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 ?
8751	2^338028-38705	101757	Stefano Morozzi	12/2022
8752	2^338028-140459	101757	Stefano Morozzi	01/2023
8753	2^338024-128495	101756	Stefano Morozzi	01/2022
8754	2^338025+34785	101756	Stefano Morozzi	03/2022
8755	2^338025-181765	101756	Stefano Morozzi	03/2022
8756	2^338024+63765	101756	Stefano Morozzi	05/2022
8757	2^338023-160621	101756	Stefano Morozzi	06/2022
8758	2^338026+117553	101756	Stefano Morozzi	09/2022
8759	2^338020-52437	101755	Stefano Morozzi	12/2021
8760	2^338021+160241	101755	Stefano Morozzi	03/2022
8761	2^338022+185845	101755	Stefano Morozzi	03/2022
8762	2^338021+189587	101755	Stefano Morozzi	05/2022
8763	2^338021-85891	101755	Stefano Morozzi	06/2022
8764	2^338020-87797	101755	Stefano Morozzi	12/2022
8765	2^338018-102741	101754	Stefano Morozzi	01/2022
8766	2^338018+29937	101754	Stefano Morozzi	01/2022
8767	2^338017-29505	101754	Stefano Morozzi	02/2022
8768	2^338018-30873	101754	Stefano Morozzi	02/2022
8769	2^338018-157013	101754	Stefano Morozzi	03/2022
8770	2^338019+168929	101754	Stefano Morozzi	09/2022
8771	2^338017+172721	101754	Stefano Morozzi	11/2022
8772	2^338018-136131	101754	Stefano Morozzi	12/2022
8773	2^338016+50797	101753	Stefano Morozzi	11/2021
8774	2^338016+26707	101753	Stefano Morozzi	12/2021
8775	2^338014+104677	101753	Stefano Morozzi	01/2022
8776	2^338013+145091	101753	Stefano Morozzi	11/2022
8777	2^338016-16335	101753	Stefano Morozzi	01/2023
8780	2^338010-19833	101752	Enzo Doria	06/2013
8778	2^338011+28665	101752	Stefano Morozzi	01/2022
8779	2^338010+89505	101752	Stefano Morozzi	05/2022
8781	2^338007+58985	101751	Stefano Morozzi	03/2022
8782	2^338008+109741	101751	Stefano Morozzi	03/2022
8783	2^338009+9527	101751	Stefano Morozzi	03/2022
8784	2^338007+14511	101751	Stefano Morozzi	05/2022
8785	2^338008+67957	101751	Stefano Morozzi	09/2022
8786	2^338009-11935	101751	Stefano Morozzi	12/2022
8787	2^338007-14199	101751	Stefano Morozzi	01/2023
8788	2^338005-75829	101750	Stefano Morozzi	12/2021
8789	2^338006-125055	101750	Stefano Morozzi	12/2021
8790	2^338006+5013	101750	Stefano Morozzi	01/2022
8791	2^338003+40269	101750	Stefano Morozzi	06/2022
8792	2^338006+166495	101750	Stefano Morozzi	06/2022
8793	2^338003-188551	101750	Stefano Morozzi	12/2022
8794	2^338006-118041	101750	Stefano Morozzi	02/2023
8795	2^338000+25113	101749	Stefano Morozzi	12/2021
8797	3^213215-76	101730	Lelio R Paula	09/2016
8796	23907^17998+17998^23907	101730	Hans Havermann	01/2019
8798	10^101728+154953	101729	Patrick De Geest	02/2020
8801	2^337930+63	101728	Lelio R Paula	07/2011
8799	10^101728-987654321	101728	Robert Price	12/2019
8800	10^101728-60741	101728	Patrick De Geest	02/2020
8802	2^337920+1869661	101725	Enzo Doria	05/2016
8803	2^337922+100280245065	101725	Paul Bourdelais	10/2021
8804	24116^16509+16509^24116	101715	Hans Havermann	01/2019
8805	(2^337875+3174)/2	101711	Stefano Morozzi	09/2020
8806	2^337859-19645	101706	Enzo Doria	05/2013
8807	2^337754+1869169	101675	Enzo Doria	05/2016
8808	(710^(250830+1)-9*10^50830-7)/9	101661	Robert Price	10/2023
8809	3*10^101657-37	101658	Robert Price	07/2018
8810	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
8811	11^97605-24	101646	Lelio R Paula	10/2016
8812	(83*10^101636+133)/9	101637	Robert Price	08/2021
8813	(2^337624+3606)/2	101635	Stefano Morozzi	09/2020
8814	8^112539-112539	101633	Robert Price	01/2014
8815	(2^337575+1818)/2	101620	Stefano Morozzi	02/2021
8816	(11*10^101613+61)/9	101614	Tyler Busby	01/2023
8817	25694^9003+9003^25694	101605	Hans Havermann	12/2018
8818	2^337515-19869	101603	Enzo Doria	06/2013
8819	2^337473+719	101590	Lelio R Paula	08/2011
8820	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
8821	2^337452-108815	101584	Enzo Doria	03/2014
8822	2^337453+1185	101584	Lelio R Paula	09/2016
8823	(41*10^101583+319)/9	101584	Robert Price	06/2021
8824	2^337410-113561	101571	Enzo Doria	08/2014
8825	2^337387+855	101564	Lelio R Paula	09/2016
8826	2^337367-17295	101558	Lelio R Paula	09/2016
8827	2^337342-109035	101551	Enzo Doria	04/2014
8828	23703^19238+19238^23703	101548	Hans Havermann	12/2018
8829	(26*10^101537-167)/3	101538	Robert Price	10/2019
8830	2^337267-19	101528	Lelio R Paula	07/2011
8831	(2^337259+1766)/2	101525	Stefano Morozzi	09/2020
8832	(2^337257+2306)/2	101525	Stefano Morozzi	02/2021
8833	2^337222-340871	101514	Harrison Mesh	06/2022
8834	(2^337195+2646)/2	101506	Stefano Morozzi	09/2020
8835	2^337183-19989	101503	Enzo Doria	06/2013
8836	2^337149+72425	101492	Enzo Doria	04/2016
8837	24041^16642+16642^24041	101483	Hans Havermann	12/2018
8838	33982^969+969^33982	101482	Hans Havermann	12/2018
8839	2^337101-20241	101478	Enzo Doria	06/2013
8840	2^337035-20001	101458	Enzo Doria	06/2013
8841	(7*10^101456+89)/3	101457	Robert Price	08/2020
8842	2^337017-16995	101453	Lelio R Paula	09/2016
8843	(347^40448+1)/(347^512+1)	101451	Martin Hopf	12/2023
8844	(8677^25759-1)/8676	101445	Serge Batalov	06/2022
8845	2^336979-115315	101441	Enzo Doria	06/2015
8846	2^336970-20885	101439	Enzo Doria	06/2013
8847	2^336958+79	101435	Lelio R Paula	10/2009
8848	(1589^31687-1)/1588	101431	Serge Batalov	06/2022
8849	2^336942+169	101430	Lelio R Paula	10/2009
8850	(193929^19321-1)/(193929^139-1)	101428	Ryan Propper	11/2023
8851	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
8852	4*10^101415-89	101416	Robert Price	11/2018
8853	(14*10^101410-89)/3	101411	Robert Price	05/2020
8854	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
8855	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
8856	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
8857	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
8858	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
8859	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
8860	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
8861	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
8862	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
8863	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
8864	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
8865	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
8866	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
8867	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
8868	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
8869	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
8870	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
8871	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
8872	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
8873	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
8874	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
8875	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
8876	24097^16150+16150^24097	101405	Hans Havermann	12/2018
8877	2^336842+94065	101400	Lelio R Paula	09/2016
8878	(7*10^101395-1)/3	101396	Robert Price	08/2022
8879	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
8880	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
8881	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
8882	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
8883	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
8884	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
8885	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
8886	10^101369+203811	101370	Patrick De Geest	11/2016
8887	10^101369-99	101369	Lelio R Paula	09/2016
8888	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
8889	2^336701-113563	101358	Enzo Doria	08/2014
8890	89717!4-512	101351	Robert Price	11/2019
8891	2^336644-109023	101340	Enzo Doria	04/2014
8892	2^336601-21081	101327	Enzo Doria	06/2013
8893	(4*34^66153+227)/33	101312	Eric Chen	03/2023
8894	20^77869+63	101310	Lelio R Paula	09/2016
8895	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
8897	6^130179-137	101299	Lelio R Paula	10/2016
8896	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
8898	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
8899	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
8900	2^336369-19753	101258	Enzo Doria	05/2013
8901	23842^17653+17653^23842	101253	Hans Havermann	11/2018
8902	2^336350-344291	101252	Enzo Doria	07/2015
8903	(17*10^101251-161)/9	101252	Robert Price	02/2021
8904	(56*10^101222-47)/9	101223	Robert Price	02/2019
8905	2^336243-108777	101220	Enzo Doria	03/2014
8906	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
8907	23535^19954+19954^23535	101202	Hans Havermann	11/2018
8908	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
8909	2^336150-20393	101192	Enzo Doria	06/2013
8910	23996^16473+16473^23996	101186	Hans Havermann	11/2018
8911	2^336112-1865249	101180	Enzo Doria	03/2016
8912	2^336103-109015	101178	Enzo Doria	04/2014
8913	(2^336095+2078)/2	101175	Stefano Morozzi	09/2020
8914	2^336060+22201	101165	Enzo Doria	09/2023
8915	13^90809-96	101157	Lelio R Paula	10/2016
8916	26199^7258+7258^26199	101150	Hans Havermann	11/2018
8917	19^79098-30	101147	Lelio R Paula	10/2016
8918	19^79095+88	101144	Lelio R Paula	10/2016
8919	(30826*34^66040-59)/11	101143	Eric Chen	03/2023
8920	12401^24702-24702^12401	101117	Norbert Schneider	07/2022
8921	15^85976+32	101116	Lelio R Paula	10/2016
8922	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
8923	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
8924	(4^167933+17)/3	101106	Robert Price	02/2017
8925	2^335858+153	101104	Lelio R Paula	10/2009
8926	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
8927	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
8928	(2^335839+2114)/2	101098	Stefano Morozzi	09/2020
8929	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
8931	6^129918-35	101096	Lelio R Paula	10/2016
8930	(2*10^101096-107)/3	101096	Robert Price	11/2020
8932	3^211885-70	101095	Lelio R Paula	09/2016
8933	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
8934	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
8935	2^335818-20033	101092	Enzo Doria	06/2013
8936	2^335813-110083	101090	Enzo Doria	04/2014
8937	2^335804+2155	101088	Lelio R Paula	09/2016
8938	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
8939	2^335784-16145	101082	Enzo Doria	04/2013
8940	11^97051+62	101069	Lelio R Paula	10/2016
8941	3*10^101065+11	101066	Robert Price	07/2018
8942	27820^4293+4293^27820	101064	Hans Havermann	10/2018
8943	(2^335714+3750)/2	101060	Stefano Morozzi	01/2021
8944	(2^335690+1038)/2	101053	Stefano Morozzi	09/2020
8945	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
8946	2^335658-94395	101044	Lelio R Paula	09/2016
8947	24514^13215+13215^24514	101024	Hans Havermann	11/2018
8948	2^335586+169	101022	Lelio R Paula	10/2009
8949	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
8950	(2^335562+1258)/2	101014	Stefano Morozzi	09/2020
8951	2^335541+4849845	101008	Paul Bourdelais	04/2022
8952	(38*10^100999+169)/9	101000	Robert Price	11/2021
8953	(19*10^100997+737)/9	100998	Robert Price	07/2018
8954	47599!2+1024	100991	Robert Price	02/2015
8955	2^335468-18629	100986	Enzo Doria	05/2013
8956	2^335454-20961	100982	Enzo Doria	06/2013
8957	(2^335454+3258)/2	100982	Stefano Morozzi	02/2021
8958	10^100978+61	100979	Lelio R Paula	09/2016
8959	10^100978-156437	100978	Patrick De Geest	11/2016
8960	(2^335422+3114)/2	100972	Stefano Morozzi	09/2020
8961	(35*10^100970-89)/9	100971	Robert Price	02/2022
8962	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
8963	2^335403-1859167	100967	Enzo Doria	03/2016
8964	23599^18976+18976^23599	100962	Hans Havermann	10/2018
8965	6*10^100958+43	100959	Robert Price	07/2020
8966	9*2^335364-5	100956	Lelio R Paula	08/2014
8967	(7998^25867-1)/7997	100955	Serge Batalov	06/2022
8968	2^335349+72287	100951	Enzo Doria	04/2016
8969	2^335329+16095	100945	Lelio R Paula	09/2016
8970	232823#+233663	100937	Makoto Morimoto	10/2017
8971	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
8972	2^335237-20893	100917	Enzo Doria	06/2013
8973	2^335222-19337	100912	Enzo Doria	05/2013
8974	2^335222-109985	100912	Enzo Doria	04/2014
8975	2^335182-17237	100900	Enzo Doria	05/2013
8976	(2^335107+1634)/2	100877	Stefano Morozzi	09/2020
8977	2^335043-16737	100858	Enzo Doria	05/2013
8978	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
8979	2^335038-20633	100857	Enzo Doria	06/2013
8980	2^335031+1873373	100855	Enzo Doria	06/2016
8981	23489^19650+19650^23489	100847	Hans Havermann	10/2018
8982	3^211354-8816	100842	Enzo Doria	05/2014
8983	2^334984-112757	100841	Enzo Doria	06/2014
8984	(746*10^100827+1)/9	100829	Robert Price	03/2020
8985	29451^2648+2648^29451	100809	Hans Havermann	09/2018
8986	25583^8716+8716^25583	100806	Hans Havermann	08/2018
8988	2^334857+48527	100803	Lelio R Paula	08/2011
8987	12^93406+29	100803	Lelio R Paula	10/2016
8989	28780^3179+3179^28780	100796	Hans Havermann	09/2018
8990	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
8991	(328^40063-1)/327	100791	Serge Batalov	06/2022
8992	2^334809-13	100788	Lelio R Paula	04/2011
8993	(3552^28387-1)/3551	100784	Serge Batalov	06/2022
8994	(82*10^100780-1)/9	100781	Robert Price	12/2014
8995	31395^1622+1622^31395	100780	Hans Havermann	09/2018
8996	(2^334779+47)/5	100778	Lelio R Paula	12/2013
8997	2^334751+2049	100771	Lelio R Paula	09/2016
8998	13^90443-98	100749	Lelio R Paula	10/2016
8999	(2^334674+3190)/2	100747	Stefano Morozzi	09/2020
9000	(2^334651+1050)/2	100740	Stefano Morozzi	09/2020

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PRP Records

Probable Primes Top 10000

(295107 PRPs in the top)