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	(2^377791+3258)/2	113727	Stefano Morozzi	02/2021
7252	11^109190-270	113710	Enzo Doria	12/2012
7253	28206^10739+10739^28206	113698	Hans Havermann	01/2021
7254	7*10^113693+9	113694	Robert Price	09/2015
7255	13899^27442+27442^13899	113692	Norbert Schneider	12/2020
7256	(82*10^113681+161)/9	113682	Robert Price	10/2019
7257	26121^22478+22478^26121	113673	Hans Havermann	01/2021
7258	4*10^113658+49	113659	Robert Price	01/2019
7259	(10^113656+7)/40231/6439001	113645	Alfred Reich	06/2021
7260	(2*10^113631+529)/9	113631	Robert Price	01/2018
7261	2^377408-2798279	113612	Enzo Doria	04/2016
7262	(292^46336+1)/(292^256+1)	113605	Martin Hopf	12/2023
7263	13706^27459+27459^13706	113596	Norbert Schneider	12/2020
7264	5*10^113586+57	113587	Robert Price	12/2018
7265	Phi(150733,-7)	113582	Henri Lifchitz	12/2025
7266	(2^377242+2794)/2	113561	Stefano Morozzi	02/2021
7267	2^377222+93679	113556	Yves Minet	02/2011
7269	262147#+316847	113552	Makoto Morimoto	02/2016
7268	27172^15101+15101^27172	113552	Hans Havermann	01/2021
7270	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
7271	2^377026-458903	113497	Enzo Doria	04/2015
7272	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
7273	34791^1828+1828^34791	113488	Hans Havermann	02/2021
7274	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
7275	(29*10^113468-17)/3	113469	Robert Price	09/2019
7276	35^73477-34^73477	113454	Robert Price	05/2012
7277	(14*10^113451-89)/3	113452	Robert Price	05/2020
7278	2^376790+27	113426	Lelio R Paula	03/2013
7279	2^376786-112701	113424	Enzo Doria	06/2014
7280	2^376731+21	113408	Lelio R Paula	03/2013
7281	9*10^113394-73	113395	Robert Price	01/2021
7282	29660^6651+6651^29660	113387	Hans Havermann	01/2021
7284	2^376634+1871245	113379	Enzo Doria	05/2016
7283	(4^188318+17)/3	113379	Robert Price	02/2017
7285	E(29532)/492842728006750534663978950979381235	113367	Thomas Ritschel	01/2021
7286	2^376576-344369	113361	Enzo Doria	07/2015
7287	2^376549-4543	113353	Yves Minet	03/2019
7288	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
7289	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
7290	(2^376350+3538)/2	113293	Stefano Morozzi	09/2020
7291	27265^14272+14272^27265	113273	Hans Havermann	02/2021
7292	32174^3315+3315^32174	113269	Hans Havermann	02/2021
7293	(2*10^113248+73)/3	113248	Robert Price	09/2020
7294	2^376128-21237	113226	Enzo Doria	06/2013
7295	5*10^113224-81	113225	Robert Price	01/2019
7296	10^113220+51409	113221	Patrick De Geest	02/2021
7298	10^113220-1000001	113220	Robert Price	08/2020
7297	10^113220-61779	113220	Patrick De Geest	02/2021
7299	(2^376102+1578)/2	113218	Stefano Morozzi	09/2020
7300	(2^375996+3102)/2	113186	Stefano Morozzi	09/2020
7301	37258^1091+1091^37258	113184	Hans Havermann	02/2021
7302	(94*10^113176+11)/3	113178	Robert Price	04/2020
7303	(46*10^113162+521)/9	113163	Robert Price	02/2019
7304	14*29^77375+17875	113155	Eric Chen	06/2025
7305	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
7306	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
7307	3*10^113137+23	113138	Robert Price	03/2022
7308	(8*10^113135-269)/9	113135	Robert Price	09/2021
7309	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
7310	26050^21959+21959^26050	113100	Hans Havermann	02/2021
7311	2^375638-1787171	113079	Enzo Doria	03/2016
7312	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
7313	2^375537+4847	113048	Yves Minet	02/2011
7314	(17^91837+16^91837)/33	113000	Robert Price	08/2013
7315	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
7316	2^375350-3221	112992	Yves Minet	07/2011
7317	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
7318	2^375305+76757	112979	Enzo Doria	05/2016
7319	2^375258+1874989	112964	Enzo Doria	07/2016
7320	(29^77237-1)/28	112950	Robert Price	04/2012
7321	26620^17483+17483^26620	112939	Hans Havermann	01/2021
7322	2^375154+74959	112933	Enzo Doria	04/2016
7323	(266*10^112930-17)/3	112932	Robert Price	07/2020
7324	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
7325	(85*10^112919+293)/9	112920	Robert Price	12/2019
7326	29412^6899+6899^29412	112907	Hans Havermann	02/2021
7327	(191*10^112903-17)/3	112905	Robert Price	11/2021
7328	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
7329	25992^22039+22039^25992	112889	Hans Havermann	02/2021
7330	2^374993-2787163	112885	Enzo Doria	11/2015
7331	(697*10^112869+23)/9	112871	Robert Price	04/2021
7332	(19*10^112851+377)/9	112852	Alfred Reich	11/2022
7333	30420^5111+5111^30420	112813	Hans Havermann	02/2021
7334	13699^27268+27268^13699	112800	Norbert Schneider	12/2020
7335	123^53970+2	112793	Lelio R Paula	06/2013
7336	12308*27^78796+23	112790	Eric Chen	07/2023
7337	28942^7887+7887^28942	112785	Hans Havermann	01/2021
7338	2^374640-4685	112778	Yves Minet	05/2019
7339	12^104501-11	112776	Riley Fisher	12/2023
7340	57290^93+93^57290	112775	Hans Havermann	01/2021
7341	115^54726-54726^115	112774	Norman Luhn	09/2024
7342	13608^27277-27277^13608	112758	Norbert Schneider	12/2022
7343	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
7344	p(22852)#/2+512	112745	Robert Price	05/2017
7345	(11*10^112742-131)/3	112743	Robert Price	09/2018
7346	2^374441-21049	112718	Enzo Doria	06/2013
7347	(15056!^2+1)/(30113*454287444157)	112711	Michael Porter	09/2025
7348	4*10^112706-93	112707	Robert Price	07/2020
7350	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
7349	Phi(374321,-2)	112682	Henri Lifchitz	12/2025
7351	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
7352	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
7353	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
7354	3^236011-8828	112606	Enzo Doria	05/2014
7355	31854^3427+3427^31854	112602	Hans Havermann	02/2021
7356	2569^33013-2568^33013	112567	Norbert Schneider	01/2026
7357	Phi(442141,-2)	112561	Henri Lifchitz	12/2025
7358	(85*10^112530-373)/9	112531	Robert Price	05/2021
7359	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
7360	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
7361	27618^11821+11821^27618	112479	Hans Havermann	01/2021
7362	U(602921)/4823369	112479	Serge Batalov	07/2024
7363	26343^18580+18580^26343	112460	Hans Havermann	01/2021
7364	39^70666+2	112435	Lelio R Paula	11/2013
7365	(134*10^112400+7)/3	112402	Robert Price	02/2020
7366	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
7367	(2^373350-7)/3	112390	Lelio R Paula	03/2014
7368	3^235532-235532	112378	Anonymous	09/2025
7369	2^373306-1840931	112377	Enzo Doria	06/2015
7370	8*10^112371-37	112372	Robert Price	03/2022
7371	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
7372	6*10^112359-79	112360	Robert Price	03/2022
7373	34409^1842+1842^34409	112356	Hans Havermann	02/2021
7374	(142*10^112352-7)/9	112354	Robert Price	12/2019
7375	25580^24633+24633^25580	112336	Hans Havermann	01/2021
7376	2^373117+1872107	112320	Enzo Doria	05/2016
7377	(2^373083+2226)/2	112309	Stefano Morozzi	01/2021
7378	(35*10^112308+37)/9	112309	Robert Price	05/2022
7379	27963^10376+10376^27963	112301	Hans Havermann	01/2021
7380	2^373040+2792761	112297	Enzo Doria	03/2016
7381	(156^51203-1)/155	112293	Anonymous	06/2024
7382	EPrime(112280)	112280	Eric W. Weisstein	10/2010
7383	2^372950+7	112270	Lelio R Paula	03/2013
7384	2^372945+1872167	112268	Enzo Doria	05/2016
7385	36274^1243+1243^36274	112249	Hans Havermann	02/2021
7386	(55*10^112246+629)/9	112247	Robert Price	01/2022
7387	(2^372872+3798)/2	112246	Stefano Morozzi	02/2021
7388	25513^25060+25060^25513	112232	Hans Havermann	02/2021
7389	(53*10^112229-611)/9	112230	Robert Price	02/2022
7390	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020
7391	6*10^112208+43	112209	Robert Price	07/2020
7392	(2^372728+3058)/2	112203	Stefano Morozzi	09/2020
7393	32061^3158+3158^32061	112195	Hans Havermann	02/2021
7394	2^372695+72113	112193	Enzo Doria	04/2016
7395	2^372689-2563	112191	Yves Minet	07/2014
7396	2^372638-1859441	112176	Enzo Doria	03/2016
7397	3^235074-113056	112159	Enzo Doria	07/2014
7398	-E(29242)/489848365125303139750087	112140	Thomas Ritschel	01/2021
7399	(2^372514+1822)/2	112138	Stefano Morozzi	02/2021
7400	29468^6387+6387^29468	112135	Hans Havermann	02/2021
7401	(2^372428+3742)/2	112112	Stefano Morozzi	01/2021
7402	25375^25454-25454^25375	112110	Norbert Schneider	01/2021
7403	131^52949-130	112108	Norbert Schneider	02/2019
7404	(91*10^112098-1)/9	112100	Robert Price	04/2015
7405	(68*10^112087-149)/9	112088	Robert Price	07/2022
7406	2^372314+212419	112078	Enzo Doria	08/2023
7407	2^372310-85061	112077	Paul Bourdelais	02/2012
7408	(10^112067+53)/9	112067	Serge Batalov	07/2015
7409	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
7410	75^59760+2	112054	Lelio R Paula	08/2013
7411	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
7412	(10^112048+7)/8747/373157	112039	Alfred Reich	06/2021
7413	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
7414	F(536233)/825798821/1102495049/5641839306317	112036	Serge Batalov	07/2024
7415	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
7416	8*10^112018-49	112019	Robert Price	08/2019
7418	2^372108+74221	112016	Enzo Doria	04/2016
7417	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
7419	8*10^112011-73	112012	Robert Price	01/2022
7420	(184*10^112007-1)/3	112009	Robert Price	02/2020
7421	5*10^112003+81	112004	Robert Price	03/2019
7422	215^48018+48018^215	112000	Norbert Schneider	10/2018
7423	Phi(82303,5#)	111990	Henri Lifchitz	12/2025
7424	25549^24148+24148^25549	111979	Hans Havermann	02/2021
7425	2^371970-459491	111975	Enzo Doria	05/2015
7426	41^69427-40^69427	111971	Robert Price	07/2012
7427	(20^86027+19^86027)/39	111923	Robert Price	09/2025
7428	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
7429	15*25^80056+446	111915	Eric Chen	10/2023
7430	(34*10^111902-547)/9	111903	Robert Price	03/2021
7431	(10^111902+71)/9	111902	Serge Batalov	07/2015
7432	((385283-70250)F(535399)-(85283-70250)*L(535399))/2	111897	Yaroslav Berezhko	09/2025
7433	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
7434	29080^7027+7027^29080	111865	Hans Havermann	01/2021
7435	3^234408+531440	111842	Alfred Reich	03/2026
7436	31307^3730+3730^31307	111820	Hans Havermann	02/2021
7437	2^371440-112865	111815	Enzo Doria	06/2014
7438	2^371426-459161	111811	Enzo Doria	05/2015
7439	25768^21771+21771^25768	111779	Hans Havermann	02/2021
7440	28022^9747+9747^28022	111777	Hans Havermann	02/2021
7441	(94*10^111770+11)/3	111772	Robert Price	04/2020
7442	2^371276-461267	111766	Enzo Doria	07/2015
7443	6*10^111760+43	111761	Robert Price	07/2020
7444	98079!4-1024	111747	Robert Price	11/2019
7445	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
7446	10^(255862+1)-410^55862-1	111725	Robert Price	07/2023
7447	2^371098-113261	111712	Enzo Doria	07/2014
7448	(7*10^111706-61)/9	111706	Erik Branger	01/2011
7449	2^371044+1869391	111696	Enzo Doria	05/2016
7450	26310^17581+17581^26310	111688	Hans Havermann	01/2021
7451	88^57416+87	111645	Norbert Schneider	11/2015
7452	2^370829-109693	111631	Enzo Doria	04/2014
7453	15^94906-2	111619	Lelio R Paula	11/2013
7454	25835^20904+20904^25835	111614	Hans Havermann	02/2021
7455	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
7456	27758^10479+10479^27758	111597	Hans Havermann	02/2021
7457	2^370695-4627	111591	Yves Minet	05/2019
7458	7*10^111579-87	111580	Robert Price	06/2020
7459	2^370643-37	111575	Yves Minet	01/2012
7460	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
7461	2^370610-3911	111565	Yves Minet	04/2017
7462	(154*10^111549+17)/9	111551	Robert Price	06/2022
7463	26200^18097+18097^26200	111550	Hans Havermann	01/2021
7464	286^45405+45405^286	111532	Norbert Schneider	04/2015
7465	4*5^159563-9	111531	Lelio R Paula	11/2014
7466	5*10^111528-21	111529	Robert Price	12/2021
7467	(4^185225+23)/3	111517	Robert Price	10/2018
7468	2^370393-2797093	111500	Enzo Doria	03/2016
7469	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
7470	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
7471	6^143273-5	111489	Paul Bourdelais	01/2021
7472	2^370292-2791979	111469	Enzo Doria	03/2016
7473	(14*10^111443-11)/3	111444	Robert Price	08/2022
7474	2^370177-461551	111435	Enzo Doria	07/2015
7475	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
7476	109^54683-108	111413	Norbert Schneider	02/2017
7478	(83*10^111406-173)/9	111407	Robert Price	04/2021
7477	959^37362-37362^959	111407	Henri Lifchitz	10/2024
7479	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
7480	32961^2396+2396^32961	111392	Hans Havermann	10/2020
7481	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
7482	(19*10^111385+11)/3	111386	Robert Price	07/2023
7483	(23*10^111380-29)/3	111381	Robert Price	03/2022
7484	2^369974+733	111374	Lelio R Paula	05/2013
7485	121^53470+120	111367	Norbert Schneider	10/2018
7486	2^369915-286267	111356	Enzo Doria	07/2015
7487	(62*10^111347-629)/9	111348	Robert Price	07/2021
7488	2^369855-1615	111338	Lelio R Paula	05/2017
7489	(27^77783+5^77783)/32	111335	Robert Price	07/2026
7490	7*10^111325+3	111326	Robert Price	08/2015
7491	51^65176+2	111293	Lelio R Paula	08/2013
7492	Phi(43329,-43329)	111283	Henri Lifchitz	06/2025
7493	2^369643-1865767	111274	Enzo Doria	03/2016
7494	2^369603+885	111262	Lelio R Paula	05/2017
7495	25555^22564+22564^25555	111252	Hans Havermann	10/2020
7496	F(532391)/89441689/1425422598617	111243	Serge Batalov	07/2024
7497	L(532277)	111240	Renaud Lifchitz	03/2004
7498	105^55033-2	111233	Lelio R Paula	10/2017
7499	(35*10^111232-737)/9	111233	Robert Price	07/2018
7500	26970^13307+13307^26970	111227	Hans Havermann	10/2020

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Probable Primes Top 10000

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