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 ?
7295	25206!+p(4114)	100001	Henri Lifchitz	09/2005
7296	25206!-p(5447)	100001	Henri Lifchitz	10/2005
7297	25206!-p(12402)	100001	Henri Lifchitz	04/2006
7298	25206!-p(16290)	100001	Henri Lifchitz	09/2006
7299	25206!-p(19647)	100001	Henri Lifchitz	02/2007
7300	2^332194+11473	100001	Henri Lifchitz	03/2007
7290	10^100000+342909	100001	Milton L. Brown	12/2007
7291	10^100000+346579	100001	Robert Price	04/2012
7292	10^100000+829767	100001	Robert Price	05/2012
7293	10^100000+871899	100001	Robert Price	05/2012
7294	10^100000+1475997	100001	Robert Price	07/2012
7283	10^100000+1751769	100001	Robert Price	08/2012
7284	10^100000+2155489	100001	Robert Price	10/2012
7285	10^100000+2483527	100001	Robert Price	12/2012
7286	10^100000+2503087	100001	Robert Price	12/2012
7287	10^100000+2686179	100001	Robert Price	12/2012
7288	10^100000+2688933	100001	Robert Price	12/2012
7289	10^100000+3667159	100001	Robert Price	08/2013
7263	10^100000+15136771	100001	Robert Price	09/2019
7264	10^100000+15219873	100001	Robert Price	10/2019
7265	10^100000+15274039	100001	Robert Price	10/2019
7266	10^100000+15394069	100001	Robert Price	10/2019
7267	10^100000+15547119	100001	Robert Price	10/2019
7268	10^100000+15932923	100001	Robert Price	11/2019
7269	10^100000+16345467	100001	Robert Price	12/2019
7270	10^100000+16672143	100001	Robert Price	01/2020
7271	10^100000+16731939	100001	Robert Price	02/2020
7272	10^100000+16907049	100001	Robert Price	03/2020
7273	10^100000+17652523	100001	Robert Price	05/2020
7274	10^100000+18047167	100001	Robert Price	05/2020
7275	10^100000+18471819	100001	Robert Price	06/2020
7276	10^100000+18494793	100001	Robert Price	07/2020
7277	10^100000+18762609	100001	Robert Price	07/2020
7278	10^100000+19204141	100001	Robert Price	08/2020
7279	10^100000+19349793	100001	Robert Price	08/2020
7280	10^100000+19495699	100001	Robert Price	09/2020
7281	10^100000+19668927	100001	Robert Price	09/2020
7282	10^100000+19704313	100001	Robert Price	09/2020
7251	10^100000+22388581	100001	Robert Price	03/2021
7252	10^100000+22390933	100001	Robert Price	03/2021
7253	10^100000+22436169	100001	Robert Price	03/2021
7254	10^100000+22714557	100001	Robert Price	04/2021
7255	10^100000+22847671	100001	Robert Price	04/2021
7256	10^100000+23178567	100001	Robert Price	05/2021
7257	10^100000+23332003	100001	Robert Price	05/2021
7258	10^100000+23414571	100001	Robert Price	05/2021
7259	10^100000+23529979	100001	Robert Price	05/2021
7260	10^100000+23749243	100001	Robert Price	06/2021
7261	10^100000+23821771	100001	Robert Price	06/2021
7262	10^100000+24179307	100001	Robert Price	07/2021
7301	10^99999+309403	100000	Daniel Heuer	01/2004
7302	10^100000-260199	100000	Patrick De Geest	01/2010
7303	10^99999-59511	99999	Patrick De Geest	07/2009
7304	10^99998+235437	99999	Patrick De Geest	02/2020
7305	10^99998-286587	99998	Patrick De Geest	02/2020
7306	10^99997+72297	99998	Patrick De Geest	02/2020
7307	10^99997-402627	99997	Patrick De Geest	02/2020
7308	10^99996+279853	99997	Patrick De Geest	02/2020
7309	10^99997-500000001	99997	Robert Price	12/2020
7310	10^99996-94961	99996	Patrick De Geest	02/2020
7311	10^99995+54633	99996	Patrick De Geest	02/2020
7312	10^99995-101429	99995	Patrick De Geest	02/2020
7313	10^99994+117271	99995	Patrick De Geest	02/2020
7314	10^99994-452289	99994	Patrick De Geest	02/2020
7315	10^99993+371311	99994	Patrick De Geest	02/2020
7316	10^99993-186491	99993	Patrick De Geest	02/2020
7317	10^99992+17431	99993	Patrick De Geest	02/2020
7318	10^99992-28607	99992	Patrick De Geest	02/2020
7319	10^99991+125391	99992	Patrick De Geest	02/2020
7320	10^99991-204573	99991	Patrick De Geest	02/2020
7321	10^99990+13899	99991	Patrick De Geest	02/2020
7322	10^99990-8111	99990	Patrick De Geest	02/2020
7323	2^332141-113073	99985	Enzo Doria	07/2014
7324	6*10^99979-79	99980	Robert Price	03/2022
7326	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
7325	23827^15702+15702^23827	99978	Hans Havermann	04/2018
7327	2^332085+1865897	99968	Enzo Doria	03/2016
7328	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
7329	2^332023+191	99949	Lelio R Paula	02/2011
7330	(6271^26321-1)/6270	99946	Serge Batalov	06/2022
7331	7*10^99944+27	99945	Robert Price	11/2020
7332	2^331938+71149	99924	Enzo Doria	04/2016
7333	2^331932-78795	99922	Lelio R Paula	09/2016
7334	2^331921+771	99919	Lelio R Paula	01/2013
7335	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
7336	2^331860-114989	99900	Enzo Doria	05/2015
7337	2^331746-11655	99866	Lelio R Paula	09/2016
7338	11^95891-28	99861	Lelio R Paula	08/2016
7339	(2^331694-5)/11	99849	Lelio R Paula	10/2013
7340	(3^209246+7)/64	99834	Lelio R Paula	09/2013
7341	25062^9617+9617^25062	99823	Hans Havermann	04/2018
7342	15^84866-52	99811	Lelio R Paula	08/2016
7343	13^89600+30	99810	Lelio R Paula	08/2016
7344	2^331527+100280245065	99800	Paul Bourdelais	10/2021
7345	22950^22309+22309^22950	99798	Hans Havermann	03/2018
7346	5^142772-38	99794	Lelio R Paula	08/2016
7347	(7482^25759-1)/7481	99787	Serge Batalov	06/2022
7348	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
7349	2^331416-331416+1	99767	Robert Price	10/2014
7350	2^331256-57	99718	Lelio R Paula	12/2012
7351	28192^3443+3443^28192	99714	Hans Havermann	03/2018
7352	2^331185+737	99697	Lelio R Paula	01/2013
7353	(4*10^99693+149)/9	99693	Robert Price	03/2017
7354	2^331154+1880527	99688	Enzo Doria	10/2016
7356	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
7355	24354^12385+12385^24354	99679	Hans Havermann	03/2018
7357	2^331110+1870459	99675	Enzo Doria	05/2016
7358	5*2^331075+7	99665	Lelio R Paula	08/2014
7359	25776^7351+7351^25776	99659	Hans Havermann	02/2018
7360	(16*10^99656-31)/3	99657	Robert Price	03/2016
7361	(6059^26347-1)/6058	99652	Serge Batalov	06/2022
7362	(15544^23773-1)/15543	99642	Serge Batalov	06/2022
7364	2^330968+345	99632	Lelio R Paula	09/2016
7363	(2^330969+690)/2	99632	Stefano Morozzi	09/2020
7366	2*5^142528-7	99624	Lelio R Paula	11/2014
7365	2^330942+77329	99624	Enzo Doria	05/2016
7367	14^86914-99	99615	Lelio R Paula	08/2016
7368	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
7369	22971^21692+21692^22971	99610	Hans Havermann	03/2018
7370	2^330845+71687	99595	Enzo Doria	04/2016
7371	(26667^22501-1)/26666	99585	Serge Batalov	06/2022
7372	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
7373	24494^11613+11613^24494	99567	Hans Havermann	03/2018
7374	2^330735+8415	99562	Lelio R Paula	09/2016
7375	2^330720+74071	99557	Enzo Doria	04/2016
7376	(10405^24781-1)/10404	99548	Serge Batalov	06/2022
7378	31^66738-2	99531	Lelio R Paula	09/2013
7377	(9002^25171-1)/9001	99531	Serge Batalov	06/2022
7379	(5023^26893-1)/5022	99527	Serge Batalov	06/2022
7380	7*3^208567+4	99513	Lelio R Paula	08/2014
7381	(15881^23689-1)/15880	99511	Serge Batalov	06/2022
7382	(13*10^99508+47)/3	99509	Robert Price	01/2017
7383	2^330553+779	99507	Lelio R Paula	01/2013
7384	15^84606-94	99505	Lelio R Paula	08/2016
7385	(10^99497+173)/3	99497	Robert Price	05/2021
7386	9*10^99493-43	99494	Robert Price	09/2021
7387	6^127858+47	99493	Lelio R Paula	08/2016
7388	5^142337+48	99490	Lelio R Paula	08/2016
7389	7^117724-20	99489	Lelio R Paula	08/2016
7390	(559^36209-1)/558	99479	Serge Batalov	06/2022
7391	(13470^24091-1)/13469	99477	Serge Batalov	06/2022
7392	(29*10^99474-17)/3	99475	Erik Branger	09/2014
7393	(185*10^99466-11)/3	99468	Robert Price	10/2020
7394	(2^330410+2038)/2	99464	Stefano Morozzi	09/2020
7395	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
7396	(2863^28771-1)/2862	99453	Serge Batalov	06/2022
7397	(2^330373+2114)/2	99452	Stefano Morozzi	09/2020
7398	(68*10^99441+7)/3	99443	Robert Price	03/2016
7399	10^99434+155571	99435	Patrick De Geest	04/2020
7400	10^99434-123456789	99434	Robert Price	02/2020
7401	10^99434-191237	99434	Patrick De Geest	04/2020
7402	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
7403	23839^14802+14802^23839	99417	Hans Havermann	02/2018
7404	(2*10^99408+529)/9	99408	Robert Price	01/2017
7405	(2^330216+3510)/2	99405	Stefano Morozzi	09/2020
7406	53^57646-2	99398	Lelio R Paula	09/2013
7407	2^330165+1870025	99390	Enzo Doria	05/2016
7408	7*10^99383+97	99384	Robert Price	09/2021
7409	2^330142-155	99383	Lelio R Paula	12/2012
7410	2^330088-115259	99367	Enzo Doria	06/2015
7411	24216^12671+12671^24216	99354	Hans Havermann	01/2018
7412	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
7413	(746*10^99303+1)/9	99305	Robert Price	02/2017
7414	3^208107+40	99293	Lelio R Paula	08/2016
7415	(3939^27617-1)/3938	99291	Serge Batalov	06/2022
7416	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
7417	8*3^208093+5	99287	Lelio R Paula	08/2014
7418	5^142043+56	99284	Lelio R Paula	08/2016
7419	(13*10^99282-157)/9	99283	Robert Price	05/2021
7420	(10^99284+7)/53/67	99281	Alfred Reich	06/2021
7421	22*10^99275+7	99277	Robert Price	04/2016
7422	2^329778+1876189	99274	Enzo Doria	07/2016
7423	(6580^25997-1)/6579	99259	Serge Batalov	06/2022
7424	(2249^29611-1)/2248	99253	Serge Batalov	06/2022
7425	(10^99239-13)/3	99239	Robert Price	02/2017
7426	(1199^32233-1)/1198	99237	Serge Batalov	06/2022
7428	3^207987+62	99236	Lelio R Paula	08/2016
7427	(62*10^99235+91)/9	99236	Robert Price	07/2021
7429	2^329638+49	99231	Lelio R Paula	12/2012
7430	7^117413-18	99226	Lelio R Paula	08/2016
7431	2^329586-458903	99216	Enzo Doria	04/2015
7432	(6290^26119-1)/6289	99214	Serge Batalov	06/2022
7434	2^329553+101	99206	Lelio R Paula	12/2012
7433	(21297^22921-1)/21296	99206	Serge Batalov	06/2022
7435	2^329551-112897	99205	Enzo Doria	06/2014
7436	(3^207925+7)/50	99204	Lelio R Paula	09/2013
7437	6^127458-17993	99182	Enzo Doria	03/2013
7438	27197^4428+4428^27197	99166	Hans Havermann	10/2017
7439	(46*10^99143-1)/9	99144	Robert Price	12/2014
7440	7*10^99133+69	99134	Robert Price	10/2017
7441	(21701^22861-1)/21700	99132	Serge Batalov	06/2022
7442	18^78968-3065	99127	Enzo Doria	03/2013
7444	25927^6654+6654^25927	99122	Hans Havermann	10/2017
7443	87915!4+16	99122	Robert Price	09/2019
7445	2^329259+189	99117	Lelio R Paula	12/2012
7446	8*10^99113+39	99114	Robert Price	01/2017
7447	6^127364+77	99109	Lelio R Paula	08/2016
7448	(82*10^99103+143)/9	99104	Robert Price	06/2021
7449	(11414^24421-1)/11413	99083	Serge Batalov	06/2022
7450	(2^329135+1110)/2	99080	Stefano Morozzi	09/2020
7451	(22089^22807-1)/22088	99074	Serge Batalov	06/2022
7452	(59*10^99069+391)/9	99070	Robert Price	03/2021
7453	(797*10^99061-41)/9	99063	Robert Price	04/2022
7454	2^329058-287681	99057	Harrison Mesh	06/2022
7455	6^127285+13	99047	Lelio R Paula	08/2016
7456	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
7457	2^329007+73283	99041	Enzo Doria	04/2016
7458	5*3^207543-8	99024	Lelio R Paula	08/2014
7459	(2^328930+570)/2	99018	Stefano Morozzi	09/2020
7460	2^328885+149	99005	Lelio R Paula	12/2012
7462	23392^17075+17075^23392	99004	Hans Havermann	09/2017
7461	(7424^25579-1)/7423	99004	Serge Batalov	06/2022
7463	(2^328879-9)/119	99001	Lelio R Paula	10/2013
7464	5^141618+54	98987	Lelio R Paula	08/2016
7465	8*10^98982+51	98983	Robert Price	05/2017
7466	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
7467	2^328794-2797601	98977	Enzo Doria	04/2016
7468	(88331^20011-1)/88330	98972	Serge Batalov	06/2022
7469	6^127176+5	98963	Lelio R Paula	11/2014
7470	2*10^98961-21	98962	Robert Price	09/2020
7471	24262^11989+11989^24262	98960	Hans Havermann	09/2017
7472	(60138^20707-1)/60137	98958	Serge Batalov	06/2022
7473	2^328700-109709	98949	Enzo Doria	04/2014
7474	(2^328698+1810)/2	98948	Stefano Morozzi	01/2021
7475	(1014^32917-1)/1013	98947	Serge Batalov	06/2022
7476	87771!4-128	98944	Robert Price	11/2019
7477	(4576^27031-1)/4575	98943	Serge Batalov	06/2022
7478	(2^328658+3042)/2	98936	Stefano Morozzi	09/2020
7479	(1933^30103-1)/1932	98923	Serge Batalov	06/2022
7480	46711!2-2^46711	98916	Robert Price	09/2015
7481	9*7^117037+4	98909	Lelio R Paula	11/2014
7482	127^47012+126	98905	Norbert Schneider	01/2019
7483	(93826^19891-1)/93825	98900	Serge Batalov	06/2022
7484	(2^328525+1250)/2	98896	Stefano Morozzi	09/2020
7485	(10^98890+149)/3	98890	Serge Batalov	12/2014
7486	22775^21978+21978^22775	98889	Hans Havermann	08/2017
7487	2^328497-216933	98888	Enzo Doria	05/2014
7488	2^328487+32769	98885	Lelio R Paula	08/2016
7489	3^207250-112358	98884	Enzo Doria	06/2014
7490	13^88754-90	98867	Lelio R Paula	08/2016
7491	2^328406+709	98861	Lelio R Paula	02/2013
7492	2*10^98860-21	98861	Robert Price	09/2020
7493	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
7494	7^116976+76	98857	Lelio R Paula	08/2016
7495	(2^328378+2710)/2	98852	Stefano Morozzi	09/2020
7496	(25411^22441-1)/25410	98849	Serge Batalov	06/2022
7497	(18668^23143-1)/18667	98842	Serge Batalov	06/2022
7499	2^328335+1155	98839	Lelio R Paula	08/2016
7498	2^328333-349003	98839	Harrison Mesh	06/2022
7500	287^40210+40210^287	98832	Norbert Schneider	11/2014

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PRP Records

Probable Primes Top 10000

(290751 PRPs in the top)