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 ?
7251	32226^3439+3439^32226	113966	Hans Havermann	02/2021
7252	(77*10^113963-149)/9	113964	Robert Price	03/2022
7253	78*10^113954-7	113956	Robert Price	10/2020
7254	2*10^113941+9	113942	Dmitry Domanov	11/2010
7255	10^113933+145897	113934	Patrick De Geest	02/2021
7258	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
7256	10^113933-8000000001	113933	Robert Price	11/2020
7257	10^113933-66167	113933	Patrick De Geest	02/2021
7259	2339662057597*10^113903+9	113916	Robert Price	03/2021
7261	4*10^113905+91	113906	Robert Price	08/2018
7260	Phi(256695,7)	113906	Henri Lifchitz	02/2026
7262	10^113894+76609	113895	Patrick De Geest	02/2021
7264	10^113894-10000001	113894	Robert Price	09/2020
7263	10^113894-373947	113894	Patrick De Geest	02/2021
7265	33933^2270+2270^33933	113881	Hans Havermann	02/2021
7266	4*10^113874-21	113875	Robert Price	09/2018
7267	2^378272-16565	113872	Enzo Doria	04/2013
7268	2^378217-109075	113855	Enzo Doria	04/2014
7269	2^378198+67	113849	Lelio R Paula	03/2013
7270	2^378173-3249	113842	Yves Minet	12/2014
7271	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
7272	2^378137+1334025	113831	Henri Lifchitz	10/2024
7273	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
7274	30030^6173+6173^30030	113829	Hans Havermann	01/2021
7275	2^378128-262977	113828	Enzo Doria	05/2014
7276	2^378123-113215	113827	Enzo Doria	07/2014
7277	6^146274-18893	113824	Enzo Doria	03/2013
7278	34596^1949+1949^34596	113815	Hans Havermann	02/2021
7279	2^378078+75	113813	Lelio R Paula	03/2013
7280	(28*10^113810+449)/9	113811	Robert Price	11/2021
7281	26273^21448+21448^26273	113799	Hans Havermann	02/2021
7282	2^377966+255255	113780	Paul Bourdelais	10/2021
7283	2^377940+63	113772	Lelio R Paula	03/2013
7284	2^377941-2785843	113772	Enzo Doria	04/2016
7285	(7*10^113757+11)/9	113757	Tyler Busby	01/2023
7286	2^377810+1875109	113733	Enzo Doria	09/2016
7287	2^377803-1838635	113731	Enzo Doria	05/2015
7288	2^377799+52223	113729	Yves Minet	08/2010
7289	(2^377791+3258)/2	113727	Stefano Morozzi	02/2021
7290	11^109190-270	113710	Enzo Doria	12/2012
7291	28206^10739+10739^28206	113698	Hans Havermann	01/2021
7292	7*10^113693+9	113694	Robert Price	09/2015
7293	13899^27442+27442^13899	113692	Norbert Schneider	12/2020
7294	(82*10^113681+161)/9	113682	Robert Price	10/2019
7295	26121^22478+22478^26121	113673	Hans Havermann	01/2021
7296	4*10^113658+49	113659	Robert Price	01/2019
7297	(10^113656+7)/40231/6439001	113645	Alfred Reich	06/2021
7298	(2*10^113631+529)/9	113631	Robert Price	01/2018
7299	2^377408-2798279	113612	Enzo Doria	04/2016
7300	(292^46336+1)/(292^256+1)	113605	Martin Hopf	12/2023
7301	13706^27459+27459^13706	113596	Norbert Schneider	12/2020
7302	5*10^113586+57	113587	Robert Price	12/2018
7303	Phi(150733,-7)	113582	Henri Lifchitz	12/2025
7304	(2^377242+2794)/2	113561	Stefano Morozzi	02/2021
7305	2^377222+93679	113556	Yves Minet	02/2011
7307	262147#+316847	113552	Makoto Morimoto	02/2016
7306	27172^15101+15101^27172	113552	Hans Havermann	01/2021
7308	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
7309	2^377026-458903	113497	Enzo Doria	04/2015
7310	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
7311	34791^1828+1828^34791	113488	Hans Havermann	02/2021
7312	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
7313	(29*10^113468-17)/3	113469	Robert Price	09/2019
7314	35^73477-34^73477	113454	Robert Price	05/2012
7315	(14*10^113451-89)/3	113452	Robert Price	05/2020
7316	2^376790+27	113426	Lelio R Paula	03/2013
7317	2^376786-112701	113424	Enzo Doria	06/2014
7318	2^376731+21	113408	Lelio R Paula	03/2013
7319	9*10^113394-73	113395	Robert Price	01/2021
7320	29660^6651+6651^29660	113387	Hans Havermann	01/2021
7322	2^376634+1871245	113379	Enzo Doria	05/2016
7321	(4^188318+17)/3	113379	Robert Price	02/2017
7323	E(29532)/492842728006750534663978950979381235	113367	Thomas Ritschel	01/2021
7324	2^376576-344369	113361	Enzo Doria	07/2015
7325	2^376549-4543	113353	Yves Minet	03/2019
7326	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
7327	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
7328	(2^376350+3538)/2	113293	Stefano Morozzi	09/2020
7329	27265^14272+14272^27265	113273	Hans Havermann	02/2021
7330	32174^3315+3315^32174	113269	Hans Havermann	02/2021
7331	(2*10^113248+73)/3	113248	Robert Price	09/2020
7332	2^376128-21237	113226	Enzo Doria	06/2013
7333	5*10^113224-81	113225	Robert Price	01/2019
7334	10^113220+51409	113221	Patrick De Geest	02/2021
7336	10^113220-1000001	113220	Robert Price	08/2020
7335	10^113220-61779	113220	Patrick De Geest	02/2021
7337	(2^376102+1578)/2	113218	Stefano Morozzi	09/2020
7338	(2^375996+3102)/2	113186	Stefano Morozzi	09/2020
7339	37258^1091+1091^37258	113184	Hans Havermann	02/2021
7340	(94*10^113176+11)/3	113178	Robert Price	04/2020
7341	(46*10^113162+521)/9	113163	Robert Price	02/2019
7342	14*29^77375+17875	113155	Eric Chen	06/2025
7343	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
7344	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
7345	3*10^113137+23	113138	Robert Price	03/2022
7346	(8*10^113135-269)/9	113135	Robert Price	09/2021
7347	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
7348	26050^21959+21959^26050	113100	Hans Havermann	02/2021
7349	2^375638-1787171	113079	Enzo Doria	03/2016
7350	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
7351	2^375537+4847	113048	Yves Minet	02/2011
7352	(17^91837+16^91837)/33	113000	Robert Price	08/2013
7353	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
7354	2^375350-3221	112992	Yves Minet	07/2011
7355	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
7356	2^375305+76757	112979	Enzo Doria	05/2016
7357	2^375258+1874989	112964	Enzo Doria	07/2016
7358	(29^77237-1)/28	112950	Robert Price	04/2012
7359	26620^17483+17483^26620	112939	Hans Havermann	01/2021
7360	2^375154+74959	112933	Enzo Doria	04/2016
7361	(266*10^112930-17)/3	112932	Robert Price	07/2020
7362	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
7363	(85*10^112919+293)/9	112920	Robert Price	12/2019
7364	29412^6899+6899^29412	112907	Hans Havermann	02/2021
7365	(191*10^112903-17)/3	112905	Robert Price	11/2021
7366	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
7367	25992^22039+22039^25992	112889	Hans Havermann	02/2021
7368	2^374993-2787163	112885	Enzo Doria	11/2015
7369	(697*10^112869+23)/9	112871	Robert Price	04/2021
7370	(19*10^112851+377)/9	112852	Alfred Reich	11/2022
7371	30420^5111+5111^30420	112813	Hans Havermann	02/2021
7372	13699^27268+27268^13699	112800	Norbert Schneider	12/2020
7373	123^53970+2	112793	Lelio R Paula	06/2013
7374	12308*27^78796+23	112790	Eric Chen	07/2023
7375	28942^7887+7887^28942	112785	Hans Havermann	01/2021
7376	2^374640-4685	112778	Yves Minet	05/2019
7377	12^104501-11	112776	Riley Fisher	12/2023
7378	57290^93+93^57290	112775	Hans Havermann	01/2021
7379	115^54726-54726^115	112774	Norman Luhn	09/2024
7380	13608^27277-27277^13608	112758	Norbert Schneider	12/2022
7381	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
7382	p(22852)#/2+512	112745	Robert Price	05/2017
7383	(11*10^112742-131)/3	112743	Robert Price	09/2018
7384	2^374441-21049	112718	Enzo Doria	06/2013
7385	(15056!^2+1)/(30113*454287444157)	112711	Michael Porter	09/2025
7386	4*10^112706-93	112707	Robert Price	07/2020
7388	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
7387	Phi(374321,-2)	112682	Henri Lifchitz	12/2025
7389	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
7390	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
7391	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
7392	3^236011-8828	112606	Enzo Doria	05/2014
7393	31854^3427+3427^31854	112602	Hans Havermann	02/2021
7394	2569^33013-2568^33013	112567	Norbert Schneider	01/2026
7395	Phi(442141,-2)	112561	Henri Lifchitz	12/2025
7396	(85*10^112530-373)/9	112531	Robert Price	05/2021
7397	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
7398	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
7399	27618^11821+11821^27618	112479	Hans Havermann	01/2021
7400	U(602921)/4823369	112479	Serge Batalov	07/2024
7401	26343^18580+18580^26343	112460	Hans Havermann	01/2021
7402	39^70666+2	112435	Lelio R Paula	11/2013
7403	(134*10^112400+7)/3	112402	Robert Price	02/2020
7404	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
7405	(2^373350-7)/3	112390	Lelio R Paula	03/2014
7406	3^235532-235532	112378	Anonymous	09/2025
7407	2^373306-1840931	112377	Enzo Doria	06/2015
7408	8*10^112371-37	112372	Robert Price	03/2022
7409	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
7410	6*10^112359-79	112360	Robert Price	03/2022
7411	34409^1842+1842^34409	112356	Hans Havermann	02/2021
7412	(142*10^112352-7)/9	112354	Robert Price	12/2019
7413	25580^24633+24633^25580	112336	Hans Havermann	01/2021
7414	2^373117+1872107	112320	Enzo Doria	05/2016
7415	(2^373083+2226)/2	112309	Stefano Morozzi	01/2021
7416	(35*10^112308+37)/9	112309	Robert Price	05/2022
7417	27963^10376+10376^27963	112301	Hans Havermann	01/2021
7418	2^373040+2792761	112297	Enzo Doria	03/2016
7419	(156^51203-1)/155	112293	Anonymous	06/2024
7420	EPrime(112280)	112280	Eric W. Weisstein	10/2010
7421	2^372950+7	112270	Lelio R Paula	03/2013
7422	2^372945+1872167	112268	Enzo Doria	05/2016
7423	36274^1243+1243^36274	112249	Hans Havermann	02/2021
7424	(55*10^112246+629)/9	112247	Robert Price	01/2022
7425	(2^372872+3798)/2	112246	Stefano Morozzi	02/2021
7426	25513^25060+25060^25513	112232	Hans Havermann	02/2021
7427	(53*10^112229-611)/9	112230	Robert Price	02/2022
7428	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020
7429	6*10^112208+43	112209	Robert Price	07/2020
7430	(2^372728+3058)/2	112203	Stefano Morozzi	09/2020
7431	32061^3158+3158^32061	112195	Hans Havermann	02/2021
7432	2^372695+72113	112193	Enzo Doria	04/2016
7433	2^372689-2563	112191	Yves Minet	07/2014
7434	2^372638-1859441	112176	Enzo Doria	03/2016
7435	3^235074-113056	112159	Enzo Doria	07/2014
7436	-E(29242)/489848365125303139750087	112140	Thomas Ritschel	01/2021
7437	(2^372514+1822)/2	112138	Stefano Morozzi	02/2021
7438	29468^6387+6387^29468	112135	Hans Havermann	02/2021
7439	(2^372428+3742)/2	112112	Stefano Morozzi	01/2021
7440	25375^25454-25454^25375	112110	Norbert Schneider	01/2021
7441	131^52949-130	112108	Norbert Schneider	02/2019
7442	(91*10^112098-1)/9	112100	Robert Price	04/2015
7443	(68*10^112087-149)/9	112088	Robert Price	07/2022
7444	2^372314+212419	112078	Enzo Doria	08/2023
7445	2^372310-85061	112077	Paul Bourdelais	02/2012
7446	(10^112067+53)/9	112067	Serge Batalov	07/2015
7447	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
7448	75^59760+2	112054	Lelio R Paula	08/2013
7449	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
7450	(10^112048+7)/8747/373157	112039	Alfred Reich	06/2021
7451	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
7452	F(536233)/825798821/1102495049/5641839306317	112036	Serge Batalov	07/2024
7453	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
7454	8*10^112018-49	112019	Robert Price	08/2019
7456	2^372108+74221	112016	Enzo Doria	04/2016
7455	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
7457	8*10^112011-73	112012	Robert Price	01/2022
7458	(184*10^112007-1)/3	112009	Robert Price	02/2020
7459	5*10^112003+81	112004	Robert Price	03/2019
7460	215^48018+48018^215	112000	Norbert Schneider	10/2018
7461	Phi(82303,5#)	111990	Henri Lifchitz	12/2025
7462	25549^24148+24148^25549	111979	Hans Havermann	02/2021
7463	2^371970-459491	111975	Enzo Doria	05/2015
7464	41^69427-40^69427	111971	Robert Price	07/2012
7465	(20^86027+19^86027)/39	111923	Robert Price	09/2025
7466	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
7467	15*25^80056+446	111915	Eric Chen	10/2023
7468	(34*10^111902-547)/9	111903	Robert Price	03/2021
7469	(10^111902+71)/9	111902	Serge Batalov	07/2015
7470	((385283-70250)F(535399)-(85283-70250)*L(535399))/2	111897	Yaroslav Berezhko	09/2025
7471	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
7472	29080^7027+7027^29080	111865	Hans Havermann	01/2021
7473	3^234408+531440	111842	Alfred Reich	03/2026
7474	31307^3730+3730^31307	111820	Hans Havermann	02/2021
7475	2^371440-112865	111815	Enzo Doria	06/2014
7476	2^371426-459161	111811	Enzo Doria	05/2015
7477	25768^21771+21771^25768	111779	Hans Havermann	02/2021
7478	28022^9747+9747^28022	111777	Hans Havermann	02/2021
7479	(94*10^111770+11)/3	111772	Robert Price	04/2020
7480	2^371276-461267	111766	Enzo Doria	07/2015
7481	6*10^111760+43	111761	Robert Price	07/2020
7482	98079!4-1024	111747	Robert Price	11/2019
7483	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
7484	10^(255862+1)-410^55862-1	111725	Robert Price	07/2023
7485	2^371098-113261	111712	Enzo Doria	07/2014
7486	(7*10^111706-61)/9	111706	Erik Branger	01/2011
7487	2^371044+1869391	111696	Enzo Doria	05/2016
7488	26310^17581+17581^26310	111688	Hans Havermann	01/2021
7489	88^57416+87	111645	Norbert Schneider	11/2015
7490	2^370829-109693	111631	Enzo Doria	04/2014
7491	15^94906-2	111619	Lelio R Paula	11/2013
7492	25835^20904+20904^25835	111614	Hans Havermann	02/2021
7493	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
7494	27758^10479+10479^27758	111597	Hans Havermann	02/2021
7495	2^370695-4627	111591	Yves Minet	05/2019
7496	7*10^111579-87	111580	Robert Price	06/2020
7497	2^370643-37	111575	Yves Minet	01/2012
7498	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
7499	2^370610-3911	111565	Yves Minet	04/2017
7500	(154*10^111549+17)/9	111551	Robert Price	06/2022

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