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 ?
6501	3^242337-4042	115625	Enzo Doria	05/2014
6502	(17699*31^77516-29)/30	115608	Eric Chen	05/2024
6503	(2^383931+674)/2	115575	Stefano Morozzi	09/2020
6504	7*10^115561+79	115562	Robert Price	07/2019
6505	(2^383872+3046)/2	115557	Stefano Morozzi	09/2020
6506	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
6507	2^383780-3149	115530	Yves Minet	10/2014
6508	(41*10^115523-383)/9	115524	Robert Price	11/2018
6509	27316^16923+16923^27316	115506	Hans Havermann	02/2021
6510	(2^383618+618)/2	115481	Stefano Morozzi	09/2020
6511	2^383560-455	115464	Yves Minet	03/2012
6512	(2^383544+5)/3	115458	Lelio R Paula	03/2014
6513	(22*10^115454+119)/3	115455	Robert Price	04/2021
6514	89^59221-88^59221	115445	Robert Price	06/2015
6515	(7^136559-5^136559)/2	115406	Jon Grantham	08/2023
6516	2^383347+1869413	115399	Enzo Doria	05/2016
6517	(103*10^115366+17)/3	115368	Robert Price	08/2020
6518	(2^383232+750)/2	115365	Stefano Morozzi	09/2020
6519	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
6520	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
6521	29961^7060+7060^29961	115315	Hans Havermann	01/2021
6523	2^383039+1869509	115307	Enzo Doria	05/2016
6522	32918^3183+3183^32918	115307	Hans Havermann	01/2021
6524	(109^56597-1)/90183471012	115302	Paul Vanderveen	06/2025
6525	36964^1315+1315^36964	115288	Hans Havermann	02/2021
6526	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
6527	(22*10^115282+29)/3	115283	Robert Price	02/2021
6528	(2^382945+2046)/2	115278	Stefano Morozzi	09/2020
6529	(2^382789+3182)/2	115231	Stefano Morozzi	09/2020
6530	30416^6141+6141^30416	115224	Hans Havermann	02/2021
6531	6*10^115211+79	115212	Robert Price	09/2020
6532	(2^382722+3598)/2	115211	Stefano Morozzi	09/2020
6533	27987^13078+13078^27987	115210	Hans Havermann	02/2021
6534	(2^382699+2090)/2	115204	Stefano Morozzi	09/2020
6535	(22*10^115188-193)/9	115189	Robert Price	07/2022
6536	2^382633+73697	115185	Enzo Doria	04/2016
6537	2^382509-113593	115147	Enzo Doria	08/2014
6538	2^382502-2791721	115145	Enzo Doria	03/2016
6539	(2^382495+1274)/2	115143	Stefano Morozzi	01/2021
6540	2^382464+22741	115134	Enzo Doria	09/2023
6541	26752^20065+20065^26752	115099	Hans Havermann	02/2021
6542	26383^23008+23008^26383	115080	Hans Havermann	02/2021
6543	9^120590-120590	115073	Robert Price	03/2014
6544	28203^12016+12016^28203	115062	Hans Havermann	02/2021
6545	2^382198+9	115054	Lelio R Paula	03/2013
6546	18268*31^77131+22839	115035	Eric Chen	05/2024
6547	30101^6630+6630^30101	115032	Hans Havermann	01/2021
6548	(89*10^115030-179)/9	115031	Robert Price	12/2019
6549	25554^26089-26089^25554	114987	Frank Doornink	02/2024
6550	25142^26129-26129^25142	114979	Frank Doornink	12/2023
6551	(2^381935+2774)/2	114974	Stefano Morozzi	02/2021
6552	27300^16271+16271^27300	114972	Hans Havermann	02/2021
6553	(23*10^114962+7)/3	114963	Robert Price	05/2023
6554	2^381883-59197	114959	Enzo Doria	10/2015
6555	27423^15542+15542^27423	114944	Hans Havermann	02/2021
6556	(2^381820+1626)/2	114939	Stefano Morozzi	09/2020
6558	2^381806-4481	114936	Yves Minet	07/2011
6557	2^381808-1851507	114936	Enzo Doria	08/2015
6559	(2^381792+2502)/2	114931	Stefano Morozzi	09/2020
6560	2^381774-112373	114926	Enzo Doria	06/2014
6561	26341^22980+22980^26341	114883	Hans Havermann	01/2021
6562	(79^60539-1)/61747564999146	114867	Paul Vanderveen	05/2025
6563	2^381555-109051	114860	Enzo Doria	04/2014
6564	2^381551+213683	114859	Enzo Doria	09/2023
6565	2^381546-113501	114857	Enzo Doria	08/2014
6566	(7*10^114845-19)/3	114846	Robert Price	10/2020
6567	26675^20178+20178^26675	114833	Hans Havermann	02/2021
6568	(2^381436+1182)/2	114824	Stefano Morozzi	09/2020
6569	3^240644+16	114817	Robert Price	04/2020
6570	(13^114814)%(10^114814)	114814	Henri Lifchitz	05/2025
6571	2^381360-110429	114801	Enzo Doria	05/2014
6572	(17*10^114795+79)/3	114796	Robert Price	04/2019
6573	(66^63079+1)/67	114774	Paul Bourdelais	09/2017
6574	2^381252-115079	114769	Enzo Doria	06/2015
6575	(2^381251+3186)/2	114768	Stefano Morozzi	09/2020
6576	2^381209-29323	114756	Enzo Doria	07/2015
6577	2^381207-111546435	114755	Paul Bourdelais	10/2021
6578	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
6579	2^381201+1873205	114753	Enzo Doria	06/2016
6581	(85*10^114737+293)/9	114738	Robert Price	12/2019
6582	(265*10^114736+17)/3	114738	Robert Price	03/2020
6580	379*10^114735+9	114738	Jason Yuen	01/2025
6583	(2^381062+2170)/2	114711	Stefano Morozzi	09/2020
6584	2^380974-112991	114685	Enzo Doria	07/2014
6585	37097^1234+1234^37097	114679	Hans Havermann	02/2021
6586	(26*10^114658-119)/3	114659	Robert Price	07/2023
6587	88^58949-87	114626	Norbert Schneider	11/2015
6588	(2^380773+662)/2	114624	Stefano Morozzi	09/2020
6589	Phi(155285,10)/242674820198201	114610	Makoto Kamada	02/2024
6590	(10^155285-1)(10^2389-1)(10^13-1)*11111/(10^31057-1)/(10^11945-1)/(10^65-1)/242674820198201	114610	Anonymous	04/2025
6591	29913^6782+6782^29913	114608	Hans Havermann	02/2021
6592	(331*10^114605-7)/9	114607	Robert Price	04/2022
6593	2^380700+91	114603	Lelio R Paula	03/2013
6594	(2^380632+2578)/2	114582	Stefano Morozzi	09/2020
6595	7*10^114577+27	114578	Robert Price	11/2020
6597	10^114575+3^114576	114576	Mike Oakes	09/2010
6596	10^114575+66561	114576	Patrick De Geest	02/2017
6598	10^114575-581081	114575	Patrick De Geest	02/2017
6599	2^380587-115315	114569	Enzo Doria	06/2015
6600	31874^3927+3927^31874	114558	Hans Havermann	02/2021
6601	2^380513-216925	114546	Enzo Doria	05/2014
6602	2^380451-1840087	114528	Enzo Doria	06/2015
6603	(2^380426+1510)/2	114520	Stefano Morozzi	09/2020
6604	(15*2^380388-1)/539	114507	Lelio R Paula	04/2014
6605	2^380279-461347	114476	Enzo Doria	07/2015
6606	(331*10^114454-7)/9	114456	Robert Price	04/2022
6607	27121^16590+16590^27121	114447	Hans Havermann	01/2021
6608	25966^25555+25555^25966	114445	Hans Havermann	01/2021
6609	(611*32^76029-53)/31	114437	Eric Chen	11/2023
6610	(11*10^114400+529)/9	114401	Robert Price	09/2021
6611	2^380021+1871147	114398	Enzo Doria	05/2016
6612	2^380005+1869707	114393	Enzo Doria	05/2016
6613	2^379958-113297	114379	Enzo Doria	07/2014
6614	(2^379897+1274)/2	114361	Stefano Morozzi	01/2021
6615	2^379881-109105	114356	Enzo Doria	04/2014
6616	(21*2^379857-1)/13	114349	Lelio R Paula	03/2014
6617	(4*10^114340+83)/3	114341	Robert Price	02/2018
6618	(26*10^114317-77)/3	114318	Robert Price	11/2019
6619	(4*10^114296+149)/9	114296	Robert Price	04/2018
6620	88^58773-87	114284	Norbert Schneider	11/2015
6621	27764^13065+13065^27764	114280	Hans Havermann	01/2021
6622	(132^53891-1)/131	114278	Anonymous	06/2024
6623	2^379529-2790283	114250	Enzo Doria	03/2016
6624	2^379522+1869115	114248	Enzo Doria	05/2016
6625	(145*10^114226-1)/9	114228	Serge Batalov	12/2014
6626	2^379317-115033	114186	Enzo Doria	06/2015
6627	(22*10^114178+47)/3	114179	Robert Price	06/2021
6628	(17*2^379246-1)/17407	114162	Lelio R Paula	03/2014
6629	(2^379192+226)/2	114148	Stefano Morozzi	09/2020
6630	(228^48407-1)/227	114139	Alexander Zhirkov	03/2023
6631	6*10^114091+23	114092	Robert Price	09/2020
6632	(4*10^114076+143)/3	114077	Robert Price	03/2018
6633	332*25^81584+12357	114053	Eric Chen	10/2023
6634	(2^378820+3226)/2	114036	Stefano Morozzi	01/2021
6635	(2^378754+2058)/2	114017	Stefano Morozzi	09/2020
6636	13643^27572-27572^13643	114008	Norbert Schneider	12/2022
6638	(46*10^113969+683)/9	113970	Robert Price	03/2019
6637	(83*10^113969+133)/9	113970	Robert Price	08/2021
6639	32226^3439+3439^32226	113966	Hans Havermann	02/2021
6640	(77*10^113963-149)/9	113964	Robert Price	03/2022
6641	78*10^113954-7	113956	Robert Price	10/2020
6642	2*10^113941+9	113942	Dmitry Domanov	11/2010
6643	10^113933+145897	113934	Patrick De Geest	02/2021
6646	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
6644	10^113933-8000000001	113933	Robert Price	11/2020
6645	10^113933-66167	113933	Patrick De Geest	02/2021
6647	2339662057597*10^113903+9	113916	Robert Price	03/2021
6648	4*10^113905+91	113906	Robert Price	08/2018
6649	10^113894+76609	113895	Patrick De Geest	02/2021
6651	10^113894-10000001	113894	Robert Price	09/2020
6650	10^113894-373947	113894	Patrick De Geest	02/2021
6652	33933^2270+2270^33933	113881	Hans Havermann	02/2021
6653	4*10^113874-21	113875	Robert Price	09/2018
6654	2^378272-16565	113872	Enzo Doria	04/2013
6655	2^378217-109075	113855	Enzo Doria	04/2014
6656	2^378198+67	113849	Lelio R Paula	03/2013
6657	2^378173-3249	113842	Yves Minet	12/2014
6658	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
6659	2^378137+1334025	113831	Henri Lifchitz	10/2024
6660	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
6661	30030^6173+6173^30030	113829	Hans Havermann	01/2021
6662	2^378128-262977	113828	Enzo Doria	05/2014
6663	2^378123-113215	113827	Enzo Doria	07/2014
6664	6^146274-18893	113824	Enzo Doria	03/2013
6665	34596^1949+1949^34596	113815	Hans Havermann	02/2021
6666	2^378078+75	113813	Lelio R Paula	03/2013
6667	(28*10^113810+449)/9	113811	Robert Price	11/2021
6668	26273^21448+21448^26273	113799	Hans Havermann	02/2021
6669	2^377966+255255	113780	Paul Bourdelais	10/2021
6670	2^377940+63	113772	Lelio R Paula	03/2013
6671	2^377941-2785843	113772	Enzo Doria	04/2016
6672	(7*10^113757+11)/9	113757	Tyler Busby	01/2023
6673	2^377810+1875109	113733	Enzo Doria	09/2016
6674	2^377803-1838635	113731	Enzo Doria	05/2015
6675	2^377799+52223	113729	Yves Minet	08/2010
6676	(2^377791+3258)/2	113727	Stefano Morozzi	02/2021
6677	11^109190-270	113710	Enzo Doria	12/2012
6678	28206^10739+10739^28206	113698	Hans Havermann	01/2021
6679	7*10^113693+9	113694	Robert Price	09/2015
6680	13899^27442+27442^13899	113692	Norbert Schneider	12/2020
6681	(82*10^113681+161)/9	113682	Robert Price	10/2019
6682	26121^22478+22478^26121	113673	Hans Havermann	01/2021
6683	4*10^113658+49	113659	Robert Price	01/2019
6684	(10^113656+7)/40231/6439001	113645	Alfred Reich	06/2021
6685	(2*10^113631+529)/9	113631	Robert Price	01/2018
6686	2^377408-2798279	113612	Enzo Doria	04/2016
6687	(292^46336+1)/(292^256+1)	113605	Martin Hopf	12/2023
6688	13706^27459+27459^13706	113596	Norbert Schneider	12/2020
6689	5*10^113586+57	113587	Robert Price	12/2018
6690	(2^377242+2794)/2	113561	Stefano Morozzi	02/2021
6691	2^377222+93679	113556	Yves Minet	02/2011
6693	262147#+316847	113552	Makoto Morimoto	02/2016
6692	27172^15101+15101^27172	113552	Hans Havermann	01/2021
6694	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
6695	2^377026-458903	113497	Enzo Doria	04/2015
6696	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
6697	34791^1828+1828^34791	113488	Hans Havermann	02/2021
6698	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
6699	(29*10^113468-17)/3	113469	Robert Price	09/2019
6700	35^73477-34^73477	113454	Robert Price	05/2012
6701	(14*10^113451-89)/3	113452	Robert Price	05/2020
6702	2^376790+27	113426	Lelio R Paula	03/2013
6703	2^376786-112701	113424	Enzo Doria	06/2014
6704	2^376731+21	113408	Lelio R Paula	03/2013
6705	9*10^113394-73	113395	Robert Price	01/2021
6706	29660^6651+6651^29660	113387	Hans Havermann	01/2021
6708	2^376634+1871245	113379	Enzo Doria	05/2016
6707	(4^188318+17)/3	113379	Robert Price	02/2017
6709	E(29532)/492842728006750534663978950979381235	113367	Thomas Ritschel	01/2021
6710	2^376576-344369	113361	Enzo Doria	07/2015
6711	2^376549-4543	113353	Yves Minet	03/2019
6712	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
6713	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
6714	(2^376350+3538)/2	113293	Stefano Morozzi	09/2020
6715	27265^14272+14272^27265	113273	Hans Havermann	02/2021
6716	32174^3315+3315^32174	113269	Hans Havermann	02/2021
6717	(2*10^113248+73)/3	113248	Robert Price	09/2020
6718	2^376128-21237	113226	Enzo Doria	06/2013
6719	5*10^113224-81	113225	Robert Price	01/2019
6720	10^113220+51409	113221	Patrick De Geest	02/2021
6722	10^113220-1000001	113220	Robert Price	08/2020
6721	10^113220-61779	113220	Patrick De Geest	02/2021
6723	(2^376102+1578)/2	113218	Stefano Morozzi	09/2020
6724	(2^375996+3102)/2	113186	Stefano Morozzi	09/2020
6725	37258^1091+1091^37258	113184	Hans Havermann	02/2021
6726	(94*10^113176+11)/3	113178	Robert Price	04/2020
6727	(46*10^113162+521)/9	113163	Robert Price	02/2019
6728	14*29^77375+17875	113155	Eric Chen	06/2025
6729	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
6730	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
6731	3*10^113137+23	113138	Robert Price	03/2022
6732	(8*10^113135-269)/9	113135	Robert Price	09/2021
6733	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
6734	26050^21959+21959^26050	113100	Hans Havermann	02/2021
6735	2^375638-1787171	113079	Enzo Doria	03/2016
6736	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
6737	2^375537+4847	113048	Yves Minet	02/2011
6738	(17^91837+16^91837)/33	113000	Robert Price	08/2013
6739	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
6740	2^375350-3221	112992	Yves Minet	07/2011
6741	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
6742	2^375305+76757	112979	Enzo Doria	05/2016
6743	2^375258+1874989	112964	Enzo Doria	07/2016
6744	(29^77237-1)/28	112950	Robert Price	04/2012
6745	26620^17483+17483^26620	112939	Hans Havermann	01/2021
6746	2^375154+74959	112933	Enzo Doria	04/2016
6747	(266*10^112930-17)/3	112932	Robert Price	07/2020
6748	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
6749	(85*10^112919+293)/9	112920	Robert Price	12/2019
6750	29412^6899+6899^29412	112907	Hans Havermann	02/2021

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Probable Primes Top 10000

(301723 PRPs in the top)