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	2^336350-344291	101252	Enzo Doria	07/2015
7752	(17*10^101251-161)/9	101252	Robert Price	02/2021
7753	(56*10^101222-47)/9	101223	Robert Price	02/2019
7754	2^336243-108777	101220	Enzo Doria	03/2014
7755	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
7756	23535^19954+19954^23535	101202	Hans Havermann	11/2018
7757	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
7758	2^336150-20393	101192	Enzo Doria	06/2013
7759	23996^16473+16473^23996	101186	Hans Havermann	11/2018
7760	2^336112-1865249	101180	Enzo Doria	03/2016
7761	2^336103-109015	101178	Enzo Doria	04/2014
7762	(2^336095+2078)/2	101175	Stefano Morozzi	09/2020
7763	13^90809-96	101157	Lelio R Paula	10/2016
7764	26199^7258+7258^26199	101150	Hans Havermann	11/2018
7765	19^79098-30	101147	Lelio R Paula	10/2016
7766	19^79095+88	101144	Lelio R Paula	10/2016
7767	12401^24702-24702^12401	101117	Norbert Schneider	07/2022
7768	15^85976+32	101116	Lelio R Paula	10/2016
7769	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
7770	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
7771	(4^167933+17)/3	101106	Robert Price	02/2017
7772	2^335858+153	101104	Lelio R Paula	10/2009
7773	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
7774	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
7775	(2^335839+2114)/2	101098	Stefano Morozzi	09/2020
7776	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
7778	6^129918-35	101096	Lelio R Paula	10/2016
7777	(2*10^101096-107)/3	101096	Robert Price	11/2020
7779	3^211885-70	101095	Lelio R Paula	09/2016
7780	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
7781	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
7782	2^335818-20033	101092	Enzo Doria	06/2013
7783	2^335813-110083	101090	Enzo Doria	04/2014
7784	2^335804+2155	101088	Lelio R Paula	09/2016
7785	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
7786	2^335784-16145	101082	Enzo Doria	04/2013
7787	11^97051+62	101069	Lelio R Paula	10/2016
7788	3*10^101065+11	101066	Robert Price	07/2018
7789	27820^4293+4293^27820	101064	Hans Havermann	10/2018
7790	(2^335714+3750)/2	101060	Stefano Morozzi	01/2021
7791	(2^335690+1038)/2	101053	Stefano Morozzi	09/2020
7792	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
7793	2^335658-94395	101044	Lelio R Paula	09/2016
7794	24514^13215+13215^24514	101024	Hans Havermann	11/2018
7795	2^335586+169	101022	Lelio R Paula	10/2009
7796	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
7797	(2^335562+1258)/2	101014	Stefano Morozzi	09/2020
7798	2^335541+4849845	101008	Paul Bourdelais	04/2022
7799	(38*10^100999+169)/9	101000	Robert Price	11/2021
7800	(19*10^100997+737)/9	100998	Robert Price	07/2018
7801	47599!2+1024	100991	Robert Price	02/2015
7802	2^335468-18629	100986	Enzo Doria	05/2013
7803	2^335454-20961	100982	Enzo Doria	06/2013
7804	(2^335454+3258)/2	100982	Stefano Morozzi	02/2021
7805	10^100978+61	100979	Lelio R Paula	09/2016
7806	10^100978-156437	100978	Patrick De Geest	11/2016
7807	(2^335422+3114)/2	100972	Stefano Morozzi	09/2020
7808	(35*10^100970-89)/9	100971	Robert Price	02/2022
7809	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
7810	2^335403-1859167	100967	Enzo Doria	03/2016
7811	23599^18976+18976^23599	100962	Hans Havermann	10/2018
7812	6*10^100958+43	100959	Robert Price	07/2020
7813	9*2^335364-5	100956	Lelio R Paula	08/2014
7814	(7998^25867-1)/7997	100955	Serge Batalov	06/2022
7815	2^335349+72287	100951	Enzo Doria	04/2016
7816	2^335329+16095	100945	Lelio R Paula	09/2016
7817	232823#+233663	100937	Makoto Morimoto	10/2017
7818	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
7819	2^335237-20893	100917	Enzo Doria	06/2013
7820	2^335222-19337	100912	Enzo Doria	05/2013
7821	2^335222-109985	100912	Enzo Doria	04/2014
7822	2^335182-17237	100900	Enzo Doria	05/2013
7823	(2^335107+1634)/2	100877	Stefano Morozzi	09/2020
7824	2^335043-16737	100858	Enzo Doria	05/2013
7825	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
7826	2^335038-20633	100857	Enzo Doria	06/2013
7827	2^335031+1873373	100855	Enzo Doria	06/2016
7828	23489^19650+19650^23489	100847	Hans Havermann	10/2018
7829	3^211354-8816	100842	Enzo Doria	05/2014
7830	2^334984-112757	100841	Enzo Doria	06/2014
7831	(746*10^100827+1)/9	100829	Robert Price	03/2020
7832	29451^2648+2648^29451	100809	Hans Havermann	09/2018
7833	25583^8716+8716^25583	100806	Hans Havermann	08/2018
7835	2^334857+48527	100803	Lelio R Paula	08/2011
7834	12^93406+29	100803	Lelio R Paula	10/2016
7836	28780^3179+3179^28780	100796	Hans Havermann	09/2018
7837	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
7838	(328^40063-1)/327	100791	Serge Batalov	06/2022
7839	2^334809-13	100788	Lelio R Paula	04/2011
7840	(3552^28387-1)/3551	100784	Serge Batalov	06/2022
7841	(82*10^100780-1)/9	100781	Robert Price	12/2014
7842	31395^1622+1622^31395	100780	Hans Havermann	09/2018
7843	(2^334779+47)/5	100778	Lelio R Paula	12/2013
7844	2^334751+2049	100771	Lelio R Paula	09/2016
7845	13^90443-98	100749	Lelio R Paula	10/2016
7846	(2^334674+3190)/2	100747	Stefano Morozzi	09/2020
7847	(2^334651+1050)/2	100740	Stefano Morozzi	09/2020
7848	(7*10^100737+71)/3	100738	Robert Price	05/2018
7849	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
7850	15^85639-28	100720	Lelio R Paula	10/2016
7851	27068^5259+5259^27068	100718	Hans Havermann	08/2018
7852	2^334562+577294575	100711	Lelio R Paula	09/2016
7853	4*3^211077-5	100710	Lelio R Paula	08/2014
7854	2^334524+145	100702	Lelio R Paula	07/2009
7855	(2^334451+714)/2	100680	Stefano Morozzi	09/2020
7856	27648^4375+4375^27648	100666	Hans Havermann	09/2018
7857	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
7858	(2^334309+3122)/2	100637	Stefano Morozzi	09/2020
7859	2^334294-113111	100633	Enzo Doria	07/2014
7860	25581^8582+8582^25581	100626	Hans Havermann	08/2018
7862	6^129308-17723	100622	Enzo Doria	03/2013
7861	(19*10^100627+287)/9/292157	100622	Alfred Reich	11/2022
7863	6^129305+95	100619	Lelio R Paula	10/2016
7864	2^334244-1167	100618	Lelio R Paula	09/2016
7865	(2^334233+3066)/2	100614	Stefano Morozzi	09/2020
7866	(76*10^100611+77)/9	100612	Robert Price	10/2019
7867	7*10^100606-93	100607	Robert Price	08/2020
7868	(26*10^100566+49)/3	100567	Robert Price	08/2019
7869	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
7870	24885^10984+10984^24885	100555	Hans Havermann	07/2018
7871	(1351^32119-1)/1350	100551	Serge Batalov	06/2022
7872	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
7873	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
7874	23578^18367+18367^23578	100538	Hans Havermann	07/2018
7875	13^90251+24	100535	Lelio R Paula	10/2016
7876	2^333963+789	100533	Lelio R Paula	08/2011
7877	2^333919-1840087	100520	Enzo Doria	06/2015
7878	(2^333916+1698)/2	100519	Stefano Morozzi	09/2020
7879	2^333911+72623	100518	Enzo Doria	04/2016
7880	24605^12168+12168^24605	100517	Hans Havermann	08/2018
7881	66*10^100502+7	100504	Robert Price	07/2020
7882	18^80064-67	100503	Lelio R Paula	10/2016
7883	(13*10^100487+137)/3	100488	Robert Price	06/2021
7884	5^143742-48	100472	Lelio R Paula	10/2016
7885	24095^14784+14784^24095	100472	Hans Havermann	08/2018
7886	2^333757-112123	100471	Enzo Doria	06/2014
7887	(7953^25759-1)/7952	100470	Serge Batalov	06/2022
7888	7*10^100457-57	100458	Robert Price	06/2020
7889	27358^4693+4693^27358	100444	Hans Havermann	07/2018
7890	8*10^100439-51	100440	Robert Price	08/2019
7891	2^333603-108861	100425	Enzo Doria	03/2014
7892	9*7^118818-2	100414	Lelio R Paula	11/2014
7893	2^333546-17097	100408	Enzo Doria	05/2013
7894	(19*10^100403+287)/9/3	100403	Alfred Reich	11/2022
7895	17^81597+72	100401	Lelio R Paula	10/2016
7896	(3613^28219-1)/3612	100396	Serge Batalov	06/2022
7897	p(20559)#/2+8	100384	Robert Price	01/2017
7898	11^96390-24	100380	Lelio R Paula	10/2016
7899	(2^333385+2730)/2	100359	Stefano Morozzi	09/2020
7900	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
7901	23565^18136+18136^23565	100353	Hans Havermann	07/2018
7902	2^333354+763	100350	Lelio R Paula	08/2011
7903	(1608961*2^333333+1)/3	100349	Alex_soldier	09/2022
7904	(424517*2^333333+1)/5	100349	Alex_soldier	09/2022
7905	(887087*2^333333+1)/5	100349	Alex_soldier	09/2022
7906	(1159703*2^333333+1)/7	100349	Alex_soldier	09/2022
7907	(25*10^100343-67)/3	100344	Robert Price	06/2019
7908	2^333289-109483	100330	Enzo Doria	04/2014
7909	2^333240-2790209	100316	Enzo Doria	03/2016
7910	23601^17798+17798^23601	100314	Hans Havermann	05/2018
7912	(2^333227-2^166614+1)/5	100311		11/2006
7911	2^333225+719	100311	Lelio R Paula	08/2011
7913	2^333221-2785333	100310	Enzo Doria	10/2015
7914	76^53332-75	100308	Norbert Schneider	02/2015
7915	(29*10^100302+583)/9	100303	Robert Price	06/2021
7916	6^128892-17573	100298	Enzo Doria	03/2013
7917	(47*10^100283-119)/9	100284	Robert Price	05/2019
7918	2^333105-113215	100275	Enzo Doria	07/2014
7919	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
7920	4*10^100257-83	100258	Robert Price	10/2018
7921	17^81476-74	100253	Lelio R Paula	10/2016
7922	23392^19207+19207^23392	100199	Hans Havermann	06/2018
7923	(2^332830+750)/2	100192	Stefano Morozzi	09/2020
7924	(206*10^100189-17)/9	100191	Robert Price	01/2020
7925	17^81417-16	100180	Theodore Burton	11/2005
7926	(2^332773+590)/2	100175	Stefano Morozzi	09/2020
7927	2^332739-113215	100165	Enzo Doria	07/2014
7928	2^332730-1865621	100162	Enzo Doria	03/2016
7929	91^51127-2	100160	Lelio R Paula	09/2013
7930	15^85159-32	100155	Lelio R Paula	10/2016
7931	6^128661+97	100118	Lelio R Paula	10/2016
7932	19^78285+40	100108	Lelio R Paula	07/2016
7933	6^128640+5	100102	Lelio R Paula	11/2014
7934	10^100095+89973	100096	Patrick De Geest	10/2022
7935	10^100095-400001	100095	Robert Price	09/2021
7936	10^100095-203693	100095	Patrick De Geest	10/2022
7937	22779^22970-22970^22779	100093	Norbert Schneider	08/2020
7938	(2^332468+3130)/2	100083	Stefano Morozzi	09/2020
7939	(14*10^100075+61)/3	100076	Robert Price	12/2018
7940	(2^332435+3098)/2	100073	Stefano Morozzi	09/2020
7941	28562^3189+3189^28562	100072	Hans Havermann	05/2018
7942	6^128565-127	100044	Lelio R Paula	08/2016
7943	(2^332317+2106)/2	100038	Stefano Morozzi	09/2020
7944	2^332309-133	100035	Lelio R Paula	02/2011
7945	2^332307+731	100035	Lelio R Paula	07/2011
7946	2^332301+12927	100033	Lelio R Paula	04/2013
7947	23406^18781+18781^23406	100031	Hans Havermann	04/2018
7948	2^332277-4573	100026	Yves Minet	03/2019
7949	12^92684-13	100023	Lelio R Paula	07/2016
7950	78557*2^332193+55669	100005	Jorge Menendez	04/2019
7951	78557*2^332192+72689	100005	Jorge Menendez	04/2019
7952	10^100003+45799	100004	Stefano Morozzi	04/2019
7953	10^100003+155461	100004	Stefano Morozzi	04/2019
7954	10^100003+211389	100004	Stefano Morozzi	04/2019
7955	10^100003+381027	100004	Stefano Morozzi	04/2019
7956	10^100003+540703	100004	Stefano Morozzi	04/2019
7957	10^100003+823977	100004	Stefano Morozzi	04/2019
7969	10^100002+236023	100003	Stefano Morozzi	05/2018
7970	10^100002+433741	100003	Stefano Morozzi	05/2018
7958	2^332202+104659	100003	Stefano Morozzi	04/2019
7959	2^332202+857539	100003	Stefano Morozzi	04/2019
7960	2^332202+181773	100003	Stefano Morozzi	04/2019
7961	2^332202+687543	100003	Stefano Morozzi	04/2019
7962	2^332202+941595	100003	Stefano Morozzi	04/2019
7963	2^332202+445813	100003	Stefano Morozzi	04/2019
7964	2^332202+1599727	100003	Stefano Morozzi	04/2019
7965	2^332202+1389567	100003	Stefano Morozzi	04/2019
7966	2^332202+1206315	100003	Stefano Morozzi	04/2019
7967	2^332202+1958647	100003	Stefano Morozzi	04/2019
7968	10^100003-562857	100003	Patrick De Geest	07/2019
7971	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
7972	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
7973	10^100002-249519	100002	Patrick De Geest	07/2018
7974	10^100001+314199	100002	Patrick De Geest	07/2018
7994	10^100000+3938473	100001	Robert Price	05/2015
7995	10^100000+3979761	100001	Robert Price	05/2015
7996	10^100000+4293973	100001	Robert Price	09/2015
7991	10^100000+4858267	100001	Robert Price	12/2015
7992	10^100000+5113299	100001	Robert Price	02/2016
7993	10^100000+5169411	100001	Robert Price	02/2016
7983	10^100000+5354043	100001	Robert Price	05/2016
7984	10^100000+5717979	100001	Robert Price	05/2016
7985	10^100000+6080631	100001	Robert Price	07/2016
7986	10^100000+6308469	100001	Robert Price	07/2016
7987	10^100000+6512023	100001	Robert Price	08/2016
7988	10^100000+6596557	100001	Robert Price	08/2016
7989	10^100000+7115409	100001	Robert Price	10/2016
7990	10^100000+7235803	100001	Robert Price	10/2016
7997	10^100000+7867333	100001	Robert Price	12/2016
7998	10^100000+8743093	100001	Robert Price	02/2017
7999	10^100000+8955391	100001	Robert Price	03/2017
8000	10^100000+9180019	100001	Robert Price	03/2017
7975	10^100000+11187931	100001	Robert Price	03/2018
7976	10^100000+11264721	100001	Robert Price	04/2018
7977	10^100000+11477661	100001	Robert Price	05/2018
7978	10^100000+11644653	100001	Robert Price	07/2018
7979	10^100001-431439	100001	Patrick De Geest	07/2018
7980	10^100000+11769399	100001	Robert Price	08/2018
7981	10^100000+11848159	100001	Robert Price	08/2018
7982	10^100000+11863467	100001	Robert Price	08/2018

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PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)