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 ?
7001	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
7002	3^236011-8828	112606	Enzo Doria	05/2014
7003	31854^3427+3427^31854	112602	Hans Havermann	02/2021
7004	(85*10^112530-373)/9	112531	Robert Price	05/2021
7005	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
7006	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
7007	27618^11821+11821^27618	112479	Hans Havermann	01/2021
7008	U(602921)/4823369	112479	Serge Batalov	07/2024
7009	26343^18580+18580^26343	112460	Hans Havermann	01/2021
7010	39^70666+2	112435	Lelio R Paula	11/2013
7011	(134*10^112400+7)/3	112402	Robert Price	02/2020
7012	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
7013	(2^373350-7)/3	112390	Lelio R Paula	03/2014
7014	3^235532-235532	112378	Anonymous	09/2025
7015	2^373306-1840931	112377	Enzo Doria	06/2015
7016	8*10^112371-37	112372	Robert Price	03/2022
7017	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
7018	6*10^112359-79	112360	Robert Price	03/2022
7019	34409^1842+1842^34409	112356	Hans Havermann	02/2021
7020	(142*10^112352-7)/9	112354	Robert Price	12/2019
7021	25580^24633+24633^25580	112336	Hans Havermann	01/2021
7022	2^373117+1872107	112320	Enzo Doria	05/2016
7023	(2^373083+2226)/2	112309	Stefano Morozzi	01/2021
7024	(35*10^112308+37)/9	112309	Robert Price	05/2022
7025	27963^10376+10376^27963	112301	Hans Havermann	01/2021
7026	2^373040+2792761	112297	Enzo Doria	03/2016
7027	(156^51203-1)/155	112293	Anonymous	06/2024
7028	EPrime(112280)	112280	Eric W. Weisstein	10/2010
7029	2^372950+7	112270	Lelio R Paula	03/2013
7030	2^372945+1872167	112268	Enzo Doria	05/2016
7031	36274^1243+1243^36274	112249	Hans Havermann	02/2021
7032	(55*10^112246+629)/9	112247	Robert Price	01/2022
7033	(2^372872+3798)/2	112246	Stefano Morozzi	02/2021
7034	25513^25060+25060^25513	112232	Hans Havermann	02/2021
7035	(53*10^112229-611)/9	112230	Robert Price	02/2022
7036	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020
7037	6*10^112208+43	112209	Robert Price	07/2020
7038	(2^372728+3058)/2	112203	Stefano Morozzi	09/2020
7039	32061^3158+3158^32061	112195	Hans Havermann	02/2021
7040	2^372695+72113	112193	Enzo Doria	04/2016
7041	2^372689-2563	112191	Yves Minet	07/2014
7042	2^372638-1859441	112176	Enzo Doria	03/2016
7043	3^235074-113056	112159	Enzo Doria	07/2014
7044	-E(29242)/489848365125303139750087	112140	Thomas Ritschel	01/2021
7045	(2^372514+1822)/2	112138	Stefano Morozzi	02/2021
7046	29468^6387+6387^29468	112135	Hans Havermann	02/2021
7047	(2^372428+3742)/2	112112	Stefano Morozzi	01/2021
7048	25375^25454-25454^25375	112110	Norbert Schneider	01/2021
7049	131^52949-130	112108	Norbert Schneider	02/2019
7050	(91*10^112098-1)/9	112100	Robert Price	04/2015
7051	(68*10^112087-149)/9	112088	Robert Price	07/2022
7052	2^372314+212419	112078	Enzo Doria	08/2023
7053	2^372310-85061	112077	Paul Bourdelais	02/2012
7054	(10^112067+53)/9	112067	Serge Batalov	07/2015
7055	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
7056	75^59760+2	112054	Lelio R Paula	08/2013
7057	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
7058	(10^112048+7)/8747/373157	112039	Alfred Reich	06/2021
7059	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
7060	F(536233)/825798821/1102495049/5641839306317	112036	Serge Batalov	07/2024
7061	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
7062	8*10^112018-49	112019	Robert Price	08/2019
7064	2^372108+74221	112016	Enzo Doria	04/2016
7063	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
7065	8*10^112011-73	112012	Robert Price	01/2022
7066	(184*10^112007-1)/3	112009	Robert Price	02/2020
7067	5*10^112003+81	112004	Robert Price	03/2019
7068	215^48018+48018^215	112000	Norbert Schneider	10/2018
7069	25549^24148+24148^25549	111979	Hans Havermann	02/2021
7070	2^371970-459491	111975	Enzo Doria	05/2015
7071	41^69427-40^69427	111971	Robert Price	07/2012
7072	(20^86027+19^86027)/39	111923	Robert Price	09/2025
7073	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
7074	15*25^80056+446	111915	Eric Chen	10/2023
7075	(34*10^111902-547)/9	111903	Robert Price	03/2021
7076	(10^111902+71)/9	111902	Serge Batalov	07/2015
7077	((385283-70250)F(535399)-(85283-70250)*L(535399))/2	111897	Yaroslav Berezhko	09/2025
7078	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
7079	29080^7027+7027^29080	111865	Hans Havermann	01/2021
7080	31307^3730+3730^31307	111820	Hans Havermann	02/2021
7081	2^371440-112865	111815	Enzo Doria	06/2014
7082	2^371426-459161	111811	Enzo Doria	05/2015
7083	25768^21771+21771^25768	111779	Hans Havermann	02/2021
7084	28022^9747+9747^28022	111777	Hans Havermann	02/2021
7085	(94*10^111770+11)/3	111772	Robert Price	04/2020
7086	2^371276-461267	111766	Enzo Doria	07/2015
7087	6*10^111760+43	111761	Robert Price	07/2020
7088	98079!4-1024	111747	Robert Price	11/2019
7089	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
7090	10^(255862+1)-410^55862-1	111725	Robert Price	07/2023
7091	2^371098-113261	111712	Enzo Doria	07/2014
7092	(7*10^111706-61)/9	111706	Erik Branger	01/2011
7093	2^371044+1869391	111696	Enzo Doria	05/2016
7094	26310^17581+17581^26310	111688	Hans Havermann	01/2021
7095	88^57416+87	111645	Norbert Schneider	11/2015
7096	2^370829-109693	111631	Enzo Doria	04/2014
7097	15^94906-2	111619	Lelio R Paula	11/2013
7098	25835^20904+20904^25835	111614	Hans Havermann	02/2021
7099	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
7100	27758^10479+10479^27758	111597	Hans Havermann	02/2021
7101	2^370695-4627	111591	Yves Minet	05/2019
7102	7*10^111579-87	111580	Robert Price	06/2020
7103	2^370643-37	111575	Yves Minet	01/2012
7104	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
7105	2^370610-3911	111565	Yves Minet	04/2017
7106	(154*10^111549+17)/9	111551	Robert Price	06/2022
7107	26200^18097+18097^26200	111550	Hans Havermann	01/2021
7108	286^45405+45405^286	111532	Norbert Schneider	04/2015
7109	4*5^159563-9	111531	Lelio R Paula	11/2014
7110	5*10^111528-21	111529	Robert Price	12/2021
7111	(4^185225+23)/3	111517	Robert Price	10/2018
7112	2^370393-2797093	111500	Enzo Doria	03/2016
7113	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
7114	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
7115	6^143273-5	111489	Paul Bourdelais	01/2021
7116	2^370292-2791979	111469	Enzo Doria	03/2016
7117	(14*10^111443-11)/3	111444	Robert Price	08/2022
7118	2^370177-461551	111435	Enzo Doria	07/2015
7119	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
7120	109^54683-108	111413	Norbert Schneider	02/2017
7121	(83*10^111406-173)/9	111407	Robert Price	04/2021
7122	959^37362-37362^959	111407	Henri Lifchitz	10/2024
7123	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
7124	32961^2396+2396^32961	111392	Hans Havermann	10/2020
7125	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
7126	(19*10^111385+11)/3	111386	Robert Price	07/2023
7127	(23*10^111380-29)/3	111381	Robert Price	03/2022
7128	2^369974+733	111374	Lelio R Paula	05/2013
7129	121^53470+120	111367	Norbert Schneider	10/2018
7130	2^369915-286267	111356	Enzo Doria	07/2015
7131	(62*10^111347-629)/9	111348	Robert Price	07/2021
7132	2^369855-1615	111338	Lelio R Paula	05/2017
7133	7*10^111325+3	111326	Robert Price	08/2015
7134	51^65176+2	111293	Lelio R Paula	08/2013
7135	Phi(43329,-43329)	111283	Henri Lifchitz	06/2025
7136	2^369643-1865767	111274	Enzo Doria	03/2016
7137	2^369603+885	111262	Lelio R Paula	05/2017
7138	25555^22564+22564^25555	111252	Hans Havermann	10/2020
7139	F(532391)/89441689/1425422598617	111243	Serge Batalov	07/2024
7140	L(532277)	111240	Renaud Lifchitz	03/2004
7141	105^55033-2	111233	Lelio R Paula	10/2017
7142	(35*10^111232-737)/9	111233	Robert Price	07/2018
7143	26970^13307+13307^26970	111227	Hans Havermann	10/2020
7144	25419^23716+23716^25419	111210	Hans Havermann	10/2020
7145	(26^78593-3^78593)/23	111206	Robert Price	02/2025
7146	9*10^111201-29	111202	Robert Price	09/2019
7147	2^369392+29835	111199	Lelio R Paula	05/2017
7148	3^233059+16	111198	Robert Price	03/2020
7149	2^369354-3413	111187	Yves Minet	12/2016
7150	2^369296-27	111170	Lelio R Paula	02/2013
7151	(2468^40960+1)/(2468^8192+1)	111161	Martin Hopf	08/2024
7152	2^369239-109837	111153	Enzo Doria	05/2014
7153	2^369224-291839	111148	Enzo Doria	07/2015
7154	2^369216+2798881	111146	Enzo Doria	04/2016
7155	26842^13817+13817^26842	111137	Hans Havermann	11/2020
7156	(5*10^111119-191)/3	111120	Robert Price	05/2021
7157	(29*10^111112-23)/3	111113	Robert Price	03/2022
7158	10^111111+163849	111112	Patrick De Geest	03/2017
7159	10^111111-312911	111111	Patrick De Geest	03/2017
7160	2^369092-216923	111108	Enzo Doria	05/2014
7161	2^369081-55	111105	Lelio R Paula	02/2013
7162	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
7163	88^57124-87	111077	Norbert Schneider	11/2015
7164	2^368980+753	111075	Lelio R Paula	05/2013
7165	2^368946-3623	111064	Yves Minet	03/2017
7166	2^368929+29835	111059	Lelio R Paula	05/2017
7167	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
7168	111^54298+110	111057	Norbert Schneider	04/2017
7169	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
7170	(29*10^111020-41)/3	111021	Tyler Busby	03/2024
7171	35799^1262+1262^35799	111015	Hans Havermann	10/2020
7172	(298*10^111004+11)/3	111006	Robert Price	11/2020
7173	27648^10349+10349^27648	111004	Hans Havermann	11/2020
7174	28899^6932+6932^28899	110997	Hans Havermann	11/2020
7175	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
7176	2^368641-460303	110972	Enzo Doria	06/2015
7177	2^368619-109087	110966	Enzo Doria	04/2014
7178	(74*10^110961+313)/9	110962	Robert Price	06/2019
7179	25258^24711+24711^25258	110956	Hans Havermann	11/2020
7180	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
7181	3*2^368489+7	110927	Lelio R Paula	09/2014
7182	(14*10^110922+61)/3	110923	Robert Price	12/2018
7183	97411!4-2	110913	Robert Price	07/2017
7184	(301*10^110903+23)/9	110905	Robert Price	06/2021
7185	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
7186	25830^19619+19619^25830	110880	Hans Havermann	10/2020
7187	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
7188	26022^18191+18191^26022	110850	Hans Havermann	10/2020
7189	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
7190	(37*10^110813+251)/9	110814	Robert Price	09/2021
7191	2^368050-64875	110795	Lelio R Paula	05/2017
7192	2^368048+25	110794	Lelio R Paula	02/2013
7193	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
7194	69^60239-2	110771	Lelio R Paula	10/2013
7195	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
7196	2^367924-69	110757	Lelio R Paula	02/2013
7197	(23*10^110738+61)/3	110739	Robert Price	01/2022
7198	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
7199	2^367709-109723	110692	Enzo Doria	04/2014
7200	2^367687+213413	110685	Enzo Doria	09/2023
7201	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
7202	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
7203	(1288676*34^72242-455)/33	110642	Eric Chen	03/2023
7204	379*10^110616+9	110619	Jason Yuen	01/2025
7205	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
7206	140^51515-139	110558	Norbert Schneider	04/2019
7207	2^367215+1879223	110543	Enzo Doria	09/2016
7208	25782^19375+19375^25782	110534	Hans Havermann	10/2020
7209	26117^17058+17058^26117	110526	Hans Havermann	10/2020
7210	2^367141+41	110521	Lelio R Paula	02/2013
7211	2^367126+29835	110516	Lelio R Paula	05/2017
7212	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
7213	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
7214	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
7215	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
7216	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
7217	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
7218	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
7219	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020
7220	(10^110503-1)/9+510^99423+510^11079	110503	Makoto Morimoto	09/2020
7221	(10^110503-1)/9+7(10^23617-1)/910^43443	110503	Makoto Morimoto	09/2020
7222	(10^110503-1)/9+8(10^30251-1)/910^40126	110503	Makoto Morimoto	09/2020
7223	3(10^110503-1)/9+110^106036+1*10^4466	110503	Makoto Morimoto	09/2020
7224	3(10^110503-1)/9+110^58962+1*10^51540	110503	Makoto Morimoto	09/2020
7225	3(10^110503-1)/9+110^78213+1*10^32289	110503	Makoto Morimoto	09/2020
7226	3(10^110503-1)/9+210^76898+2*10^33604	110503	Makoto Morimoto	09/2020
7227	3(10^110503-1)/9-110^100802-1*10^9700	110503	Makoto Morimoto	09/2020
7228	3(10^110503-1)/9-110^76355-1*10^34147	110503	Makoto Morimoto	09/2020
7229	3(10^110503-1)/9-210^105704-2*10^4798	110503	Makoto Morimoto	09/2020
7230	7(10^110503-1)/9+1(10^27685-1)/9*10^41409	110503	Makoto Morimoto	09/2020
7231	7(10^110503-1)/9+1(10^91035-1)/9*10^9734	110503	Makoto Morimoto	09/2020
7232	7(10^110503-1)/9-1(10^23717-1)/9*10^43393	110503	Makoto Morimoto	09/2020
7233	7(10^110503-1)/9-110^57906-1*10^52596	110503	Makoto Morimoto	09/2020
7234	7(10^110503-1)/9-110^72287-1*10^38215	110503	Makoto Morimoto	09/2020
7235	7(10^110503-1)/9-2(10^53823-1)/9*10^28340	110503	Makoto Morimoto	09/2020
7236	7(10^110503-1)/9-2(10^88659-1)/9*10^10922	110503	Makoto Morimoto	09/2020
7237	7(10^110503-1)/9-3(10^79921-1)/9*10^15291	110503	Makoto Morimoto	09/2020
7238	7(10^110503-1)/9-310^60024-3*10^50478	110503	Makoto Morimoto	09/2020
7239	7(10^110503-1)/9-4(10^103091-1)/9*10^3706	110503	Makoto Morimoto	09/2020
7240	7(10^110503-1)/9-410^103658-4*10^6844	110503	Makoto Morimoto	09/2020
7241	7(10^110503-1)/9-410^78188-4*10^32314	110503	Makoto Morimoto	09/2020
7242	7(10^110503-1)/9-5(10^35035-1)/9*10^37734	110503	Makoto Morimoto	09/2020
7243	7(10^110503-1)/9-6(10^67347-1)/9*10^21578	110503	Makoto Morimoto	09/2020
7244	7(10^110503-1)/9-610^60391-6*10^50111	110503	Makoto Morimoto	09/2020
7245	(10^110503-1)-4(10^96247-1)/910^7128	110503	Makoto Morimoto	09/2020
7246	(10^110503-1)-410^74037-410^36465	110503	Makoto Morimoto	09/2020
7247	(10^110503-1)-410^77787-410^32715	110503	Makoto Morimoto	09/2020
7248	(10^110503-1)-410^91179-410^19323	110503	Makoto Morimoto	09/2020
7249	(10^110503-1)-5(10^99143-1)/910^5680	110503	Makoto Morimoto	09/2020
7250	(10^110503-1)-7(10^85075-1)/910^12714	110503	Makoto Morimoto	09/2020

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PRP Records

Probable Primes Top 10000

(302010 PRPs in the top)