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	2^338008+67957	101751	Stefano Morozzi	09/2022
8752	2^338009-11935	101751	Stefano Morozzi	12/2022
8753	2^338007-14199	101751	Stefano Morozzi	01/2023
8754	2^338005-75829	101750	Stefano Morozzi	12/2021
8755	2^338006-125055	101750	Stefano Morozzi	12/2021
8756	2^338006+5013	101750	Stefano Morozzi	01/2022
8757	2^338003+40269	101750	Stefano Morozzi	06/2022
8758	2^338006+166495	101750	Stefano Morozzi	06/2022
8759	2^338003-188551	101750	Stefano Morozzi	12/2022
8760	2^338006-118041	101750	Stefano Morozzi	02/2023
8761	2^338000+25113	101749	Stefano Morozzi	12/2021
8763	3^213215-76	101730	Lelio R Paula	09/2016
8762	23907^17998+17998^23907	101730	Hans Havermann	01/2019
8764	10^101728+154953	101729	Patrick De Geest	02/2020
8767	2^337930+63	101728	Lelio R Paula	07/2011
8765	10^101728-987654321	101728	Robert Price	12/2019
8766	10^101728-60741	101728	Patrick De Geest	02/2020
8768	2^337920+1869661	101725	Enzo Doria	05/2016
8769	2^337922+100280245065	101725	Paul Bourdelais	10/2021
8770	24116^16509+16509^24116	101715	Hans Havermann	01/2019
8771	(2^337875+3174)/2	101711	Stefano Morozzi	09/2020
8772	2^337859-19645	101706	Enzo Doria	05/2013
8773	2^337754+1869169	101675	Enzo Doria	05/2016
8774	(710^(250830+1)-9*10^50830-7)/9	101661	Robert Price	10/2023
8775	3*10^101657-37	101658	Robert Price	07/2018
8776	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
8777	11^97605-24	101646	Lelio R Paula	10/2016
8778	(83*10^101636+133)/9	101637	Robert Price	08/2021
8779	(2^337624+3606)/2	101635	Stefano Morozzi	09/2020
8780	8^112539-112539	101633	Robert Price	01/2014
8781	(2^337575+1818)/2	101620	Stefano Morozzi	02/2021
8782	(11*10^101613+61)/9	101614	Tyler Busby	01/2023
8783	25694^9003+9003^25694	101605	Hans Havermann	12/2018
8784	2^337515-19869	101603	Enzo Doria	06/2013
8785	2^337473+719	101590	Lelio R Paula	08/2011
8786	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
8787	2^337452-108815	101584	Enzo Doria	03/2014
8788	2^337453+1185	101584	Lelio R Paula	09/2016
8789	(41*10^101583+319)/9	101584	Robert Price	06/2021
8790	2^337410-113561	101571	Enzo Doria	08/2014
8791	2^337387+855	101564	Lelio R Paula	09/2016
8792	2^337367-17295	101558	Lelio R Paula	09/2016
8793	2^337342-109035	101551	Enzo Doria	04/2014
8794	23703^19238+19238^23703	101548	Hans Havermann	12/2018
8795	(26*10^101537-167)/3	101538	Robert Price	10/2019
8796	2^337267-19	101528	Lelio R Paula	07/2011
8797	(2^337259+1766)/2	101525	Stefano Morozzi	09/2020
8798	(2^337257+2306)/2	101525	Stefano Morozzi	02/2021
8799	2^337222-340871	101514	Harrison Mesh	06/2022
8800	(2^337195+2646)/2	101506	Stefano Morozzi	09/2020
8801	2^337183-19989	101503	Enzo Doria	06/2013
8802	2^337149+72425	101492	Enzo Doria	04/2016
8803	24041^16642+16642^24041	101483	Hans Havermann	12/2018
8804	33982^969+969^33982	101482	Hans Havermann	12/2018
8805	2^337101-20241	101478	Enzo Doria	06/2013
8806	2^337035-20001	101458	Enzo Doria	06/2013
8807	(7*10^101456+89)/3	101457	Robert Price	08/2020
8808	2^337017-16995	101453	Lelio R Paula	09/2016
8809	(347^40448+1)/(347^512+1)	101451	Martin Hopf	12/2023
8810	(8677^25759-1)/8676	101445	Serge Batalov	06/2022
8811	2^336979-115315	101441	Enzo Doria	06/2015
8812	2^336970-20885	101439	Enzo Doria	06/2013
8813	2^336958+79	101435	Lelio R Paula	10/2009
8814	(1589^31687-1)/1588	101431	Serge Batalov	06/2022
8815	2^336942+169	101430	Lelio R Paula	10/2009
8816	(193929^19321-1)/(193929^139-1)	101428	Ryan Propper	11/2023
8817	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
8818	4*10^101415-89	101416	Robert Price	11/2018
8819	(14*10^101410-89)/3	101411	Robert Price	05/2020
8820	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
8821	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
8822	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
8823	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
8824	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
8825	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
8826	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
8827	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
8828	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
8829	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
8830	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
8831	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
8832	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
8833	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
8834	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
8835	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
8836	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
8837	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
8838	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
8839	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
8840	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
8841	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
8842	24097^16150+16150^24097	101405	Hans Havermann	12/2018
8843	2^336842+94065	101400	Lelio R Paula	09/2016
8844	(7*10^101395-1)/3	101396	Robert Price	08/2022
8845	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
8846	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
8847	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
8848	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
8849	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
8850	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
8851	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
8852	10^101369+203811	101370	Patrick De Geest	11/2016
8853	10^101369-99	101369	Lelio R Paula	09/2016
8854	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
8855	2^336701-113563	101358	Enzo Doria	08/2014
8856	89717!4-512	101351	Robert Price	11/2019
8857	2^336644-109023	101340	Enzo Doria	04/2014
8858	2^336601-21081	101327	Enzo Doria	06/2013
8859	(4*34^66153+227)/33	101312	Eric Chen	03/2023
8860	20^77869+63	101310	Lelio R Paula	09/2016
8861	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
8863	6^130179-137	101299	Lelio R Paula	10/2016
8862	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
8864	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
8865	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
8866	2^336369-19753	101258	Enzo Doria	05/2013
8867	23842^17653+17653^23842	101253	Hans Havermann	11/2018
8868	2^336350-344291	101252	Enzo Doria	07/2015
8869	(17*10^101251-161)/9	101252	Robert Price	02/2021
8870	(56*10^101222-47)/9	101223	Robert Price	02/2019
8871	2^336243-108777	101220	Enzo Doria	03/2014
8872	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
8873	23535^19954+19954^23535	101202	Hans Havermann	11/2018
8874	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
8875	2^336150-20393	101192	Enzo Doria	06/2013
8876	23996^16473+16473^23996	101186	Hans Havermann	11/2018
8877	2^336112-1865249	101180	Enzo Doria	03/2016
8878	2^336103-109015	101178	Enzo Doria	04/2014
8879	(2^336095+2078)/2	101175	Stefano Morozzi	09/2020
8880	2^336060+22201	101165	Enzo Doria	09/2023
8881	13^90809-96	101157	Lelio R Paula	10/2016
8882	26199^7258+7258^26199	101150	Hans Havermann	11/2018
8883	19^79098-30	101147	Lelio R Paula	10/2016
8884	19^79095+88	101144	Lelio R Paula	10/2016
8885	(30826*34^66040-59)/11	101143	Eric Chen	03/2023
8886	12401^24702-24702^12401	101117	Norbert Schneider	07/2022
8887	15^85976+32	101116	Lelio R Paula	10/2016
8888	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
8889	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
8890	(4^167933+17)/3	101106	Robert Price	02/2017
8891	2^335858+153	101104	Lelio R Paula	10/2009
8892	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
8893	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
8894	(2^335839+2114)/2	101098	Stefano Morozzi	09/2020
8895	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
8897	6^129918-35	101096	Lelio R Paula	10/2016
8896	(2*10^101096-107)/3	101096	Robert Price	11/2020
8898	3^211885-70	101095	Lelio R Paula	09/2016
8899	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
8900	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
8901	2^335818-20033	101092	Enzo Doria	06/2013
8902	2^335813-110083	101090	Enzo Doria	04/2014
8903	2^335804+2155	101088	Lelio R Paula	09/2016
8904	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
8905	2^335784-16145	101082	Enzo Doria	04/2013
8906	11^97051+62	101069	Lelio R Paula	10/2016
8907	3*10^101065+11	101066	Robert Price	07/2018
8908	27820^4293+4293^27820	101064	Hans Havermann	10/2018
8909	(2^335714+3750)/2	101060	Stefano Morozzi	01/2021
8910	(2^335690+1038)/2	101053	Stefano Morozzi	09/2020
8911	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
8912	2^335658-94395	101044	Lelio R Paula	09/2016
8913	24514^13215+13215^24514	101024	Hans Havermann	11/2018
8914	2^335586+169	101022	Lelio R Paula	10/2009
8915	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
8916	(2^335562+1258)/2	101014	Stefano Morozzi	09/2020
8917	2^335541+4849845	101008	Paul Bourdelais	04/2022
8918	(38*10^100999+169)/9	101000	Robert Price	11/2021
8919	(19*10^100997+737)/9	100998	Robert Price	07/2018
8920	47599!2+1024	100991	Robert Price	02/2015
8921	2^335468-18629	100986	Enzo Doria	05/2013
8922	2^335454-20961	100982	Enzo Doria	06/2013
8923	(2^335454+3258)/2	100982	Stefano Morozzi	02/2021
8924	10^100978+61	100979	Lelio R Paula	09/2016
8925	10^100978-156437	100978	Patrick De Geest	11/2016
8926	(2^335422+3114)/2	100972	Stefano Morozzi	09/2020
8927	(35*10^100970-89)/9	100971	Robert Price	02/2022
8928	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
8929	2^335403-1859167	100967	Enzo Doria	03/2016
8930	23599^18976+18976^23599	100962	Hans Havermann	10/2018
8931	6*10^100958+43	100959	Robert Price	07/2020
8932	9*2^335364-5	100956	Lelio R Paula	08/2014
8933	(7998^25867-1)/7997	100955	Serge Batalov	06/2022
8934	2^335349+72287	100951	Enzo Doria	04/2016
8935	2^335329+16095	100945	Lelio R Paula	09/2016
8936	232823#+233663	100937	Makoto Morimoto	10/2017
8937	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
8938	2^335237-20893	100917	Enzo Doria	06/2013
8939	2^335222-19337	100912	Enzo Doria	05/2013
8940	2^335222-109985	100912	Enzo Doria	04/2014
8941	2^335182-17237	100900	Enzo Doria	05/2013
8942	(2^335107+1634)/2	100877	Stefano Morozzi	09/2020
8943	2^335043-16737	100858	Enzo Doria	05/2013
8944	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
8945	2^335038-20633	100857	Enzo Doria	06/2013
8946	2^335031+1873373	100855	Enzo Doria	06/2016
8947	23489^19650+19650^23489	100847	Hans Havermann	10/2018
8948	3^211354-8816	100842	Enzo Doria	05/2014
8949	2^334984-112757	100841	Enzo Doria	06/2014
8950	(746*10^100827+1)/9	100829	Robert Price	03/2020
8951	29451^2648+2648^29451	100809	Hans Havermann	09/2018
8952	25583^8716+8716^25583	100806	Hans Havermann	08/2018
8954	2^334857+48527	100803	Lelio R Paula	08/2011
8953	12^93406+29	100803	Lelio R Paula	10/2016
8955	28780^3179+3179^28780	100796	Hans Havermann	09/2018
8956	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
8957	(328^40063-1)/327	100791	Serge Batalov	06/2022
8958	2^334809-13	100788	Lelio R Paula	04/2011
8959	(3552^28387-1)/3551	100784	Serge Batalov	06/2022
8960	(82*10^100780-1)/9	100781	Robert Price	12/2014
8961	31395^1622+1622^31395	100780	Hans Havermann	09/2018
8962	(2^334779+47)/5	100778	Lelio R Paula	12/2013
8963	2^334751+2049	100771	Lelio R Paula	09/2016
8964	13^90443-98	100749	Lelio R Paula	10/2016
8965	(2^334674+3190)/2	100747	Stefano Morozzi	09/2020
8966	(2^334651+1050)/2	100740	Stefano Morozzi	09/2020
8967	(7*10^100737+71)/3	100738	Robert Price	05/2018
8968	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
8969	15^85639-28	100720	Lelio R Paula	10/2016
8970	27068^5259+5259^27068	100718	Hans Havermann	08/2018
8971	2^334562+577294575	100711	Lelio R Paula	09/2016
8972	4*3^211077-5	100710	Lelio R Paula	08/2014
8973	2^334524+145	100702	Lelio R Paula	07/2009
8974	(2^334451+714)/2	100680	Stefano Morozzi	09/2020
8975	27648^4375+4375^27648	100666	Hans Havermann	09/2018
8976	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
8977	(2^334309+3122)/2	100637	Stefano Morozzi	09/2020
8978	2^334294-113111	100633	Enzo Doria	07/2014
8979	25581^8582+8582^25581	100626	Hans Havermann	08/2018
8981	6^129308-17723	100622	Enzo Doria	03/2013
8980	(19*10^100627+287)/9/292157	100622	Alfred Reich	11/2022
8982	6^129305+95	100619	Lelio R Paula	10/2016
8983	2^334244-1167	100618	Lelio R Paula	09/2016
8984	(2^334233+3066)/2	100614	Stefano Morozzi	09/2020
8985	(76*10^100611+77)/9	100612	Robert Price	10/2019
8986	7*10^100606-93	100607	Robert Price	08/2020
8987	(26*10^100566+49)/3	100567	Robert Price	08/2019
8988	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
8989	24885^10984+10984^24885	100555	Hans Havermann	07/2018
8990	(1351^32119-1)/1350	100551	Serge Batalov	06/2022
8991	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
8992	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
8993	23578^18367+18367^23578	100538	Hans Havermann	07/2018
8994	13^90251+24	100535	Lelio R Paula	10/2016
8995	2^333963+789	100533	Lelio R Paula	08/2011
8996	2^333919-1840087	100520	Enzo Doria	06/2015
8997	(2^333916+1698)/2	100519	Stefano Morozzi	09/2020
8998	2^333911+72623	100518	Enzo Doria	04/2016
8999	24605^12168+12168^24605	100517	Hans Havermann	08/2018
9000	66*10^100502+7	100504	Robert Price	07/2020

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PRP Records

Probable Primes Top 10000

(295036 PRPs in the top)