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 ?
5751	9*10^130998-19	130999	Robert Price	07/2019
5752	36243^4108+4108^36243	130969	Hans Havermann	04/2021
5753	(32^86981-5^86981)/27	130919	Robert Price	04/2026
5754	(445^49433+1)/446	130914	Jinyuan Wang	05/2024
5755	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
5756	2^434835-111937	130899	Enzo Doria	05/2014
5757	(62*10^130895-629)/9	130896	Robert Price	07/2021
5758	2^434807+225	130890	Henri Lifchitz	11/2024
5759	2^434685+72257	130854	Enzo Doria	04/2016
5760	Phi(64497,-1105)	130853	Henri Lifchitz	12/2025
5761	(7*10^130825+113)/3	130826	Robert Price	02/2018
5762	2^434539-29317	130810	Enzo Doria	07/2015
5763	(74*10^130791+637)/9	130792	Robert Price	01/2022
5764	2^434469-114259	130789	Enzo Doria	01/2015
5765	(5*10^130763+103)/9	130763	Robert Price	04/2022
5766	2^434246+33	130722	Robert Price	11/2015
5767	30156^21599+21599^30156	130710	Hans Havermann	04/2021
5768	(41^81041-3^81041)/38	130701	Robert Price	09/2025
5769	(17*10^130695-161)/9	130696	Robert Price	02/2021
5770	30513^19148+19148^30513	130661	Hans Havermann	03/2021
5771	29736^24761+24761^29736	130654	Hans Havermann	04/2021
5772	9*10^130638+41	130639	Robert Price	08/2020
5773	2^433911-91	130621	Lelio R Paula	06/2017
5774	30786^17449+17449^30786	130588	Hans Havermann	03/2021
5775	2^433744-114419	130570	Enzo Doria	02/2015
5777	2^433708+1869451	130560	Enzo Doria	05/2016
5776	2^433710+93	130560	Lelio R Paula	06/2017
5778	7*10^130535-27	130536	Robert Price	11/2022
5779	(17^130533)%(10^130533)	130533	Henri Lifchitz	05/2025
5780	(9629^32768+1)/120501441265666	130520	Kellen Shenton	05/2021
5781	804*34^85220+713	130516	Eric Chen	08/2023
5782	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
5783	3^273521+10	130503	Tyler NeSmith	01/2021
5784	41659^1356+1356^41659	130487	Hans Havermann	03/2021
5785	4*10^130480+9	130481	Robert Price	05/2015
5786	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
5787	3*2^433422+5	130474	Jon Grantham	07/2023
5788	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
5789	(31*10^130414-49)/9	130415	Robert Price	11/2021
5790	26462^29485-29485^26462	130402	Frank Doornink	03/2024
5791	33481^7848+7848^33481	130401	Hans Havermann	03/2021
5792	(17*10^130393+7)/3	130394	Robert Price	06/2023
5793	(22*10^130392+203)/9	130393	Robert Price	10/2021
5794	29773^23950+23950^29773	130386	Hans Havermann	04/2021
5795	2^433023-113497	130353	Enzo Doria	08/2014
5796	31175^15178+15178^31175	130350	Hans Havermann	04/2021
5797	2^433002+1179379	130347	Enzo Doria	06/2016
5798	2^432974+19	130339	Robert Price	08/2015
5799	31903^12168+12168^31903	130331	Hans Havermann	04/2021
5800	2^432917+22217	130322	Enzo Doria	09/2023
5801	29387^27112+27112^29387	130278	Hans Havermann	04/2021
5802	2^432768+213181	130277	Enzo Doria	09/2023
5803	29577^25370+25370^29577	130267	Hans Havermann	04/2021
5804	31738^12685+12685^31738	130231	Hans Havermann	03/2021
5805	44235^878+878^44235	130206	Hans Havermann	04/2021
5806	32160^11171+11171^32160	130187	Hans Havermann	04/2021
5807	29489^25956+25956^29489	130172	Hans Havermann	04/2021
5808	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
5809	33005^8766+8766^33005	130133	Hans Havermann	04/2021
5810	(35*10^130132-611)/9	130133	Robert Price	02/2022
5811	(444^49408+1)/(444^256+1)	130125	Martin Hopf	12/2023
5812	2^432217+41	130111	Lelio R Paula	06/2017
5813	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
5814	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
5815	97^65480-2	130094	Lelio R Paula	05/2017
5816	36007^4102+4102^36007	130094	Hans Havermann	04/2021
5817	4*10^130088-89	130089	Robert Price	11/2018
5818	2^432117-113215	130081	Enzo Doria	07/2014
5819	(4*10^130080+41)/9	130080	Serge Batalov	11/2022
5820	9583*29^88890+736	129997	Eric Chen	06/2025
5821	2^431804+72511	129986	Enzo Doria	04/2016
5822	27902^29237-29237^27902	129978	Frank Doornink	03/2024
5823	33^85579+32	129953	Alfred Reich	10/2025
5824	(2313^38809-1)/(2313^197-1)	129898	Ryan Propper	11/2023
5825	(13*10^129896+137)/3	129897	Robert Price	06/2021
5826	(13*10^129890+71)/3	129891	Robert Price	06/2021
5827	128^61638+127	129885	Alfred Reich	06/2026
5828	29048^29101-29101^29048	129882	Norbert Schneider	03/2022
5829	37832^2709+2709^37832	129871	Hans Havermann	04/2021
5830	31055^15184+15184^31055	129853	Hans Havermann	04/2021
5832	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
5831	Phi(1632846L,3)	129844	Anonymous	03/2025
5833	31385^13702+13702^31385	129833	Hans Havermann	04/2021
5834	(13*10^129826+41)/9	129827	Tyler Busby	02/2023
5835	28901^29102-29102^28901	129822	Norbert Schneider	03/2022
5836	(47*10^129789-119)/9	129790	Robert Price	05/2019
5837	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
5838	25999^29384-29384^25999	129730	Frank Doornink	03/2024
5839	25771^29408-29408^25771	129723	Frank Doornink	02/2024
5840	(166*10^129712+17)/3	129714	Robert Price	07/2022
5841	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
5842	2^430807+1869563	129686	Enzo Doria	05/2016
5843	2^430721-21429	129660	Enzo Doria	07/2013
5844	Phi(326081,3)	129648	Henri Lifchitz	12/2025
5845	(4*10^129618+89)/3	129619	Robert Price	08/2021
5846	(142^60223-1)/141	129616	Anonymous	06/2024
5847	(10^129587-7^129587)/3	129587	Jon Grantham	07/2023
5848	2^430415-276271	129568	Enzo Doria	07/2015
5849	32282^10311+10311^32282	129558	Hans Havermann	04/2021
5850	29486^24741+24741^29486	129545	Hans Havermann	04/2021
5851	(29*10^129543+313)/9	129544	Robert Price	04/2021
5852	37095^3104+3104^37095	129533	Hans Havermann	04/2021
5853	31132^14459+14459^31132	129514	Hans Havermann	04/2021
5854	32582^9435+9435^32582	129506	Hans Havermann	03/2021
5855	30442^17953+17953^30442	129505	Hans Havermann	03/2021
5856	(199*10^129487-7)/3	129489	Robert Price	05/2020
5857	2^430142-2791721	129486	Enzo Doria	03/2016
5858	(7*10^129472-13)/3	129473	Robert Price	07/2018
5859	(8*10^129469+79)/3	129470	Robert Price	10/2020
5860	31678^12213+12213^31678	129463	Hans Havermann	04/2021
5861	10620^32143-10619^32143	129412	Norbert Schneider	08/2023
5862	(772*10^129406-7)/9	129408	Robert Price	06/2022
5863	(535^47431-1)/534	129406	Tom Wu	09/2024
5864	((320425-8193)F(618977)-(20425-8193)*L(618977))/2	129363	Yaroslav Berezhko	03/2025
5865	31100^14439+14439^31100	129362	Hans Havermann	04/2021
5866	33009^8288+8288^33009	129345	Hans Havermann	04/2021
5867	25895^29306-29306^25895	129334	Frank Doornink	03/2024
5868	(44^78697+43^78697)/87	129333	Aurel Gibier	11/2023
5869	29675^22804+22804^29675	129324	Hans Havermann	04/2021
5870	29068^28099+28099^29068	129315	Hans Havermann	04/2021
5871	2^429568-21017	129313	Enzo Doria	07/2013
5872	(10^129295+83)/3	129295	Robert Price	08/2021
5873	(853*10^129274-7)/9	129276	Robert Price	07/2021
5874	998^43100+997	129263	Alfred Reich	03/2026
5875	30958^14961+14961^30958	129249	Hans Havermann	04/2021
5876	(11*10^129239-179)/3	129240	Robert Price	09/2018
5877	28659^28988+28988^28659	129208	Norbert Schneider	02/2021
5878	29423^24616+24616^29423	129203	Hans Havermann	03/2021
5879	2^429194-112685	129201	Enzo Doria	06/2014
5880	31*35^83672+17398	129197	Eric Chen	05/2025
5881	2^429145-2780449	129186	Enzo Doria	04/2016
5882	32500^9427+9427^32500	129168	Hans Havermann	04/2021
5883	33577^7014+7014^33577	129136	Hans Havermann	03/2021
5884	2^428892-113453	129110	Enzo Doria	07/2014
5885	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
5886	2^428727-113959	129060	Enzo Doria	10/2014
5887	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
5888	(10^129051-31)/3	129051	Serge Batalov	12/2014
5889	(3^732836)/(2^732836)	129047	Henri Lifchitz	05/2025
5890	(134*10^129038+7)/3	129040	Robert Price	02/2020
5891	2^428564+71161	129011	Enzo Doria	04/2016
5892	28781^28930+28930^28781	129002	Norbert Schneider	02/2021
5893	29065^27424+27424^29065	128995	Hans Havermann	04/2021
5894	2^428502-113285	128992	Enzo Doria	07/2014
5895	2^428421-21373	128968	Enzo Doria	06/2013
5896	L(616787)	128901	Henri Lifchitz	09/2008
5897	(765^44701-1)/764	128900	Tom Wu	07/2024
5898	20^99055-3	128874	Paul Bourdelais	12/2020
5899	91^65772-2	128851	Lelio R Paula	05/2017
5900	2^428022+43	128848	Lelio R Paula	05/2017
5901	2^427999-459397	128841	Enzo Doria	05/2015
5902	2^427993+76847	128839	Enzo Doria	05/2016
5903	31059^14060+14060^31059	128833	Hans Havermann	03/2021
5904	10^128805+152871	128806	Patrick De Geest	05/2021
5905	10^128805-10001	128805	Robert Price	02/2021
5906	2^427824-1851507	128788	Enzo Doria	08/2015
5907	2^427807-21469	128783	Enzo Doria	07/2013
5908	29082^26783+26783^29082	128772	Hans Havermann	04/2021
5909	40055^1638+1638^40055	128750	Hans Havermann	04/2021
5910	(923^43411-1)/922	128720	Tom Wu	07/2024
5911	11^123594-240	128710	Enzo Doria	09/2012
5912	2^427504-21503	128692	Enzo Doria	07/2013
5913	37727^2574+2574^37727	128673	Hans Havermann	04/2021
5914	29686^21591+21591^29686	128668	Hans Havermann	04/2021
5915	10^128668-70000000001	128668	Robert Price	08/2021
5916	10^128668-350729	128668	Alfred Reich	08/2024
5917	Phi(57476,13#)	128668	Henri Lifchitz	12/2025
5918	2^427420+91	128667	Lelio R Paula	05/2017
5919	8*10^128651-37	128652	Robert Price	03/2022
5921	(68*10^128645-257)/9	128646	Robert Price	07/2019
5920	128^61050+127	128646	Alfred Reich	06/2026
5922	Phi(236553,7)	128631	Henri Lifchitz	12/2025
5923	2^427269-113635	128621	Enzo Doria	08/2014
5924	136^60270+135	128589	Alfred Reich	03/2026
5925	2^427130+1877569	128579	Enzo Doria	08/2016
5926	2^427068+20011	128561	Enzo Doria	06/2023
5927	2^427016-115349	128545	Enzo Doria	07/2015
5928	2^427001+1334025	128541	Henri Lifchitz	11/2024
5929	(4*10^128510+137)/3	128511	Robert Price	03/2018
5930	2^426889-112879	128507	Enzo Doria	06/2014
5931	2^426804+1869931	128481	Enzo Doria	05/2016
5932	2^426750+77635	128465	Enzo Doria	05/2016
5933	27708^28913-28913^27708	128450	Frank Doornink	03/2024
5934	36988^2969+2969^36988	128445	Hans Havermann	03/2021
5935	36664^3185+3185^36664	128439	Hans Havermann	03/2021
5936	32618^8649+8649^32618	128416	Hans Havermann	04/2021
5937	28883^27874+27874^28883	128391	Hans Havermann	04/2021
5938	2^426425-91	128367	Lelio R Paula	05/2017
5939	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
5940	2^426352+74971	128345	Enzo Doria	04/2016
5941	(199*10^128343-7)/3	128345	Robert Price	05/2020
5942	4*10^128343-21	128344	Robert Price	09/2018
5943	(65*10^128338+493)/9	128339	Robert Price	08/2021
5944	35632^3997+3997^35632	128337	Hans Havermann	04/2021
5945	2^426300-1863689	128330	Enzo Doria	03/2016
5946	2^426293+1881017	128327	Enzo Doria	11/2016
5947	(88*10^128324-637)/9	128325	Robert Price	11/2020
5948	Phi(161347,7)	128320	Henri Lifchitz	12/2025
5949	Phi(135199,-9)	128312	Henri Lifchitz	12/2025
5950	(491*10^128285+31)/9	128287	Robert Price	04/2022
5951	39103^1908+1908^39103	128281	Hans Havermann	04/2021
5952	2^426043+35	128252	Robert Price	11/2015
5953	(4*10^128244-19)/3	128245	Robert Price	03/2018
5954	26220^29021-29021^26220	128234	Frank Doornink	03/2024
5955	35489^4102+4102^35489	128222	Hans Havermann	04/2021
5956	34721^4926+4926^34721	128208	Hans Havermann	04/2021
5957	(305*10^128198+1)/9	128200	Robert Price	02/2020
5958	2^425808-459959	128181	Enzo Doria	06/2015
5959	30632^15291+15291^30632	128178	Hans Havermann	04/2021
5960	U(623603)	128177	Serge Batalov	07/2024
5961	35981^3648+3648^35981	128167	Hans Havermann	04/2021
5962	2^425627-113605	128127	Enzo Doria	08/2014
5963	(4*10^128109+119)/3	128110	Robert Price	12/2021
5964	(22*10^128094+53)/3	128095	Robert Price	07/2019
5965	(86*10^128086-221)/9	128087	Robert Price	09/2019
5966	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
5967	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
5968	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
5969	Phi(149401,10)/30037901719561	128003	Makoto Kamada	07/2022
5970	2^425205+4911	128000	Marek Hubal	02/2017
5971	29241^23836+23836^29241	127995	Hans Havermann	04/2021
5972	2^425118-113663	127974	Enzo Doria	08/2014
5973	(86*10^127967-329)/9	127968	Robert Price	01/2020
5974	2^425061+1869761	127957	Enzo Doria	05/2016
5975	746^44541+44541^746	127955	Norbert Schneider	07/2019
5976	30236^17043+17043^30236	127946	Hans Havermann	03/2021
5977	2^424938+212419	127920	Enzo Doria	08/2023
5978	2^424918-21141	127914	Enzo Doria	07/2013
5979	Phi(274823,-3)	127907	Henri Lifchitz	12/2025
5980	(62*10^127903+91)/9	127904	Robert Price	07/2021
5981	2^424864-29489	127897	Enzo Doria	08/2015
5982	30438^15893+15893^30438	127877	Hans Havermann	02/2021
5983	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
5984	28929^26258+26258^28929	127845	Hans Havermann	03/2021
5985	30563^15220+15220^30563	127828	Hans Havermann	03/2021
5986	2^424632-2786639	127827	Enzo Doria	03/2016
5987	10^127821-700001	127821	Robert Price	08/2021
5988	2^424577-113755	127811	Enzo Doria	09/2014
5989	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
5990	(56*10^127752+691)/9	127753	Robert Price	05/2019
5991	11^122629-720	127705	Enzo Doria	11/2012
5992	22*10^127645+3	127647	Robert Price	01/2020
5993	28715^27844+27844^28715	127631	Hans Havermann	03/2021
5994	(56*10^127612+187)/9	127613	Robert Price	10/2021
5995	(5*36^81995+821)/7	127609	Eric Chen	01/2021
5996	4*10^127562-39	127563	Robert Price	09/2020
5997	32595^8186+8186^32595	127547	Hans Havermann	03/2021
5998	2^423696-21429	127546	Enzo Doria	07/2013
5999	2^423664-1864559	127536	Enzo Doria	03/2016
6000	37889^2322+2322^37889	127530	Hans Havermann	03/2021

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Probable Primes Top 10000

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