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 ?
7751	26985^8684+8684^26985	106287	Hans Havermann	10/2020
7752	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
7754	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
7753	(46*10^106277+107)/9	106278	Robert Price	06/2022
7755	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
7756	2^353025+72257	106272	Enzo Doria	04/2016
7759	2^352932-20345	106244	Enzo Doria	06/2013
7757	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
7758	25628^13983+13983^25628	106244	Hans Havermann	10/2020
7760	2^352883-187	106229	Lelio R Paula	10/2011
7761	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
7762	(55*10^106222+377)/9	106223	Robert Price	02/2019
7763	2^352814-131	106208	Lelio R Paula	10/2011
7764	2^352752+73951	106189	Enzo Doria	04/2016
7765	11876*25^75945+357	106171	Eric Chen	10/2023
7766	6^136434+5	106167	Lelio R Paula	11/2014
7767	25296^15737+15737^25296	106166	Hans Havermann	09/2020
7768	8*10^106157-13	106158	Robert Price	08/2019
7769	2^352641+225677	106156	Enzo Doria	08/2024
7770	7*5^151872-8	106155	Lelio R Paula	11/2014
7771	105^52520-2	106153	Lelio R Paula	10/2017
7772	(23*10^106152-29)/3	106153	Robert Price	03/2022
7773	2^352601-1604809	106144	Enzo Doria	05/2015
7774	12^98353-43	106141	Lelio R Paula	02/2017
7775	2^352585-18901	106139	Enzo Doria	05/2013
7776	26363^10614+10614^26363	106135	Hans Havermann	09/2020
7777	(2^352554-3)/193	106128	Lelio R Paula	12/2013
7778	2^352540+15015	106126	Lelio R Paula	01/2017
7779	25068^17119+17119^25068	106125	Hans Havermann	09/2020
7780	2^352524-3149	106121	Yves Minet	10/2014
7781	(7*10^106119-67)/3	106120	Robert Price	10/2021
7782	2^352486-1858781	106109	Enzo Doria	04/2016
7783	2^352444+12705	106097	Lelio R Paula	01/2017
7784	28561^5182+5182^28561	106090	Hans Havermann	10/2020
7785	(182*10^106083+43)/9	106085	Robert Price	02/2020
7786	(266*10^106066+1)/3	106068	Robert Price	04/2020
7787	(7*10^106066-187)/9	106066	Tyler Busby	01/2023
7788	2^352228-18953	106032	Enzo Doria	05/2013
7789	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
7790	(2^352212+2250)/2	106027	Stefano Morozzi	01/2021
7791	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
7792	2^352107+1872533	105995	Enzo Doria	05/2016
7793	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
7794	2^352066-2591	105983	Yves Minet	07/2014
7795	2^352030+715	105972	Lelio R Paula	10/2011
7796	9*6^136176-5	105967	Lelio R Paula	11/2014
7797	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
7798	122^50789-50789^122	105965	Norman Luhn	09/2024
7799	28582^5097+5097^28582	105963	Hans Havermann	09/2020
7800	155^48377+2	105962	Lelio R Paula	08/2013
7801	(23*10^105944-119)/3	105945	Robert Price	07/2021
7802	2^351865+1869707	105922	Enzo Doria	05/2016
7803	24974^17427+17427^24974	105921	Hans Havermann	09/2020
7804	25163^16194+16194^25163	105920	Hans Havermann	09/2020
7805	2^351831+23	105912	Lelio R Paula	10/2011
7806	(2^351818+3798)/2	105908	Stefano Morozzi	02/2021
7807	9*2^351784-5	105899	Lelio R Paula	09/2014
7808	(2^351776+2766)/2	105895	Stefano Morozzi	01/2021
7809	(85*10^105881+203)/9	105882	Robert Price	09/2020
7810	2^351671-112387	105864	Enzo Doria	06/2014
7811	2^351669-109501	105863	Enzo Doria	04/2014
7812	2^351644+74731	105856	Enzo Doria	04/2016
7813	13^95025-42	105853	Lelio R Paula	12/2016
7814	2^351599+15015	105842	Lelio R Paula	01/2017
7815	19^82763+90	105834	Lelio R Paula	01/2017
7816	(205*10^105831-1)/3	105833	Robert Price	11/2021
7817	26050^11551+11551^26050	105832	Hans Havermann	09/2020
7818	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
7819	20^81329-51	105812	Lelio R Paula	01/2017
7820	(5*10^105811+211)/9	105811	Robert Price	02/2018
7821	2^351483+28425	105807	Lelio R Paula	01/2017
7822	25231^15610+15610^25231	105804	Hans Havermann	09/2020
7823	15^89960+86	105802	Lelio R Paula	02/2017
7824	2^351460-17289	105801	Enzo Doria	05/2013
7825	19^82735+22	105798	Lelio R Paula	01/2017
7826	2^351435-109077	105793	Enzo Doria	04/2014
7827	2^351393+1089	105780	Lelio R Paula	01/2017
7828	2^351364+72631	105772	Enzo Doria	04/2016
7829	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
7830	26818^8783+8783^26818	105761	Hans Havermann	09/2020
7833	2^351305+1872467	105754	Enzo Doria	05/2016
7832	3^221649+16	105754	Lelio R Paula	11/2016
7831	32511^1790+1790^32511	105754	Hans Havermann	09/2020
7834	8*3^221637-5	105749	Lelio R Paula	09/2014
7835	2^351279-2780449	105746	Enzo Doria	03/2016
7836	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
7837	15^89903-26	105735	Lelio R Paula	02/2017
7839	2^351213-73	105726	Lelio R Paula	10/2011
7838	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
7840	2^351192-4589	105720	Yves Minet	07/2011
7841	20^81250-33	105709	Lelio R Paula	12/2016
7842	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
7843	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
7844	2^351076-113159	105685	Enzo Doria	07/2014
7845	93^53688-2	105684	Lelio R Paula	09/2013
7846	2^351060-4559	105680	Yves Minet	07/2011
7847	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
7848	11^101473-750	105674	Enzo Doria	11/2012
7849	3*5^151181-8	105672	Lelio R Paula	11/2014
7850	15^89831-34	105650	Lelio R Paula	02/2017
7852	11^101448-360	105648	Enzo Doria	08/2012
7851	3*7^125011+4	105648	Lelio R Paula	11/2014
7853	2^350943-113269	105645	Enzo Doria	07/2014
7854	2*10^105636-91	105637	Robert Price	04/2020
7855	24231^22880+22880^24231	105634	Hans Havermann	09/2020
7856	35296^983+983^35296	105626	Hans Havermann	09/2020
7857	2^350868-19725	105622	Enzo Doria	06/2013
7858	2^350858-59291	105619	Enzo Doria	10/2015
7859	V(758484)/1516967/19720583	105618	Serge Batalov	07/2024
7860	2^350851+135	105617	Lelio R Paula	10/2011
7861	2^350841-741	105614	Lelio R Paula	01/2017
7862	3*10^105582+77	105583	Robert Price	09/2018
7863	24915^17284+17284^24915	105581	Hans Havermann	09/2020
7864	(5*10^105576-53)/3	105577	Robert Price	09/2020
7865	8*10^105571+3	105572	Robert Price	08/2015
7866	2^350674-78557	105564	Jorge Menendez	03/2018
7867	2*5^151026-3	105563	Lelio R Paula	11/2014
7868	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
7869	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
7870	3^221211+236	105545	Lelio R Paula	11/2016
7871	(32*10^105530-77)/9	105531	Robert Price	06/2018
7872	10^105515+33	105516	Lelio R Paula	11/2016
7873	24644^19125+19125^24644	105516	Hans Havermann	10/2020
7874	10^105515-41033	105515	Patrick De Geest	12/2016
7875	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
7876	2^350455-430567	105498	Harrison Mesh	06/2022
7877	17^85732-72	105489	Lelio R Paula	01/2017
7878	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
7879	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
7880	2^350356+24241	105468	Enzo Doria	10/2023
7881	25233^15118+15118^25233	105462	Hans Havermann	09/2020
7882	26261^10366+10366^26261	105454	Hans Havermann	09/2020
7883	2^350307-110329	105453	Enzo Doria	05/2014
7884	2^350253-20365	105437	Enzo Doria	06/2013
7885	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
7886	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
7887	4*10^105415-69	105416	Robert Price	01/2022
7888	21^79725-22	105414	Anonymous	09/2024
7889	(22*10^105407+179)/3	105408	Robert Price	02/2022
7890	2^350139-109009	105403	Enzo Doria	04/2014
7891	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
7892	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
7893	3*5^150763+4	105380	Lelio R Paula	11/2014
7894	12^97643+91	105375	Lelio R Paula	02/2017
7895	6*5^150744-7	105367	Lelio R Paula	11/2014
7896	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
7897	4*10^105364-39	105365	Robert Price	09/2020
7899	2^349996-112169	105360	Enzo Doria	06/2014
7898	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
7900	(418*10^105343+23)/9	105345	Robert Price	02/2020
7901	25490^13563+13563^25490	105334	Hans Havermann	10/2020
7902	(5^504004)%F(504004)	105330	Henri Lifchitz	06/2025
7903	11^101142-1080	105329	Enzo Doria	12/2012
7904	(68*10^105320-41)/9	105321	Robert Price	10/2013
7905	24800^17649+17649^24800	105319	Hans Havermann	09/2020
7906	3^220712-9934	105307	Enzo Doria	05/2014
7907	7*10^105296+9	105297	Robert Price	09/2015
7908	89*10^105284-7	105286	Robert Price	04/2020
7909	2^349739+1873373	105282	Enzo Doria	06/2016
7910	7^124574+24	105278	Lelio R Paula	11/2016
7911	2^349708-20957	105273	Enzo Doria	06/2013
7912	34115^1218+1218^34115	105267	Hans Havermann	09/2020
7913	24029^24029-24020^24020	105265	Henri Lifchitz	09/2024
7914	2^349649-20469	105255	Enzo Doria	06/2013
7915	2^349607-20109	105243	Enzo Doria	06/2013
7916	(85*10^105242+473)/9	105243	Robert Price	01/2020
7917	2^349594-19085	105239	Enzo Doria	05/2013
7918	2^349530+1874479	105220	Enzo Doria	06/2016
7919	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
7920	(106*10^105199+17)/3	105201	Robert Price	04/2021
7921	(2^349452+3570)/2	105196	Stefano Morozzi	09/2020
7922	3^220464-112852	105189	Enzo Doria	07/2014
7923	2^349419-17349	105186	Enzo Doria	05/2013
7924	2^349400-2579	105180	Yves Minet	07/2014
7925	8*5^150471+3	105176	Lelio R Paula	11/2014
7926	(2^349359+2298)/2	105168	Stefano Morozzi	02/2021
7927	655^37342+37342^655	105165	Norbert Schneider	08/2018
7928	13^94403+94	105160	Lelio R Paula	12/2016
7929	349315*2^349315+3	105160	Anonymous	09/2025
7930	2^349301-112309	105151	Enzo Doria	06/2014
7931	30291^2960+2960^30291	105149	Hans Havermann	09/2020
7932	27350^6981+6981^27350	105132	Hans Havermann	09/2020
7934	9*2^349220+5	105127	Lelio R Paula	09/2014
7933	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
7935	7*3^220317+8	105119	Lelio R Paula	09/2014
7936	7^124386+88	105119	Lelio R Paula	11/2016
7937	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
7938	2^349171-19657	105111	Enzo Doria	06/2013
7939	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
7940	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
7941	(2^349111-5)/3	105093	Lelio R Paula	12/2013
7942	675^37142+37142^675	105087	Norbert Schneider	08/2018
7943	2^348981-2797573	105054	Enzo Doria	04/2016
7944	(445^39667+1)/446	105050	Jinyuan Wang	05/2024
7945	2^348869-6555	105021	Lelio R Paula	01/2017
7946	10^105003-17319	105003	Alfred Reich	08/2024
7947	5^150217+78	104998	Lelio R Paula	11/2016
7948	(88*10^104989-1)/3	104991	Robert Price	04/2020
7949	(28*10^104972+149)/3	104973	Robert Price	12/2019
7950	24927^16262+16262^24927	104972	Hans Havermann	10/2020
7951	2^348703-113005	104971	Enzo Doria	06/2014
7952	(191*10^104956-17)/3	104958	Robert Price	11/2021
7953	2^348612-809	104943	Yves Minet	05/2013
7954	(73*10^104942-1)/9	104943	Robert Price	01/2015
7955	2^348583-350407	104934	Enzo Doria	06/2015
7956	2^348531-949	104919	Yves Minet	05/2012
7957	20^80636-59	104910	Lelio R Paula	12/2016
7958	8*10^104893-13	104894	Robert Price	08/2019
7960	2^348437+35	104890	Lelio R Paula	09/2011
7959	25208^14487+14487^25208	104890	Hans Havermann	09/2020
7961	2^348348+135	104864	Lelio R Paula	09/2011
7962	(29*10^104858+349)/9	104859	Robert Price	06/2021
7963	6*10^104852-31	104853	Robert Price	07/2020
7965	(2^348284+9)/25	104843	Lelio R Paula	12/2013
7964	75^55914-74	104843	Norbert Schneider	01/2015
7966	2^348268+255255	104840	Lelio R Paula	01/2017
7967	35540^891+891^35540	104839	Hans Havermann	09/2020
7968	5^149985-52	104836	Lelio R Paula	11/2016
7969	2^348224-20249	104826	Enzo Doria	06/2013
7970	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
7971	2^348212-20105	104823	Enzo Doria	06/2013
7972	24647^17898+17898^24647	104819	Hans Havermann	10/2020
7973	20^80562+19	104814	Lelio R Paula	12/2016
7974	2*10^104811-87	104812	Robert Price	04/2018
7975	2^348149-20053	104804	Enzo Doria	06/2013
7976	2^348095-171	104788	Lelio R Paula	09/2011
7977	25383^13412+13412^25383	104769	Hans Havermann	09/2020
7978	2^348003-20377	104760	Enzo Doria	06/2013
7979	26^74036-27	104759	Anonymous	09/2024
7981	2^347994-741	104757	Lelio R Paula	12/2016
7980	(2^347993+2234)/2	104757	Stefano Morozzi	01/2021
7982	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
7983	25137^14702+14702^25137	104756	Hans Havermann	09/2020
7984	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
7985	12883^25484-25484^12883	104740	Norbert Schneider	08/2022
7986	2^347910-109937	104732	Enzo Doria	04/2014
7987	(88*10^104709-637)/9	104710	Robert Price	11/2020
7988	(13*10^104702+71)/3	104703	Robert Price	06/2021
7989	5^149794+28	104702	Lelio R Paula	11/2016
7990	105^51800-2	104698	Lelio R Paula	10/2017
7991	(16^86939+3^86939)/19	104684	Robert Price	06/2013
7992	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
7993	2^347731-18609	104678	Enzo Doria	05/2013
7994	4*6^134519+7	104677	Lelio R Paula	11/2014
7995	(34*10^104672-259)/9	104673	Robert Price	12/2021
7996	25321^13588+13588^25321	104656	Hans Havermann	09/2020
7997	2^347625+5367	104646	Riley Fisher	04/2023
7998	2^347612-18545	104642	Enzo Doria	05/2013
7999	6^134465+95	104635	Lelio R Paula	11/2016
8000	(166*10^104633-7)/3	104635	Robert Price	11/2020

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PRP Records

Probable Primes Top 10000

(301955 PRPs in the top)