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	37258^1091+1091^37258	113184	Hans Havermann	02/2021
7252	(94*10^113176+11)/3	113178	Robert Price	04/2020
7253	(46*10^113162+521)/9	113163	Robert Price	02/2019
7254	14*29^77375+17875	113155	Eric Chen	06/2025
7255	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
7256	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
7257	3*10^113137+23	113138	Robert Price	03/2022
7258	(8*10^113135-269)/9	113135	Robert Price	09/2021
7259	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
7260	26050^21959+21959^26050	113100	Hans Havermann	02/2021
7261	2^375638-1787171	113079	Enzo Doria	03/2016
7262	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
7263	2^375537+4847	113048	Yves Minet	02/2011
7264	(17^91837+16^91837)/33	113000	Robert Price	08/2013
7265	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
7266	2^375350-3221	112992	Yves Minet	07/2011
7267	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
7268	2^375305+76757	112979	Enzo Doria	05/2016
7269	2^375258+1874989	112964	Enzo Doria	07/2016
7270	(29^77237-1)/28	112950	Robert Price	04/2012
7271	26620^17483+17483^26620	112939	Hans Havermann	01/2021
7272	2^375154+74959	112933	Enzo Doria	04/2016
7273	(266*10^112930-17)/3	112932	Robert Price	07/2020
7274	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
7275	(85*10^112919+293)/9	112920	Robert Price	12/2019
7276	29412^6899+6899^29412	112907	Hans Havermann	02/2021
7277	(191*10^112903-17)/3	112905	Robert Price	11/2021
7278	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
7279	25992^22039+22039^25992	112889	Hans Havermann	02/2021
7280	2^374993-2787163	112885	Enzo Doria	11/2015
7281	(697*10^112869+23)/9	112871	Robert Price	04/2021
7282	(19*10^112851+377)/9	112852	Alfred Reich	11/2022
7283	30420^5111+5111^30420	112813	Hans Havermann	02/2021
7284	13699^27268+27268^13699	112800	Norbert Schneider	12/2020
7285	123^53970+2	112793	Lelio R Paula	06/2013
7286	12308*27^78796+23	112790	Eric Chen	07/2023
7287	28942^7887+7887^28942	112785	Hans Havermann	01/2021
7288	2^374640-4685	112778	Yves Minet	05/2019
7289	12^104501-11	112776	Riley Fisher	12/2023
7290	57290^93+93^57290	112775	Hans Havermann	01/2021
7291	115^54726-54726^115	112774	Norman Luhn	09/2024
7292	13608^27277-27277^13608	112758	Norbert Schneider	12/2022
7293	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
7294	p(22852)#/2+512	112745	Robert Price	05/2017
7295	(11*10^112742-131)/3	112743	Robert Price	09/2018
7296	2^374441-21049	112718	Enzo Doria	06/2013
7297	(15056!^2+1)/(30113*454287444157)	112711	Michael Porter	09/2025
7298	4*10^112706-93	112707	Robert Price	07/2020
7300	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
7299	Phi(374321,-2)	112682	Henri Lifchitz	12/2025
7301	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
7302	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
7303	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
7304	3^236011-8828	112606	Enzo Doria	05/2014
7305	31854^3427+3427^31854	112602	Hans Havermann	02/2021
7306	2569^33013-2568^33013	112567	Norbert Schneider	01/2026
7307	Phi(442141,-2)	112561	Henri Lifchitz	12/2025
7308	(85*10^112530-373)/9	112531	Robert Price	05/2021
7309	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
7310	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
7311	27618^11821+11821^27618	112479	Hans Havermann	01/2021
7312	U(602921)/4823369	112479	Serge Batalov	07/2024
7313	26343^18580+18580^26343	112460	Hans Havermann	01/2021
7314	39^70666+2	112435	Lelio R Paula	11/2013
7315	(134*10^112400+7)/3	112402	Robert Price	02/2020
7316	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
7317	(2^373350-7)/3	112390	Lelio R Paula	03/2014
7318	3^235532-235532	112378	Anonymous	09/2025
7319	2^373306-1840931	112377	Enzo Doria	06/2015
7320	8*10^112371-37	112372	Robert Price	03/2022
7321	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
7322	6*10^112359-79	112360	Robert Price	03/2022
7323	34409^1842+1842^34409	112356	Hans Havermann	02/2021
7324	(142*10^112352-7)/9	112354	Robert Price	12/2019
7325	25580^24633+24633^25580	112336	Hans Havermann	01/2021
7326	2^373117+1872107	112320	Enzo Doria	05/2016
7327	(2^373083+2226)/2	112309	Stefano Morozzi	01/2021
7328	(35*10^112308+37)/9	112309	Robert Price	05/2022
7329	27963^10376+10376^27963	112301	Hans Havermann	01/2021
7330	2^373040+2792761	112297	Enzo Doria	03/2016
7331	(156^51203-1)/155	112293	Anonymous	06/2024
7332	EPrime(112280)	112280	Eric W. Weisstein	10/2010
7333	2^372950+7	112270	Lelio R Paula	03/2013
7334	2^372945+1872167	112268	Enzo Doria	05/2016
7335	36274^1243+1243^36274	112249	Hans Havermann	02/2021
7336	(55*10^112246+629)/9	112247	Robert Price	01/2022
7337	(2^372872+3798)/2	112246	Stefano Morozzi	02/2021
7338	25513^25060+25060^25513	112232	Hans Havermann	02/2021
7339	(53*10^112229-611)/9	112230	Robert Price	02/2022
7340	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020
7341	6*10^112208+43	112209	Robert Price	07/2020
7342	(2^372728+3058)/2	112203	Stefano Morozzi	09/2020
7343	32061^3158+3158^32061	112195	Hans Havermann	02/2021
7344	2^372695+72113	112193	Enzo Doria	04/2016
7345	2^372689-2563	112191	Yves Minet	07/2014
7346	2^372638-1859441	112176	Enzo Doria	03/2016
7347	3^235074-113056	112159	Enzo Doria	07/2014
7348	-E(29242)/489848365125303139750087	112140	Thomas Ritschel	01/2021
7349	(2^372514+1822)/2	112138	Stefano Morozzi	02/2021
7350	29468^6387+6387^29468	112135	Hans Havermann	02/2021
7351	(2^372428+3742)/2	112112	Stefano Morozzi	01/2021
7352	25375^25454-25454^25375	112110	Norbert Schneider	01/2021
7353	131^52949-130	112108	Norbert Schneider	02/2019
7354	(91*10^112098-1)/9	112100	Robert Price	04/2015
7355	(68*10^112087-149)/9	112088	Robert Price	07/2022
7356	2^372314+212419	112078	Enzo Doria	08/2023
7357	2^372310-85061	112077	Paul Bourdelais	02/2012
7358	(10^112067+53)/9	112067	Serge Batalov	07/2015
7359	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
7360	75^59760+2	112054	Lelio R Paula	08/2013
7361	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
7362	(10^112048+7)/8747/373157	112039	Alfred Reich	06/2021
7363	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
7364	F(536233)/825798821/1102495049/5641839306317	112036	Serge Batalov	07/2024
7365	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
7366	8*10^112018-49	112019	Robert Price	08/2019
7368	2^372108+74221	112016	Enzo Doria	04/2016
7367	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
7369	8*10^112011-73	112012	Robert Price	01/2022
7370	(184*10^112007-1)/3	112009	Robert Price	02/2020
7371	5*10^112003+81	112004	Robert Price	03/2019
7372	215^48018+48018^215	112000	Norbert Schneider	10/2018
7373	Phi(82303,5#)	111990	Henri Lifchitz	12/2025
7374	25549^24148+24148^25549	111979	Hans Havermann	02/2021
7375	2^371970-459491	111975	Enzo Doria	05/2015
7376	41^69427-40^69427	111971	Robert Price	07/2012
7377	(20^86027+19^86027)/39	111923	Robert Price	09/2025
7378	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
7379	15*25^80056+446	111915	Eric Chen	10/2023
7380	(34*10^111902-547)/9	111903	Robert Price	03/2021
7381	(10^111902+71)/9	111902	Serge Batalov	07/2015
7382	((385283-70250)F(535399)-(85283-70250)*L(535399))/2	111897	Yaroslav Berezhko	09/2025
7383	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
7384	29080^7027+7027^29080	111865	Hans Havermann	01/2021
7385	3^234408+531440	111842	Alfred Reich	03/2026
7386	31307^3730+3730^31307	111820	Hans Havermann	02/2021
7387	2^371440-112865	111815	Enzo Doria	06/2014
7388	2^371426-459161	111811	Enzo Doria	05/2015
7389	25768^21771+21771^25768	111779	Hans Havermann	02/2021
7390	28022^9747+9747^28022	111777	Hans Havermann	02/2021
7391	(94*10^111770+11)/3	111772	Robert Price	04/2020
7392	2^371276-461267	111766	Enzo Doria	07/2015
7393	6*10^111760+43	111761	Robert Price	07/2020
7394	98079!4-1024	111747	Robert Price	11/2019
7395	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
7396	10^(255862+1)-410^55862-1	111725	Robert Price	07/2023
7397	2^371098-113261	111712	Enzo Doria	07/2014
7398	(7*10^111706-61)/9	111706	Erik Branger	01/2011
7399	2^371044+1869391	111696	Enzo Doria	05/2016
7400	26310^17581+17581^26310	111688	Hans Havermann	01/2021
7401	88^57416+87	111645	Norbert Schneider	11/2015
7402	2^370829-109693	111631	Enzo Doria	04/2014
7403	15^94906-2	111619	Lelio R Paula	11/2013
7404	25835^20904+20904^25835	111614	Hans Havermann	02/2021
7405	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
7406	27758^10479+10479^27758	111597	Hans Havermann	02/2021
7407	2^370695-4627	111591	Yves Minet	05/2019
7408	7*10^111579-87	111580	Robert Price	06/2020
7409	2^370643-37	111575	Yves Minet	01/2012
7410	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
7411	2^370610-3911	111565	Yves Minet	04/2017
7412	(154*10^111549+17)/9	111551	Robert Price	06/2022
7413	26200^18097+18097^26200	111550	Hans Havermann	01/2021
7414	286^45405+45405^286	111532	Norbert Schneider	04/2015
7415	4*5^159563-9	111531	Lelio R Paula	11/2014
7416	5*10^111528-21	111529	Robert Price	12/2021
7417	(4^185225+23)/3	111517	Robert Price	10/2018
7418	2^370393-2797093	111500	Enzo Doria	03/2016
7419	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
7420	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
7421	6^143273-5	111489	Paul Bourdelais	01/2021
7422	2^370292-2791979	111469	Enzo Doria	03/2016
7423	(14*10^111443-11)/3	111444	Robert Price	08/2022
7424	2^370177-461551	111435	Enzo Doria	07/2015
7425	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
7426	109^54683-108	111413	Norbert Schneider	02/2017
7428	(83*10^111406-173)/9	111407	Robert Price	04/2021
7427	959^37362-37362^959	111407	Henri Lifchitz	10/2024
7429	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
7430	32961^2396+2396^32961	111392	Hans Havermann	10/2020
7431	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
7432	(19*10^111385+11)/3	111386	Robert Price	07/2023
7433	(23*10^111380-29)/3	111381	Robert Price	03/2022
7434	2^369974+733	111374	Lelio R Paula	05/2013
7435	121^53470+120	111367	Norbert Schneider	10/2018
7436	2^369915-286267	111356	Enzo Doria	07/2015
7437	(62*10^111347-629)/9	111348	Robert Price	07/2021
7438	2^369855-1615	111338	Lelio R Paula	05/2017
7439	7*10^111325+3	111326	Robert Price	08/2015
7440	51^65176+2	111293	Lelio R Paula	08/2013
7441	Phi(43329,-43329)	111283	Henri Lifchitz	06/2025
7442	2^369643-1865767	111274	Enzo Doria	03/2016
7443	2^369603+885	111262	Lelio R Paula	05/2017
7444	25555^22564+22564^25555	111252	Hans Havermann	10/2020
7445	F(532391)/89441689/1425422598617	111243	Serge Batalov	07/2024
7446	L(532277)	111240	Renaud Lifchitz	03/2004
7447	105^55033-2	111233	Lelio R Paula	10/2017
7448	(35*10^111232-737)/9	111233	Robert Price	07/2018
7449	26970^13307+13307^26970	111227	Hans Havermann	10/2020
7450	25419^23716+23716^25419	111210	Hans Havermann	10/2020
7451	(26^78593-3^78593)/23	111206	Robert Price	02/2025
7452	9*10^111201-29	111202	Robert Price	09/2019
7453	2^369392+29835	111199	Lelio R Paula	05/2017
7454	3^233059+16	111198	Robert Price	03/2020
7455	2^369354-3413	111187	Yves Minet	12/2016
7456	2^369296-27	111170	Lelio R Paula	02/2013
7457	(2468^40960+1)/(2468^8192+1)	111161	Martin Hopf	08/2024
7458	2^369239-109837	111153	Enzo Doria	05/2014
7459	2^369224-291839	111148	Enzo Doria	07/2015
7460	2^369216+2798881	111146	Enzo Doria	04/2016
7461	26842^13817+13817^26842	111137	Hans Havermann	11/2020
7462	(5*10^111119-191)/3	111120	Robert Price	05/2021
7463	(29*10^111112-23)/3	111113	Robert Price	03/2022
7464	10^111111+163849	111112	Patrick De Geest	03/2017
7465	10^111111-312911	111111	Patrick De Geest	03/2017
7466	2^369092-216923	111108	Enzo Doria	05/2014
7467	2^369081-55	111105	Lelio R Paula	02/2013
7468	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
7469	88^57124-87	111077	Norbert Schneider	11/2015
7470	2^368980+753	111075	Lelio R Paula	05/2013
7471	2^368946-3623	111064	Yves Minet	03/2017
7472	2^368929+29835	111059	Lelio R Paula	05/2017
7473	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
7474	111^54298+110	111057	Norbert Schneider	04/2017
7475	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
7476	(29*10^111020-41)/3	111021	Tyler Busby	03/2024
7477	35799^1262+1262^35799	111015	Hans Havermann	10/2020
7478	(298*10^111004+11)/3	111006	Robert Price	11/2020
7479	27648^10349+10349^27648	111004	Hans Havermann	11/2020
7480	28899^6932+6932^28899	110997	Hans Havermann	11/2020
7481	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
7482	2^368641-460303	110972	Enzo Doria	06/2015
7483	2^368619-109087	110966	Enzo Doria	04/2014
7484	(74*10^110961+313)/9	110962	Robert Price	06/2019
7485	25258^24711+24711^25258	110956	Hans Havermann	11/2020
7486	2^368550+1125899906842623	110945	Alfred Reich	05/2026
7487	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
7488	3*2^368489+7	110927	Lelio R Paula	09/2014
7489	(14*10^110922+61)/3	110923	Robert Price	12/2018
7490	97411!4-2	110913	Robert Price	07/2017
7491	(301*10^110903+23)/9	110905	Robert Price	06/2021
7492	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
7493	25830^19619+19619^25830	110880	Hans Havermann	10/2020
7494	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
7495	Phi(119761,10)/85476950837250449	110864	Anonymous	01/2026
7496	26022^18191+18191^26022	110850	Hans Havermann	10/2020
7497	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
7498	(37*10^110813+251)/9	110814	Robert Price	09/2021
7499	2^368050-64875	110795	Lelio R Paula	05/2017
7500	2^368048+25	110794	Lelio R Paula	02/2013

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