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 ?
6751	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
6752	2^355001+335931	106866	Enzo Doria	08/2024
6753	2^354946-3	106850	M. Frind & P. Underwood	08/2002
6754	(2^354945+3134)/2	106849	Stefano Morozzi	09/2020
6755	(46^64384+1)/(46^128+1)	106843	Martin Hopf	12/2023
6756	2^354873-18693	106828	Enzo Doria	05/2013
6757	(2^354831+3186)/2	106815	Stefano Morozzi	09/2020
6759	2^354828+4257	106814	Lelio R Paula	01/2017
6758	25216^17217+17217^25216	106814	Hans Havermann	10/2020
6760	(2^354799+1218)/2	106805	Stefano Morozzi	09/2020
6761	436^40459+40459^436	106791	Norbert Schneider	03/2019
6762	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
6763	(115*10^106772-7)/9	106774	Robert Price	02/2020
6764	2^354640-354640+1	106758	Robert Price	10/2014
6765	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
6766	2^354585+95	106741	Lelio R Paula	10/2011
6767	(206*10^106737+1)/9	106739	Robert Price	04/2022
6768	2^354553+189	106732	Lelio R Paula	10/2011
6770	(2^354546+1338)/2	106729	Stefano Morozzi	02/2021
6769	(8*10^106729-71)/9	106729	Serge Batalov	11/2022
6771	2^354514-109031	106720	Enzo Doria	04/2014
6772	2^354509-109465	106718	Enzo Doria	04/2014
6773	fibonacci(510628)+2	106715	Jon Grantham	08/2023
6774	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
6775	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
6776	15^90710+28	106684	Lelio R Paula	04/2017
6777	7^126237+34	106683	Lelio R Paula	03/2017
6778	2^354385-115315	106681	Enzo Doria	06/2015
6779	2^354327-19305	106664	Enzo Doria	06/2013
6780	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
6781	10^106636+97	106637	Lelio R Paula	02/2017
6782	10^106636-22923	106636	Patrick De Geest	03/2017
6783	2^354220-57	106631	Lelio R Paula	10/2011
6784	(68*10^106628-329)/9	106629	Robert Price	03/2021
6785	(29*10^106620-77)/3	106621	Robert Price	02/2020
6786	(746*10^106618+1)/9	106620	Robert Price	03/2020
6787	2*10^106613+29	106614	Robert Price	02/2021
6788	2^354157-17041	106612	Enzo Doria	05/2013
6789	12^98778+73	106600	Lelio R Paula	02/2017
6790	33333^1576+1576^33333	106585	Hans Havermann	11/2020
6791	2^354064+1870651	106584	Enzo Doria	05/2016
6792	24568^21779+21779^24568	106577	Hans Havermann	11/2020
6793	2^353992-57	106563	Lelio R Paula	10/2011
6794	9*10^106559+59	106560	Robert Price	01/2020
6795	7*10^106553+27	106554	Robert Price	11/2020
6796	28847^4938+4938^28847	106548	Hans Havermann	10/2020
6797	NSW(139160)	106535	Robert Price	12/2018
6798	f(278321)	106535	Robert Price	07/2023
6799	(7*10^106516+113)/3	106517	Robert Price	02/2018
6800	2^353832-1853849	106515	Enzo Doria	09/2015
6801	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
6802	2^353794-18453	106503	Enzo Doria	05/2013
6803	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
6804	2^353728+7695	106483	Lelio R Paula	01/2017
6805	26476^10509+10509^26476	106475	Hans Havermann	10/2020
6806	2^353672-303	106466	Yves Minet	02/2012
6807	6^136811+101	106460	Lelio R Paula	02/2017
6808	2^353641+1871981	106457	Enzo Doria	05/2016
6809	(8*10^106454-29)/3	106455	Robert Price	07/2018
6810	27845^6654+6654^27845	106454	Hans Havermann	11/2020
6811	10^106449-700001	106449	Robert Price	08/2021
6812	25316^16017+16017^25316	106444	Hans Havermann	11/2020
6813	2^353553+54615	106431	Lelio R Paula	01/2017
6814	2^353544-18897	106428	Enzo Doria	05/2013
6815	28894^4823+4823^28894	106426	Hans Havermann	11/2020
6816	(19*10^106422+29)/3	106423	Robert Price	12/2021
6817	(694*10^106418+53)/9	106420	Robert Price	02/2022
6818	6*10^106412-13	106413	Robert Price	07/2022
6819	25696^13829+13829^25696	106402	Hans Havermann	11/2020
6820	6^136729-133	106396	Lelio R Paula	02/2017
6821	2^353418+1605	106390	Lelio R Paula	01/2017
6822	2^353387+65	106381	Lelio R Paula	10/2011
6823	2^353372+74311	106376	Enzo Doria	04/2016
6824	2^353344-3693	106368	Yves Minet	03/2017
6825	(772*10^106365-7)/9	106367	Robert Price	06/2022
6826	(56*10^106351+619)/9	106352	Robert Price	05/2021
6827	2^353277-20089	106347	Enzo Doria	06/2013
6828	2^353275+72173	106347	Enzo Doria	04/2016
6829	2^353268-17705	106345	Enzo Doria	05/2013
6830	2^353267-19857	106344	Enzo Doria	06/2013
6831	(46*10^106343+143)/9	106344	Robert Price	01/2019
6833	(2^353189+3054)/2	106321	Stefano Morozzi	09/2020
6832	35087^1072+1072^35087	106321	Hans Havermann	10/2020
6834	(2^353184+1290)/2	106319	Stefano Morozzi	01/2021
6835	F(508799)/24738824977/1990778864897	106310	Serge Batalov	07/2024
6836	26985^8684+8684^26985	106287	Hans Havermann	10/2020
6837	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
6839	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
6838	(46*10^106277+107)/9	106278	Robert Price	06/2022
6840	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
6841	2^353025+72257	106272	Enzo Doria	04/2016
6844	2^352932-20345	106244	Enzo Doria	06/2013
6842	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
6843	25628^13983+13983^25628	106244	Hans Havermann	10/2020
6845	2^352883-187	106229	Lelio R Paula	10/2011
6846	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
6847	(55*10^106222+377)/9	106223	Robert Price	02/2019
6848	2^352814-131	106208	Lelio R Paula	10/2011
6849	2^352752+73951	106189	Enzo Doria	04/2016
6850	11876*25^75945+357	106171	Eric Chen	10/2023
6851	6^136434+5	106167	Lelio R Paula	11/2014
6852	25296^15737+15737^25296	106166	Hans Havermann	09/2020
6853	8*10^106157-13	106158	Robert Price	08/2019
6854	2^352641+225677	106156	Enzo Doria	08/2024
6855	7*5^151872-8	106155	Lelio R Paula	11/2014
6856	105^52520-2	106153	Lelio R Paula	10/2017
6857	(23*10^106152-29)/3	106153	Robert Price	03/2022
6858	2^352601-1604809	106144	Enzo Doria	05/2015
6859	12^98353-43	106141	Lelio R Paula	02/2017
6860	2^352585-18901	106139	Enzo Doria	05/2013
6861	26363^10614+10614^26363	106135	Hans Havermann	09/2020
6862	(2^352554-3)/193	106128	Lelio R Paula	12/2013
6863	2^352540+15015	106126	Lelio R Paula	01/2017
6864	25068^17119+17119^25068	106125	Hans Havermann	09/2020
6865	2^352524-3149	106121	Yves Minet	10/2014
6866	(7*10^106119-67)/3	106120	Robert Price	10/2021
6867	2^352486-1858781	106109	Enzo Doria	04/2016
6868	2^352444+12705	106097	Lelio R Paula	01/2017
6869	28561^5182+5182^28561	106090	Hans Havermann	10/2020
6870	(182*10^106083+43)/9	106085	Robert Price	02/2020
6871	(266*10^106066+1)/3	106068	Robert Price	04/2020
6872	(7*10^106066-187)/9	106066	Tyler Busby	01/2023
6873	2^352228-18953	106032	Enzo Doria	05/2013
6874	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
6875	(2^352212+2250)/2	106027	Stefano Morozzi	01/2021
6876	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
6877	2^352107+1872533	105995	Enzo Doria	05/2016
6878	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
6879	2^352066-2591	105983	Yves Minet	07/2014
6880	2^352030+715	105972	Lelio R Paula	10/2011
6881	9*6^136176-5	105967	Lelio R Paula	11/2014
6882	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
6883	122^50789-50789^122	105965	Norman Luhn	09/2024
6884	28582^5097+5097^28582	105963	Hans Havermann	09/2020
6885	155^48377+2	105962	Lelio R Paula	08/2013
6886	(23*10^105944-119)/3	105945	Robert Price	07/2021
6887	2^351865+1869707	105922	Enzo Doria	05/2016
6888	24974^17427+17427^24974	105921	Hans Havermann	09/2020
6889	25163^16194+16194^25163	105920	Hans Havermann	09/2020
6890	2^351831+23	105912	Lelio R Paula	10/2011
6891	(2^351818+3798)/2	105908	Stefano Morozzi	02/2021
6892	9*2^351784-5	105899	Lelio R Paula	09/2014
6893	(2^351776+2766)/2	105895	Stefano Morozzi	01/2021
6894	(85*10^105881+203)/9	105882	Robert Price	09/2020
6895	2^351671-112387	105864	Enzo Doria	06/2014
6896	2^351669-109501	105863	Enzo Doria	04/2014
6897	2^351644+74731	105856	Enzo Doria	04/2016
6898	13^95025-42	105853	Lelio R Paula	12/2016
6899	2^351599+15015	105842	Lelio R Paula	01/2017
6900	19^82763+90	105834	Lelio R Paula	01/2017
6901	(205*10^105831-1)/3	105833	Robert Price	11/2021
6902	26050^11551+11551^26050	105832	Hans Havermann	09/2020
6903	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
6904	20^81329-51	105812	Lelio R Paula	01/2017
6905	(5*10^105811+211)/9	105811	Robert Price	02/2018
6906	2^351483+28425	105807	Lelio R Paula	01/2017
6907	25231^15610+15610^25231	105804	Hans Havermann	09/2020
6908	15^89960+86	105802	Lelio R Paula	02/2017
6909	2^351460-17289	105801	Enzo Doria	05/2013
6910	19^82735+22	105798	Lelio R Paula	01/2017
6911	2^351435-109077	105793	Enzo Doria	04/2014
6912	2^351393+1089	105780	Lelio R Paula	01/2017
6913	2^351364+72631	105772	Enzo Doria	04/2016
6914	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
6915	26818^8783+8783^26818	105761	Hans Havermann	09/2020
6918	2^351305+1872467	105754	Enzo Doria	05/2016
6917	3^221649+16	105754	Lelio R Paula	11/2016
6916	32511^1790+1790^32511	105754	Hans Havermann	09/2020
6919	8*3^221637-5	105749	Lelio R Paula	09/2014
6920	2^351279-2780449	105746	Enzo Doria	03/2016
6921	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
6922	15^89903-26	105735	Lelio R Paula	02/2017
6924	2^351213-73	105726	Lelio R Paula	10/2011
6923	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
6925	2^351192-4589	105720	Yves Minet	07/2011
6926	20^81250-33	105709	Lelio R Paula	12/2016
6927	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
6928	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
6929	2^351076-113159	105685	Enzo Doria	07/2014
6930	93^53688-2	105684	Lelio R Paula	09/2013
6931	2^351060-4559	105680	Yves Minet	07/2011
6932	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
6933	11^101473-750	105674	Enzo Doria	11/2012
6934	3*5^151181-8	105672	Lelio R Paula	11/2014
6935	15^89831-34	105650	Lelio R Paula	02/2017
6937	11^101448-360	105648	Enzo Doria	08/2012
6936	3*7^125011+4	105648	Lelio R Paula	11/2014
6938	2^350943-113269	105645	Enzo Doria	07/2014
6939	2*10^105636-91	105637	Robert Price	04/2020
6940	24231^22880+22880^24231	105634	Hans Havermann	09/2020
6941	35296^983+983^35296	105626	Hans Havermann	09/2020
6942	2^350868-19725	105622	Enzo Doria	06/2013
6943	2^350858-59291	105619	Enzo Doria	10/2015
6944	V(758484)/1516967/19720583	105618	Serge Batalov	07/2024
6945	2^350851+135	105617	Lelio R Paula	10/2011
6946	2^350841-741	105614	Lelio R Paula	01/2017
6947	3*10^105582+77	105583	Robert Price	09/2018
6948	24915^17284+17284^24915	105581	Hans Havermann	09/2020
6949	(5*10^105576-53)/3	105577	Robert Price	09/2020
6950	8*10^105571+3	105572	Robert Price	08/2015
6951	2^350674-78557	105564	Jorge Menendez	03/2018
6952	2*5^151026-3	105563	Lelio R Paula	11/2014
6953	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
6954	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
6955	3^221211+236	105545	Lelio R Paula	11/2016
6956	(32*10^105530-77)/9	105531	Robert Price	06/2018
6957	10^105515+33	105516	Lelio R Paula	11/2016
6958	24644^19125+19125^24644	105516	Hans Havermann	10/2020
6959	10^105515-41033	105515	Patrick De Geest	12/2016
6960	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
6961	2^350455-430567	105498	Harrison Mesh	06/2022
6962	17^85732-72	105489	Lelio R Paula	01/2017
6963	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
6964	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
6965	2^350356+24241	105468	Enzo Doria	10/2023
6966	25233^15118+15118^25233	105462	Hans Havermann	09/2020
6967	26261^10366+10366^26261	105454	Hans Havermann	09/2020
6968	2^350307-110329	105453	Enzo Doria	05/2014
6969	2^350253-20365	105437	Enzo Doria	06/2013
6970	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
6971	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
6972	4*10^105415-69	105416	Robert Price	01/2022
6973	(22*10^105407+179)/3	105408	Robert Price	02/2022
6974	2^350139-109009	105403	Enzo Doria	04/2014
6975	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
6976	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
6977	3*5^150763+4	105380	Lelio R Paula	11/2014
6978	12^97643+91	105375	Lelio R Paula	02/2017
6979	6*5^150744-7	105367	Lelio R Paula	11/2014
6980	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
6981	4*10^105364-39	105365	Robert Price	09/2020
6983	2^349996-112169	105360	Enzo Doria	06/2014
6982	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
6984	(418*10^105343+23)/9	105345	Robert Price	02/2020
6985	25490^13563+13563^25490	105334	Hans Havermann	10/2020
6986	11^101142-1080	105329	Enzo Doria	12/2012
6987	(68*10^105320-41)/9	105321	Robert Price	10/2013
6988	24800^17649+17649^24800	105319	Hans Havermann	09/2020
6989	3^220712-9934	105307	Enzo Doria	05/2014
6990	7*10^105296+9	105297	Robert Price	09/2015
6991	89*10^105284-7	105286	Robert Price	04/2020
6992	2^349739+1873373	105282	Enzo Doria	06/2016
6993	7^124574+24	105278	Lelio R Paula	11/2016
6994	2^349708-20957	105273	Enzo Doria	06/2013
6995	34115^1218+1218^34115	105267	Hans Havermann	09/2020
6996	24029^24029-24020^24020	105265	Henri Lifchitz	09/2024
6997	2^349649-20469	105255	Enzo Doria	06/2013
6998	2^349607-20109	105243	Enzo Doria	06/2013
6999	(85*10^105242+473)/9	105243	Robert Price	01/2020
7000	2^349594-19085	105239	Enzo Doria	05/2013

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