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	10^100978-156437	100978	Patrick De Geest	11/2016
7002	(2^335422+3114)/2	100972	Stefano Morozzi	09/2020
7003	(35*10^100970-89)/9	100971	Robert Price	02/2022
7004	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
7005	2^335403-1859167	100967	Enzo Doria	03/2016
7006	23599^18976+18976^23599	100962	Hans Havermann	10/2018
7007	6*10^100958+43	100959	Robert Price	07/2020
7008	9*2^335364-5	100956	Lelio R Paula	08/2014
7009	(7998^25867-1)/7997	100955	Serge Batalov	06/2022
7010	2^335349+72287	100951	Enzo Doria	04/2016
7011	2^335329+16095	100945	Lelio R Paula	09/2016
7012	232823#+233663	100937	Makoto Morimoto	10/2017
7013	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
7014	2^335237-20893	100917	Enzo Doria	06/2013
7015	2^335222-19337	100912	Enzo Doria	05/2013
7016	2^335222-109985	100912	Enzo Doria	04/2014
7017	2^335182-17237	100900	Enzo Doria	05/2013
7018	(2^335107+1634)/2	100877	Stefano Morozzi	09/2020
7019	2^335043-16737	100858	Enzo Doria	05/2013
7020	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
7021	2^335038-20633	100857	Enzo Doria	06/2013
7022	2^335031+1873373	100855	Enzo Doria	06/2016
7023	23489^19650+19650^23489	100847	Hans Havermann	10/2018
7024	3^211354-8816	100842	Enzo Doria	05/2014
7025	2^334984-112757	100841	Enzo Doria	06/2014
7026	(746*10^100827+1)/9	100829	Robert Price	03/2020
7027	29451^2648+2648^29451	100809	Hans Havermann	09/2018
7028	25583^8716+8716^25583	100806	Hans Havermann	08/2018
7030	2^334857+48527	100803	Lelio R Paula	08/2011
7029	12^93406+29	100803	Lelio R Paula	10/2016
7031	28780^3179+3179^28780	100796	Hans Havermann	09/2018
7032	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
7033	(328^40063-1)/327	100791	Serge Batalov	06/2022
7034	2^334809-13	100788	Lelio R Paula	04/2011
7035	(3552^28387-1)/3551	100784	Serge Batalov	06/2022
7036	(82*10^100780-1)/9	100781	Robert Price	12/2014
7037	31395^1622+1622^31395	100780	Hans Havermann	09/2018
7038	(2^334779+47)/5	100778	Lelio R Paula	12/2013
7039	2^334751+2049	100771	Lelio R Paula	09/2016
7040	13^90443-98	100749	Lelio R Paula	10/2016
7041	(2^334674+3190)/2	100747	Stefano Morozzi	09/2020
7042	(2^334651+1050)/2	100740	Stefano Morozzi	09/2020
7043	(7*10^100737+71)/3	100738	Robert Price	05/2018
7044	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
7045	15^85639-28	100720	Lelio R Paula	10/2016
7046	27068^5259+5259^27068	100718	Hans Havermann	08/2018
7047	2^334562+577294575	100711	Lelio R Paula	09/2016
7048	4*3^211077-5	100710	Lelio R Paula	08/2014
7049	2^334524+145	100702	Lelio R Paula	07/2009
7050	(2^334451+714)/2	100680	Stefano Morozzi	09/2020
7051	27648^4375+4375^27648	100666	Hans Havermann	09/2018
7052	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
7053	(2^334309+3122)/2	100637	Stefano Morozzi	09/2020
7054	2^334294-113111	100633	Enzo Doria	07/2014
7055	25581^8582+8582^25581	100626	Hans Havermann	08/2018
7056	6^129308-17723	100622	Enzo Doria	03/2013
7057	6^129305+95	100619	Lelio R Paula	10/2016
7058	2^334244-1167	100618	Lelio R Paula	09/2016
7059	(2^334233+3066)/2	100614	Stefano Morozzi	09/2020
7060	(76*10^100611+77)/9	100612	Robert Price	10/2019
7061	7*10^100606-93	100607	Robert Price	08/2020
7062	(26*10^100566+49)/3	100567	Robert Price	08/2019
7063	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
7064	24885^10984+10984^24885	100555	Hans Havermann	07/2018
7065	(1351^32119-1)/1350	100551	Serge Batalov	06/2022
7066	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
7067	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
7068	23578^18367+18367^23578	100538	Hans Havermann	07/2018
7069	13^90251+24	100535	Lelio R Paula	10/2016
7070	2^333963+789	100533	Lelio R Paula	08/2011
7071	2^333919-1840087	100520	Enzo Doria	06/2015
7072	(2^333916+1698)/2	100519	Stefano Morozzi	09/2020
7073	2^333911+72623	100518	Enzo Doria	04/2016
7074	24605^12168+12168^24605	100517	Hans Havermann	08/2018
7075	66*10^100502+7	100504	Robert Price	07/2020
7076	18^80064-67	100503	Lelio R Paula	10/2016
7077	(13*10^100487+137)/3	100488	Robert Price	06/2021
7078	5^143742-48	100472	Lelio R Paula	10/2016
7079	24095^14784+14784^24095	100472	Hans Havermann	08/2018
7080	2^333757-112123	100471	Enzo Doria	06/2014
7081	(7953^25759-1)/7952	100470	Serge Batalov	06/2022
7082	7*10^100457-57	100458	Robert Price	06/2020
7083	27358^4693+4693^27358	100444	Hans Havermann	07/2018
7084	8*10^100439-51	100440	Robert Price	08/2019
7085	2^333603-108861	100425	Enzo Doria	03/2014
7086	9*7^118818-2	100414	Lelio R Paula	11/2014
7087	2^333546-17097	100408	Enzo Doria	05/2013
7088	17^81597+72	100401	Lelio R Paula	10/2016
7089	(3613^28219-1)/3612	100396	Serge Batalov	06/2022
7090	p(20559)#/2+8	100384	Robert Price	01/2017
7091	11^96390-24	100380	Lelio R Paula	10/2016
7092	(2^333385+2730)/2	100359	Stefano Morozzi	09/2020
7093	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
7094	23565^18136+18136^23565	100353	Hans Havermann	07/2018
7095	2^333354+763	100350	Lelio R Paula	08/2011
7096	(25*10^100343-67)/3	100344	Robert Price	06/2019
7097	2^333289-109483	100330	Enzo Doria	04/2014
7098	2^333240-2790209	100316	Enzo Doria	03/2016
7099	23601^17798+17798^23601	100314	Hans Havermann	05/2018
7101	(2^333227-2^166614+1)/5	100311		11/2006
7100	2^333225+719	100311	Lelio R Paula	08/2011
7102	2^333221-2785333	100310	Enzo Doria	10/2015
7103	76^53332-75	100308	Norbert Schneider	02/2015
7104	(29*10^100302+583)/9	100303	Robert Price	06/2021
7105	6^128892-17573	100298	Enzo Doria	03/2013
7106	(47*10^100283-119)/9	100284	Robert Price	05/2019
7107	2^333105-113215	100275	Enzo Doria	07/2014
7108	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
7109	4*10^100257-83	100258	Robert Price	10/2018
7110	17^81476-74	100253	Lelio R Paula	10/2016
7111	23392^19207+19207^23392	100199	Hans Havermann	06/2018
7112	(2^332830+750)/2	100192	Stefano Morozzi	09/2020
7113	(206*10^100189-17)/9	100191	Robert Price	01/2020
7114	17^81417-16	100180	Theodore Burton	11/2005
7115	(2^332773+590)/2	100175	Stefano Morozzi	09/2020
7116	2^332739-113215	100165	Enzo Doria	07/2014
7117	2^332730-1865621	100162	Enzo Doria	03/2016
7118	91^51127-2	100160	Lelio R Paula	09/2013
7119	15^85159-32	100155	Lelio R Paula	10/2016
7120	6^128661+97	100118	Lelio R Paula	10/2016
7121	19^78285+40	100108	Lelio R Paula	07/2016
7122	6^128640+5	100102	Lelio R Paula	11/2014
7123	10^100095-400001	100095	Robert Price	09/2021
7124	22779^22970-22970^22779	100093	Norbert Schneider	08/2020
7125	(2^332468+3130)/2	100083	Stefano Morozzi	09/2020
7126	(14*10^100075+61)/3	100076	Robert Price	12/2018
7127	(2^332435+3098)/2	100073	Stefano Morozzi	09/2020
7128	28562^3189+3189^28562	100072	Hans Havermann	05/2018
7129	6^128565-127	100044	Lelio R Paula	08/2016
7130	(2^332317+2106)/2	100038	Stefano Morozzi	09/2020
7131	2^332309-133	100035	Lelio R Paula	02/2011
7132	2^332307+731	100035	Lelio R Paula	07/2011
7133	2^332301+12927	100033	Lelio R Paula	04/2013
7134	23406^18781+18781^23406	100031	Hans Havermann	04/2018
7135	2^332277-4573	100026	Yves Minet	03/2019
7136	12^92684-13	100023	Lelio R Paula	07/2016
7137	78557*2^332193+55669	100005	Jorge Menendez	04/2019
7138	78557*2^332192+72689	100005	Jorge Menendez	04/2019
7139	10^100003+45799	100004	Stefano Morozzi	04/2019
7140	10^100003+155461	100004	Stefano Morozzi	04/2019
7141	10^100003+211389	100004	Stefano Morozzi	04/2019
7142	10^100003+381027	100004	Stefano Morozzi	04/2019
7143	10^100003+540703	100004	Stefano Morozzi	04/2019
7144	10^100003+823977	100004	Stefano Morozzi	04/2019
7156	10^100002+236023	100003	Stefano Morozzi	05/2018
7157	10^100002+433741	100003	Stefano Morozzi	05/2018
7145	2^332202+104659	100003	Stefano Morozzi	04/2019
7146	2^332202+857539	100003	Stefano Morozzi	04/2019
7147	2^332202+181773	100003	Stefano Morozzi	04/2019
7148	2^332202+687543	100003	Stefano Morozzi	04/2019
7149	2^332202+941595	100003	Stefano Morozzi	04/2019
7150	2^332202+445813	100003	Stefano Morozzi	04/2019
7151	2^332202+1599727	100003	Stefano Morozzi	04/2019
7152	2^332202+1389567	100003	Stefano Morozzi	04/2019
7153	2^332202+1206315	100003	Stefano Morozzi	04/2019
7154	2^332202+1958647	100003	Stefano Morozzi	04/2019
7155	10^100003-562857	100003	Patrick De Geest	07/2019
7158	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
7159	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
7160	10^100002-249519	100002	Patrick De Geest	07/2018
7161	10^100001+314199	100002	Patrick De Geest	07/2018
7181	10^100000+3938473	100001	Robert Price	05/2015
7182	10^100000+3979761	100001	Robert Price	05/2015
7183	10^100000+4293973	100001	Robert Price	09/2015
7178	10^100000+4858267	100001	Robert Price	12/2015
7179	10^100000+5113299	100001	Robert Price	02/2016
7180	10^100000+5169411	100001	Robert Price	02/2016
7170	10^100000+5354043	100001	Robert Price	05/2016
7171	10^100000+5717979	100001	Robert Price	05/2016
7172	10^100000+6080631	100001	Robert Price	07/2016
7173	10^100000+6308469	100001	Robert Price	07/2016
7174	10^100000+6512023	100001	Robert Price	08/2016
7175	10^100000+6596557	100001	Robert Price	08/2016
7176	10^100000+7115409	100001	Robert Price	10/2016
7177	10^100000+7235803	100001	Robert Price	10/2016
7184	10^100000+7867333	100001	Robert Price	12/2016
7185	10^100000+8743093	100001	Robert Price	02/2017
7186	10^100000+8955391	100001	Robert Price	03/2017
7187	10^100000+9180019	100001	Robert Price	03/2017
7188	10^100000+9225987	100001	Robert Price	04/2017
7189	10^100000+9265587	100001	Robert Price	04/2017
7190	10^100000+9287049	100001	Robert Price	04/2017
7191	10^100000+9425053	100001	Robert Price	05/2017
7192	10^100000+9450769	100001	Robert Price	05/2017
7193	10^100000+9528747	100001	Robert Smith	05/2017
7194	10^100000+9548071	100001	Robert Price	06/2017
7195	10^100000+10064287	100001	Robert Price	08/2017
7196	10^100000+10229569	100001	Robert Price	10/2017
7162	10^100000+11187931	100001	Robert Price	03/2018
7163	10^100000+11264721	100001	Robert Price	04/2018
7164	10^100000+11477661	100001	Robert Price	05/2018
7165	10^100000+11644653	100001	Robert Price	07/2018
7166	10^100001-431439	100001	Patrick De Geest	07/2018
7167	10^100000+11769399	100001	Robert Price	08/2018
7168	10^100000+11848159	100001	Robert Price	08/2018
7169	10^100000+11863467	100001	Robert Price	08/2018
7197	10^100000+11992051	100001	Robert Price	09/2018
7198	2^332196-1-2*29696	100001	Matt Stath	11/2018
7199	10^100000+12363957	100001	Robert Price	11/2018
7200	2^332196+1+2*17152	100001	Matt Stath	12/2018
7201	10^100000+12778033	100001	Robert Price	02/2019
7202	10^100000+13581679	100001	Robert Price	05/2019
7203	10^100000+13613199	100001	Robert Price	05/2019
7204	10^100000+13752327	100001	Robert Price	05/2019
7205	10^100000+14139243	100001	Robert Price	06/2019
7206	10^100000+14151057	100001	Robert Price	06/2019
7207	10^100000+14218923	100001	Robert Price	06/2019
7232	10^100000+19956229	100001	Robert Price	09/2020
7233	10^100000+3(10^37093-1)/910^31454+1	100001	Makoto Morimoto	09/2020
7234	10^100000+4(10^36149-1)/910^31926+1	100001	Makoto Morimoto	09/2020
7235	10^100000+6(10^41029-1)/910^29486+1	100001	Makoto Morimoto	09/2020
7236	10^100000+7(10^55505-1)/910^22248+1	100001	Makoto Morimoto	09/2020
7237	10^100000+20234607	100001	Robert Price	10/2020
7238	10^100000+20752303	100001	Robert Price	11/2020
7239	10^100000+20774041	100001	Robert Price	11/2020
7240	10^100000+20854741	100001	Robert Price	11/2020
7241	10^100000+20908917	100001	Robert Price	11/2020
7242	10^100000+20994793	100001	Robert Price	11/2020
7243	10^100000+21354249	100001	Robert Price	12/2020
7244	10^100000+21455559	100001	Robert Price	12/2020
7245	10^100000+21538873	100001	Robert Price	12/2020
7246	10^100000+21830901	100001	Robert Price	01/2021
7247	10^100000+21842629	100001	Robert Price	01/2021
7248	10^100000+21930861	100001	Robert Price	01/2021
7249	10^100000+22092943	100001	Robert Price	03/2021
7250	10^100000+22278417	100001	Robert Price	03/2021
7208	10^100000+24543147	100001	Robert Price	08/2021
7209	10^100000+24781659	100001	Robert Price	08/2021
7210	10^100000+24906153	100001	Robert Price	08/2021
7211	10^100000+25682679	100001	Robert Price	10/2021
7212	10^100000+25905301	100001	Robert Price	10/2021
7213	10^100000+25923967	100001	Robert Price	10/2021
7214	10^100000+26061691	100001	Robert Price	10/2021
7215	10^100000+26173351	100001	Robert Price	11/2021
7216	10^100000+26673487	100001	Robert Price	11/2021
7217	10^100000+26849359	100001	Robert Price	12/2021
7218	10^100000+26893887	100001	Robert Price	12/2021
7219	10^100000+26954551	100001	Robert Price	12/2021
7220	10^100000+27024543	100001	Robert Price	12/2021
7221	10^100000+27060877	100001	Robert Price	12/2021
7222	10^100000+27617577	100001	Robert Price	03/2022
7223	10^100000+27869671	100001	Robert Price	03/2022
7224	10^100000+27956481	100001	Robert Price	03/2022
7225	10^100000+28078261	100001	Robert Price	03/2022
7226	10^100000+28150203	100001	Robert Price	03/2022
7227	10^100000+28626021	100001	Robert Price	05/2022
7228	10^100000+28649299	100001	Robert Price	05/2022
7229	10^100000+29409799	100001	Robert Price	06/2022
7230	10^100000+29415577	100001	Robert Price	06/2022
7231	10^100000+29424201	100001	Robert Price	06/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(290751 PRPs in the top)