	Lelio R Paula	09/2014
7656	2^351279-2780449	105746	Enzo Doria	03/2016
7657	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
7658	15^89903-26	105735	Lelio R Paula	02/2017
7660	2^351213-73	105726	Lelio R Paula	10/2011
7659	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
7661	2^351192-4589	105720	Yves Minet	07/2011
7662	20^81250-33	105709	Lelio R Paula	12/2016
7663	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
7664	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
7665	2^351076-113159	105685	Enzo Doria	07/2014
7666	93^53688-2	105684	Lelio R Paula	09/2013
7667	2^351060-4559	105680	Yves Minet	07/2011
7668	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
7669	11^101473-750	105674	Enzo Doria	11/2012
7670	3*5^151181-8	105672	Lelio R Paula	11/2014
7671	15^89831-34	105650	Lelio R Paula	02/2017
7673	11^101448-360	105648	Enzo Doria	08/2012
7672	3*7^125011+4	105648	Lelio R Paula	11/2014
7674	2^350943-113269	105645	Enzo Doria	07/2014
7675	2*10^105636-91	105637	Robert Price	04/2020
7676	24231^22880+22880^24231	105634	Hans Havermann	09/2020
7677	35296^983+983^35296	105626	Hans Havermann	09/2020
7678	2^350868-19725	105622	Enzo Doria	06/2013
7679	2^350858-59291	105619	Enzo Doria	10/2015
7680	V(758484)/1516967/19720583	105618	Serge Batalov	07/2024
7681	2^350851+135	105617	Lelio R Paula	10/2011
7682	2^350841-741	105614	Lelio R Paula	01/2017
7683	3*10^105582+77	105583	Robert Price	09/2018
7684	24915^17284+17284^24915	105581	Hans Havermann	09/2020
7685	(5*10^105576-53)/3	105577	Robert Price	09/2020
7686	8*10^105571+3	105572	Robert Price	08/2015
7687	2^350674-78557	105564	Jorge Menendez	03/2018
7688	2*5^151026-3	105563	Lelio R Paula	11/2014
7689	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
7690	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
7691	3^221211+236	105545	Lelio R Paula	11/2016
7692	(32*10^105530-77)/9	105531	Robert Price	06/2018
7693	10^105515+33	105516	Lelio R Paula	11/2016
7694	24644^19125+19125^24644	105516	Hans Havermann	10/2020
7695	10^105515-41033	105515	Patrick De Geest	12/2016
7696	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
7697	2^350455-430567	105498	Harrison Mesh	06/2022
7698	17^85732-72	105489	Lelio R Paula	01/2017
7699	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
7700	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
7701	2^350356+24241	105468	Enzo Doria	10/2023
7702	25233^15118+15118^25233	105462	Hans Havermann	09/2020
7703	26261^10366+10366^26261	105454	Hans Havermann	09/2020
7704	2^350307-110329	105453	Enzo Doria	05/2014
7705	2^350253-20365	105437	Enzo Doria	06/2013
7706	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
7707	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
7708	4*10^105415-69	105416	Robert Price	01/2022
7709	21^79725-22	105414	Anonymous	09/2024
7710	(22*10^105407+179)/3	105408	Robert Price	02/2022
7711	2^350139-109009	105403	Enzo Doria	04/2014
7712	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
7713	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
7714	3*5^150763+4	105380	Lelio R Paula	11/2014
7715	12^97643+91	105375	Lelio R Paula	02/2017
7716	6*5^150744-7	105367	Lelio R Paula	11/2014
7717	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
7718	4*10^105364-39	105365	Robert Price	09/2020
7720	2^349996-112169	105360	Enzo Doria	06/2014
7719	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
7721	(418*10^105343+23)/9	105345	Robert Price	02/2020
7722	25490^13563+13563^25490	105334	Hans Havermann	10/2020
7723	(5^504004)%F(504004)	105330	Henri Lifchitz	06/2025
7724	11^101142-1080	105329	Enzo Doria	12/2012
7725	(68*10^105320-41)/9	105321	Robert Price	10/2013
7726	24800^17649+17649^24800	105319	Hans Havermann	09/2020
7727	3^220712-9934	105307	Enzo Doria	05/2014
7728	7*10^105296+9	105297	Robert Price	09/2015
7729	89*10^105284-7	105286	Robert Price	04/2020
7730	2^349739+1873373	105282	Enzo Doria	06/2016
7731	7^124574+24	105278	Lelio R Paula	11/2016
7732	2^349708-20957	105273	Enzo Doria	06/2013
7733	34115^1218+1218^34115	105267	Hans Havermann	09/2020
7734	24029^24029-24020^24020	105265	Henri Lifchitz	09/2024
7735	2^349649-20469	105255	Enzo Doria	06/2013
7736	2^349607-20109	105243	Enzo Doria	06/2013
7737	(85*10^105242+473)/9	105243	Robert Price	01/2020
7738	2^349594-19085	105239	Enzo Doria	05/2013
7739	2^349530+1874479	105220	Enzo Doria	06/2016
7740	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
7741	(106*10^105199+17)/3	105201	Robert Price	04/2021
7742	(2^349452+3570)/2	105196	Stefano Morozzi	09/2020
7743	3^220464-112852	105189	Enzo Doria	07/2014
7744	2^349419-17349	105186	Enzo Doria	05/2013
7745	2^349400-2579	105180	Yves Minet	07/2014
7746	8*5^150471+3	105176	Lelio R Paula	11/2014
7747	(2^349359+2298)/2	105168	Stefano Morozzi	02/2021
7748	655^37342+37342^655	105165	Norbert Schneider	08/2018
7749	13^94403+94	105160	Lelio R Paula	12/2016
7750	2^349301-112309	105151	Enzo Doria	06/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301737 PRPs in the top)