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	2^351076-113159	105685	Enzo Doria	07/2014
7002	93^53688-2	105684	Lelio R Paula	09/2013
7003	2^351060-4559	105680	Yves Minet	07/2011
7004	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
7005	11^101473-750	105674	Enzo Doria	11/2012
7006	3*5^151181-8	105672	Lelio R Paula	11/2014
7007	15^89831-34	105650	Lelio R Paula	02/2017
7009	11^101448-360	105648	Enzo Doria	08/2012
7008	3*7^125011+4	105648	Lelio R Paula	11/2014
7010	2^350943-113269	105645	Enzo Doria	07/2014
7011	2*10^105636-91	105637	Robert Price	04/2020
7012	24231^22880+22880^24231	105634	Hans Havermann	09/2020
7013	35296^983+983^35296	105626	Hans Havermann	09/2020
7014	2^350868-19725	105622	Enzo Doria	06/2013
7015	2^350858-59291	105619	Enzo Doria	10/2015
7016	V(758484)/1516967/19720583	105618	Serge Batalov	07/2024
7017	2^350851+135	105617	Lelio R Paula	10/2011
7018	2^350841-741	105614	Lelio R Paula	01/2017
7019	3*10^105582+77	105583	Robert Price	09/2018
7020	24915^17284+17284^24915	105581	Hans Havermann	09/2020
7021	(5*10^105576-53)/3	105577	Robert Price	09/2020
7022	8*10^105571+3	105572	Robert Price	08/2015
7023	2^350674-78557	105564	Jorge Menendez	03/2018
7024	2*5^151026-3	105563	Lelio R Paula	11/2014
7025	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
7026	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
7027	3^221211+236	105545	Lelio R Paula	11/2016
7028	(32*10^105530-77)/9	105531	Robert Price	06/2018
7029	10^105515+33	105516	Lelio R Paula	11/2016
7030	24644^19125+19125^24644	105516	Hans Havermann	10/2020
7031	10^105515-41033	105515	Patrick De Geest	12/2016
7032	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
7033	2^350455-430567	105498	Harrison Mesh	06/2022
7034	17^85732-72	105489	Lelio R Paula	01/2017
7035	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
7036	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
7037	2^350356+24241	105468	Enzo Doria	10/2023
7038	25233^15118+15118^25233	105462	Hans Havermann	09/2020
7039	26261^10366+10366^26261	105454	Hans Havermann	09/2020
7040	2^350307-110329	105453	Enzo Doria	05/2014
7041	2^350253-20365	105437	Enzo Doria	06/2013
7042	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
7043	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
7044	4*10^105415-69	105416	Robert Price	01/2022
7045	21^79725-22	105414	Anonymous	09/2024
7046	(22*10^105407+179)/3	105408	Robert Price	02/2022
7047	2^350139-109009	105403	Enzo Doria	04/2014
7048	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
7049	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
7050	3*5^150763+4	105380	Lelio R Paula	11/2014
7051	12^97643+91	105375	Lelio R Paula	02/2017
7052	6*5^150744-7	105367	Lelio R Paula	11/2014
7053	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
7054	4*10^105364-39	105365	Robert Price	09/2020
7056	2^349996-112169	105360	Enzo Doria	06/2014
7055	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
7057	(418*10^105343+23)/9	105345	Robert Price	02/2020
7058	25490^13563+13563^25490	105334	Hans Havermann	10/2020
7059	11^101142-1080	105329	Enzo Doria	12/2012
7060	(68*10^105320-41)/9	105321	Robert Price	10/2013
7061	24800^17649+17649^24800	105319	Hans Havermann	09/2020
7062	3^220712-9934	105307	Enzo Doria	05/2014
7063	7*10^105296+9	105297	Robert Price	09/2015
7064	89*10^105284-7	105286	Robert Price	04/2020
7065	2^349739+1873373	105282	Enzo Doria	06/2016
7066	7^124574+24	105278	Lelio R Paula	11/2016
7067	2^349708-20957	105273	Enzo Doria	06/2013
7068	34115^1218+1218^34115	105267	Hans Havermann	09/2020
7069	24029^24029-24020^24020	105265	Henri Lifchitz	09/2024
7070	2^349649-20469	105255	Enzo Doria	06/2013
7071	2^349607-20109	105243	Enzo Doria	06/2013
7072	(85*10^105242+473)/9	105243	Robert Price	01/2020
7073	2^349594-19085	105239	Enzo Doria	05/2013
7074	2^349530+1874479	105220	Enzo Doria	06/2016
7075	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
7076	(106*10^105199+17)/3	105201	Robert Price	04/2021
7077	(2^349452+3570)/2	105196	Stefano Morozzi	09/2020
7078	3^220464-112852	105189	Enzo Doria	07/2014
7079	2^349419-17349	105186	Enzo Doria	05/2013
7080	2^349400-2579	105180	Yves Minet	07/2014
7081	8*5^150471+3	105176	Lelio R Paula	11/2014
7082	(2^349359+2298)/2	105168	Stefano Morozzi	02/2021
7083	655^37342+37342^655	105165	Norbert Schneider	08/2018
7084	13^94403+94	105160	Lelio R Paula	12/2016
7085	2^349301-112309	105151	Enzo Doria	06/2014
7086	30291^2960+2960^30291	105149	Hans Havermann	09/2020
7087	27350^6981+6981^27350	105132	Hans Havermann	09/2020
7089	9*2^349220+5	105127	Lelio R Paula	09/2014
7088	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
7090	7*3^220317+8	105119	Lelio R Paula	09/2014
7091	7^124386+88	105119	Lelio R Paula	11/2016
7092	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
7093	2^349171-19657	105111	Enzo Doria	06/2013
7094	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
7095	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
7096	(2^349111-5)/3	105093	Lelio R Paula	12/2013
7097	675^37142+37142^675	105087	Norbert Schneider	08/2018
7098	2^348981-2797573	105054	Enzo Doria	04/2016
7099	(445^39667+1)/446	105050	Jinyuan Wang	05/2024
7100	2^348869-6555	105021	Lelio R Paula	01/2017
7101	10^105003-17319	105003	Alfred Reich	08/2024
7102	5^150217+78	104998	Lelio R Paula	11/2016
7103	(88*10^104989-1)/3	104991	Robert Price	04/2020
7104	(28*10^104972+149)/3	104973	Robert Price	12/2019
7105	24927^16262+16262^24927	104972	Hans Havermann	10/2020
7106	2^348703-113005	104971	Enzo Doria	06/2014
7107	(191*10^104956-17)/3	104958	Robert Price	11/2021
7108	2^348612-809	104943	Yves Minet	05/2013
7109	(73*10^104942-1)/9	104943	Robert Price	01/2015
7110	2^348583-350407	104934	Enzo Doria	06/2015
7111	2^348531-949	104919	Yves Minet	05/2012
7112	20^80636-59	104910	Lelio R Paula	12/2016
7113	8*10^104893-13	104894	Robert Price	08/2019
7115	2^348437+35	104890	Lelio R Paula	09/2011
7114	25208^14487+14487^25208	104890	Hans Havermann	09/2020
7116	2^348348+135	104864	Lelio R Paula	09/2011
7117	(29*10^104858+349)/9	104859	Robert Price	06/2021
7118	6*10^104852-31	104853	Robert Price	07/2020
7120	(2^348284+9)/25	104843	Lelio R Paula	12/2013
7119	75^55914-74	104843	Norbert Schneider	01/2015
7121	2^348268+255255	104840	Lelio R Paula	01/2017
7122	35540^891+891^35540	104839	Hans Havermann	09/2020
7123	5^149985-52	104836	Lelio R Paula	11/2016
7124	2^348224-20249	104826	Enzo Doria	06/2013
7125	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
7126	2^348212-20105	104823	Enzo Doria	06/2013
7127	24647^17898+17898^24647	104819	Hans Havermann	10/2020
7128	20^80562+19	104814	Lelio R Paula	12/2016
7129	2*10^104811-87	104812	Robert Price	04/2018
7130	2^348149-20053	104804	Enzo Doria	06/2013
7131	2^348095-171	104788	Lelio R Paula	09/2011
7132	25383^13412+13412^25383	104769	Hans Havermann	09/2020
7133	2^348003-20377	104760	Enzo Doria	06/2013
7134	26^74036-27	104759	Anonymous	09/2024
7136	2^347994-741	104757	Lelio R Paula	12/2016
7135	(2^347993+2234)/2	104757	Stefano Morozzi	01/2021
7137	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
7138	25137^14702+14702^25137	104756	Hans Havermann	09/2020
7139	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
7140	12883^25484-25484^12883	104740	Norbert Schneider	08/2022
7141	2^347910-109937	104732	Enzo Doria	04/2014
7142	(88*10^104709-637)/9	104710	Robert Price	11/2020
7143	(13*10^104702+71)/3	104703	Robert Price	06/2021
7144	5^149794+28	104702	Lelio R Paula	11/2016
7145	105^51800-2	104698	Lelio R Paula	10/2017
7146	(16^86939+3^86939)/19	104684	Robert Price	06/2013
7147	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
7148	2^347731-18609	104678	Enzo Doria	05/2013
7149	4*6^134519+7	104677	Lelio R Paula	11/2014
7150	(34*10^104672-259)/9	104673	Robert Price	12/2021
7151	25321^13588+13588^25321	104656	Hans Havermann	09/2020
7152	2^347625+5367	104646	Riley Fisher	04/2023
7153	2^347612-18545	104642	Enzo Doria	05/2013
7154	6^134465+95	104635	Lelio R Paula	11/2016
7156	(2^347588+3718)/2	104635	Stefano Morozzi	09/2020
7155	(166*10^104633-7)/3	104635	Robert Price	11/2020
7157	V(750972)/15019441	104621	Serge Batalov	07/2024
7158	2^347517-17301	104614	Enzo Doria	05/2013
7159	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
7160	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
7161	3^219222-310	104596	Lelio R Paula	11/2016
7162	25993^10554+10554^25993	104581	Hans Havermann	09/2020
7163	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
7164	2^347372-17853	104570	Enzo Doria	05/2013
7165	2^347314+99	104552	Lelio R Paula	09/2011
7166	2^347300-22233	104548	Enzo Doria	06/2013
7167	2^347287-19845	104544	Enzo Doria	06/2013
7168	2^347258-231191	104536	Harrison Mesh	06/2022
7169	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
7170	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
7171	7*2^347239-3	104531	Lelio R Paula	09/2014
7172	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
7173	5*3^219047+8	104513	Lelio R Paula	09/2014
7174	2^347148-109073	104502	Enzo Doria	04/2014
7175	2^347129-20145	104497	Enzo Doria	06/2013
7176	4*10^104461-57	104462	Robert Price	10/2018
7177	(710^(252227+1)+9*10^52227-7)/9	104455	Robert Price	10/2023
7178	(2^346989+590)/2	104454	Stefano Morozzi	09/2020
7179	2^346923-19585	104435	Enzo Doria	05/2013
7180	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
7181	2^346854+346854^2+1	104414	Robert Price	06/2014
7182	2^346834+11715	104408	Lelio R Paula	04/2015
7183	24276^19961+19961^24276	104392	Hans Havermann	09/2020
7184	79^55009+78	104387	Norbert Schneider	02/2015
7185	3^218744+58	104368	Lelio R Paula	11/2016
7186	9*10^104361+89	104362	Robert Price	11/2019
7187	25048^14665+14665^25048	104358	Hans Havermann	09/2020
7188	2^346649+65	104352	Lelio R Paula	09/2011
7189	(19*33^68718-600883)/32	104350	Eric Chen	05/2023
7190	2^346638-17265	104349	Enzo Doria	05/2013
7191	(2^346606+2082)/2	104339	Stefano Morozzi	09/2020
7192	(2^346607+2070)/2	104339	Stefano Morozzi	09/2020
7193	(2^346582+3202)/2	104332	Stefano Morozzi	09/2020
7194	26092^9967+9967^26092	104331	Hans Havermann	09/2020
7195	5*10^104326+77	104327	Robert Price	12/2018
7196	(2^346564+2026)/2	104326	Stefano Morozzi	09/2020
7197	(8925^26569-1)/(8925^163-1)	104320	Ryan Propper	11/2023
7200	2^346527-111817	104316	Enzo Doria	05/2014
7199	6^134055+101	104316	Lelio R Paula	11/2016
7198	fibonacci(499147)-4	104316	Jon Grantham	08/2023
7201	92105!4+8	104312	Robert Price	09/2019
7202	(7^123407-5^123407)/2	104291	Jon Grantham	08/2023
7203	6^134013+163	104283	Lelio R Paula	11/2016
7204	10^(2*52140+1)-10^52140-1	104281	Robert Price	07/2023
7205	(22*10^104272-61)/3	104273	Robert Price	03/2022
7206	(2^346318+862)/2	104252	Stefano Morozzi	02/2021
7208	18^83049-89	104250	Lelio R Paula	01/2017
7207	(2^346311+606)/2	104250	Stefano Morozzi	09/2020
7209	(166*10^104230+11)/3	104232	Robert Price	03/2021
7210	2^346213+484049	104221	Enzo Doria	04/2017
7211	18^83021-91	104214	Lelio R Paula	01/2017
7212	10^104212+128779	104213	Patrick De Geest	05/2016
7213	10^104212+237447	104213	Patrick De Geest	05/2016
7214	10^104212+242139	104213	Patrick De Geest	05/2016
7215	10^104212+269199	104213	Patrick De Geest	05/2016
7216	24254^19803+19803^24254	104213	Hans Havermann	09/2020
7217	(10^104212-71)/1	104212	Serge Batalov	12/2014
7218	23678^23821-23821^23678	104202	Norbert Schneider	01/2020
7219	(13*31^69863+12407)/30	104191	Eric Chen	04/2024
7220	2^346078+7695	104180	Lelio R Paula	12/2016
7221	2^346055-19537	104173	Enzo Doria	05/2013
7222	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
7223	2^346037-20125	104168	Enzo Doria	06/2013
7224	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
7225	6^133854-17993	104159	Enzo Doria	03/2013
7226	2^345990+1874239	104154	Enzo Doria	06/2016
7227	2^345988-20373	104153	Enzo Doria	06/2013
7228	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
7229	(26*10^104132-503)/9	104133	Robert Price	07/2018
7230	3*5^148968+8	104125	Lelio R Paula	11/2014
7231	(7*10^104113+53)/3	104114	Robert Price	05/2018
7232	p(21253)#/2+8	104113	Robert Price	01/2017
7233	33582^1259+1259^33582	104106	Hans Havermann	09/2020
7234	32958^1441+1441^32958	104104	Hans Havermann	09/2020
7235	29127^3748+3748^29127	104095	Hans Havermann	09/2020
7236	322^41507+41507^322	104094	Norbert Schneider	12/2014
7237	6^133768-17423	104092	Enzo Doria	03/2013
7238	2^345786-19557	104092	Enzo Doria	05/2013
7240	171^46606-2	104072	Lelio R Paula	10/2017
7239	(29*10^104071+91)/3	104072	Robert Price	04/2020
7241	norm(Mod(x,x^3-x-1)^852167-1)	104070	Paul Vanderveen	09/2022
7242	2^345704-149	104068	Lelio R Paula	09/2011
7243	25821^10712+10712^25821	104056	Hans Havermann	09/2020
7244	(2^345662+2038)/2	104055	Stefano Morozzi	09/2020
7245	6^133704-17273	104042	Enzo Doria	02/2013
7246	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
7247	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
7248	2^345547+11	104021	Lelio R Paula	09/2011
7249	(19*10^104014-49)/3	104015	Robert Price	05/2019
7250	(2^345519+1794)/2	104012	Stefano Morozzi	01/2021

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