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 ?
8355	25206!+p(4114)	100001	Henri Lifchitz	09/2005
8356	25206!-p(5447)	100001	Henri Lifchitz	10/2005
8357	25206!-p(12402)	100001	Henri Lifchitz	04/2006
8358	25206!-p(16290)	100001	Henri Lifchitz	09/2006
8359	25206!-p(19647)	100001	Henri Lifchitz	02/2007
8360	2^332194+11473	100001	Henri Lifchitz	03/2007
8350	10^100000+342909	100001	Milton L. Brown	12/2007
8351	10^100000+346579	100001	Robert Price	04/2012
8352	10^100000+829767	100001	Robert Price	05/2012
8353	10^100000+871899	100001	Robert Price	05/2012
8354	10^100000+1475997	100001	Robert Price	07/2012
8343	10^100000+1751769	100001	Robert Price	08/2012
8344	10^100000+2155489	100001	Robert Price	10/2012
8345	10^100000+2483527	100001	Robert Price	12/2012
8346	10^100000+2503087	100001	Robert Price	12/2012
8347	10^100000+2686179	100001	Robert Price	12/2012
8348	10^100000+2688933	100001	Robert Price	12/2012
8349	10^100000+3667159	100001	Robert Price	08/2013
8323	10^100000+15136771	100001	Robert Price	09/2019
8324	10^100000+15219873	100001	Robert Price	10/2019
8325	10^100000+15274039	100001	Robert Price	10/2019
8326	10^100000+15394069	100001	Robert Price	10/2019
8327	10^100000+15547119	100001	Robert Price	10/2019
8328	10^100000+15932923	100001	Robert Price	11/2019
8329	10^100000+16345467	100001	Robert Price	12/2019
8330	10^100000+16672143	100001	Robert Price	01/2020
8331	10^100000+16731939	100001	Robert Price	02/2020
8332	10^100000+16907049	100001	Robert Price	03/2020
8333	10^100000+17652523	100001	Robert Price	05/2020
8334	10^100000+18047167	100001	Robert Price	05/2020
8335	10^100000+18471819	100001	Robert Price	06/2020
8336	10^100000+18494793	100001	Robert Price	07/2020
8337	10^100000+18762609	100001	Robert Price	07/2020
8338	10^100000+19204141	100001	Robert Price	08/2020
8339	10^100000+19349793	100001	Robert Price	08/2020
8340	10^100000+19495699	100001	Robert Price	09/2020
8341	10^100000+19668927	100001	Robert Price	09/2020
8342	10^100000+19704313	100001	Robert Price	09/2020
8292	10^100000+19956229	100001	Robert Price	09/2020
8293	10^100000+3(10^37093-1)/910^31454+1	100001	Makoto Morimoto	09/2020
8294	10^100000+4(10^36149-1)/910^31926+1	100001	Makoto Morimoto	09/2020
8295	10^100000+6(10^41029-1)/910^29486+1	100001	Makoto Morimoto	09/2020
8296	10^100000+7(10^55505-1)/910^22248+1	100001	Makoto Morimoto	09/2020
8297	10^100000+20234607	100001	Robert Price	10/2020
8298	10^100000+20752303	100001	Robert Price	11/2020
8299	10^100000+20774041	100001	Robert Price	11/2020
8300	10^100000+20854741	100001	Robert Price	11/2020
8301	10^100000+20908917	100001	Robert Price	11/2020
8302	10^100000+20994793	100001	Robert Price	11/2020
8303	10^100000+21354249	100001	Robert Price	12/2020
8304	10^100000+21455559	100001	Robert Price	12/2020
8305	10^100000+21538873	100001	Robert Price	12/2020
8306	10^100000+21830901	100001	Robert Price	01/2021
8307	10^100000+21842629	100001	Robert Price	01/2021
8308	10^100000+21930861	100001	Robert Price	01/2021
8309	10^100000+22092943	100001	Robert Price	03/2021
8310	10^100000+22278417	100001	Robert Price	03/2021
8311	10^100000+22388581	100001	Robert Price	03/2021
8312	10^100000+22390933	100001	Robert Price	03/2021
8313	10^100000+22436169	100001	Robert Price	03/2021
8314	10^100000+22714557	100001	Robert Price	04/2021
8315	10^100000+22847671	100001	Robert Price	04/2021
8316	10^100000+23178567	100001	Robert Price	05/2021
8317	10^100000+23332003	100001	Robert Price	05/2021
8318	10^100000+23414571	100001	Robert Price	05/2021
8319	10^100000+23529979	100001	Robert Price	05/2021
8320	10^100000+23749243	100001	Robert Price	06/2021
8321	10^100000+23821771	100001	Robert Price	06/2021
8322	10^100000+24179307	100001	Robert Price	07/2021
8251	10^100000+30762711	100001	Robert Price	07/2022
8252	10^100000+30862057	100001	Robert Price	07/2022
8253	10^100000+30998953	100001	Robert Price	07/2022
8254	10^100000+31405203	100001	Robert Price	07/2022
8255	10^100000+40159119	100001	Robert Price	07/2022
8256	10^100000+40181863	100001	Robert Price	07/2022
8257	10^100000+40277131	100001	Robert Price	07/2022
8258	10^100000+40326061	100001	Robert Price	07/2022
8259	10^100000+40417411	100001	Robert Price	07/2022
8260	10^100000+50049909	100001	Robert Price	07/2022
8261	10^100000+50510163	100001	Robert Price	07/2022
8262	10^100000+50591583	100001	Robert Price	07/2022
8263	10^100000+50850357	100001	Robert Price	07/2022
8264	10^100000+50974641	100001	Robert Price	07/2022
8265	10^100000+51046671	100001	Robert Price	07/2022
8266	10^100000+51459657	100001	Robert Price	07/2022
8267	10^100000+70081471	100001	Robert Price	07/2022
8268	10^100000+70159557	100001	Robert Price	07/2022
8269	10^100000+70262479	100001	Robert Price	07/2022
8270	10^100000+70417521	100001	Robert Price	07/2022
8271	10^100000+70476531	100001	Robert Price	07/2022
8272	10^100000+70534627	100001	Robert Price	07/2022
8273	10^100000+70873077	100001	Robert Price	07/2022
8274	10^100000+71114643	100001	Robert Price	07/2022
8275	10^100000+71272539	100001	Robert Price	07/2022
8276	10^100000+80025337	100001	Robert Price	07/2022
8277	10^100000+71580817	100001	Robert Price	07/2022
8278	10^100000+80270349	100001	Robert Price	07/2022
8279	10^100000+29831551	100001	Robert Price	07/2022
8280	10^100000+29955417	100001	Robert Price	08/2022
8281	47907206710^99992+1+21779	100001	Matt Stath	12/2022
8282	10^100000+90000000+851439	100001	Robert Price	04/2023
8283	10^100000+90000000+1088017	100001	Robert Price	04/2023
8284	10^100000+90000000+1288173	100001	Robert Price	04/2023
8285	10^100000+90000000+1324549	100001	Robert Price	04/2023
8286	10^100000+90000000+3643869	100001	Robert Price	04/2023
8287	10^100000+110000000+60221	100001	Robert Price	04/2023
8288	10^100000+110000000+373261	100001	Robert Price	04/2023
8289	10^100000+110000000+497513	100001	Robert Price	04/2023
8290	10^100000+120000000+33823	100001	Robert Price	04/2023
8291	10^100000+120000000+419053	100001	Robert Price	04/2023
8361	10^99999+309403	100000	Daniel Heuer	01/2004
8362	10^100000-260199	100000	Patrick De Geest	01/2010
8363	2^332192+10192681	100000	Sujan Das	06/2022
8364	1610172603059^8192+1610172602878^8192	100000	Youcef Lemsafer	01/2023
8366	10^99999-59511	99999	Patrick De Geest	07/2009
8365	10^99998+235437	99999	Patrick De Geest	02/2020
8367	10^99998-286587	99998	Patrick De Geest	02/2020
8368	10^99997+72297	99998	Patrick De Geest	02/2020
8369	10^99997-402627	99997	Patrick De Geest	02/2020
8370	10^99996+279853	99997	Patrick De Geest	02/2020
8371	10^99997-500000001	99997	Robert Price	12/2020
8372	10^99996-94961	99996	Patrick De Geest	02/2020
8373	10^99995+54633	99996	Patrick De Geest	02/2020
8374	10^99995-101429	99995	Patrick De Geest	02/2020
8375	10^99994+117271	99995	Patrick De Geest	02/2020
8376	10^99994-452289	99994	Patrick De Geest	02/2020
8377	10^99993+371311	99994	Patrick De Geest	02/2020
8378	10^99993-186491	99993	Patrick De Geest	02/2020
8379	10^99992+17431	99993	Patrick De Geest	02/2020
8380	10^99992-28607	99992	Patrick De Geest	02/2020
8381	10^99991+125391	99992	Patrick De Geest	02/2020
8382	10^99991-204573	99991	Patrick De Geest	02/2020
8383	10^99990+13899	99991	Patrick De Geest	02/2020
8384	10^99990-8111	99990	Patrick De Geest	02/2020
8385	2^332141-113073	99985	Enzo Doria	07/2014
8386	(1610172603037^8192+1610172602919^8192)/17110948127473666	99983	Youcef Lemsafer	01/2023
8387	6*10^99979-79	99980	Robert Price	03/2022
8389	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
8388	23827^15702+15702^23827	99978	Hans Havermann	04/2018
8390	2^332085+1865897	99968	Enzo Doria	03/2016
8391	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
8392	2^332023+191	99949	Lelio R Paula	02/2011
8393	(6271^26321-1)/6270	99946	Serge Batalov	06/2022
8394	7*10^99944+27	99945	Robert Price	11/2020
8395	2^331938+71149	99924	Enzo Doria	04/2016
8396	2^331932-78795	99922	Lelio R Paula	09/2016
8397	2^331921+771	99919	Lelio R Paula	01/2013
8398	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
8399	2^331860-114989	99900	Enzo Doria	05/2015
8400	2^331746-11655	99866	Lelio R Paula	09/2016
8401	11^95891-28	99861	Lelio R Paula	08/2016
8402	(2^331694-5)/11	99849	Lelio R Paula	10/2013
8403	(3^209246+7)/64	99834	Lelio R Paula	09/2013
8404	25062^9617+9617^25062	99823	Hans Havermann	04/2018
8405	15^84866-52	99811	Lelio R Paula	08/2016
8406	13^89600+30	99810	Lelio R Paula	08/2016
8407	2^331527+100280245065	99800	Paul Bourdelais	10/2021
8408	22950^22309+22309^22950	99798	Hans Havermann	03/2018
8409	5^142772-38	99794	Lelio R Paula	08/2016
8410	(7482^25759-1)/7481	99787	Serge Batalov	06/2022
8411	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
8412	2^331416-331416+1	99767	Robert Price	10/2014
8413	2^331256-57	99718	Lelio R Paula	12/2012
8414	28192^3443+3443^28192	99714	Hans Havermann	03/2018
8415	2^331185+737	99697	Lelio R Paula	01/2013
8416	(4*10^99693+149)/9	99693	Robert Price	03/2017
8417	2^331154+1880527	99688	Enzo Doria	10/2016
8419	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
8418	24354^12385+12385^24354	99679	Hans Havermann	03/2018
8420	2^331110+1870459	99675	Enzo Doria	05/2016
8421	5*2^331075+7	99665	Lelio R Paula	08/2014
8422	25776^7351+7351^25776	99659	Hans Havermann	02/2018
8423	(16*10^99656-31)/3	99657	Robert Price	03/2016
8424	(6059^26347-1)/6058	99652	Serge Batalov	06/2022
8425	(15544^23773-1)/15543	99642	Serge Batalov	06/2022
8427	2^330968+345	99632	Lelio R Paula	09/2016
8426	(2^330969+690)/2	99632	Stefano Morozzi	09/2020
8429	2*5^142528-7	99624	Lelio R Paula	11/2014
8428	2^330942+77329	99624	Enzo Doria	05/2016
8430	14^86914-99	99615	Lelio R Paula	08/2016
8431	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
8432	22971^21692+21692^22971	99610	Hans Havermann	03/2018
8433	2^330845+71687	99595	Enzo Doria	04/2016
8434	(26667^22501-1)/26666	99585	Serge Batalov	06/2022
8435	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
8436	24494^11613+11613^24494	99567	Hans Havermann	03/2018
8437	2^330735+8415	99562	Lelio R Paula	09/2016
8438	2^330720+74071	99557	Enzo Doria	04/2016
8439	(10405^24781-1)/10404	99548	Serge Batalov	06/2022
8441	31^66738-2	99531	Lelio R Paula	09/2013
8440	(9002^25171-1)/9001	99531	Serge Batalov	06/2022
8442	(5023^26893-1)/5022	99527	Serge Batalov	06/2022
8443	7*3^208567+4	99513	Lelio R Paula	08/2014
8444	(15881^23689-1)/15880	99511	Serge Batalov	06/2022
8445	(13*10^99508+47)/3	99509	Robert Price	01/2017
8446	2^330553+779	99507	Lelio R Paula	01/2013
8447	15^84606-94	99505	Lelio R Paula	08/2016
8448	(10^99497+173)/3	99497	Robert Price	05/2021
8449	9*10^99493-43	99494	Robert Price	09/2021
8450	6^127858+47	99493	Lelio R Paula	08/2016
8451	5^142337+48	99490	Lelio R Paula	08/2016
8452	7^117724-20	99489	Lelio R Paula	08/2016
8453	(559^36209-1)/558	99479	Serge Batalov	06/2022
8454	(13470^24091-1)/13469	99477	Serge Batalov	06/2022
8455	(29*10^99474-17)/3	99475	Erik Branger	09/2014
8456	(185*10^99466-11)/3	99468	Robert Price	10/2020
8457	(2^330410+2038)/2	99464	Stefano Morozzi	09/2020
8458	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
8459	(516*32^66077-175)/31	99458	Eric Chen	04/2023
8460	(2863^28771-1)/2862	99453	Serge Batalov	06/2022
8461	(2^330373+2114)/2	99452	Stefano Morozzi	09/2020
8462	(68*10^99441+7)/3	99443	Robert Price	03/2016
8463	10^99434+155571	99435	Patrick De Geest	04/2020
8464	10^99434-123456789	99434	Robert Price	02/2020
8465	10^99434-191237	99434	Patrick De Geest	04/2020
8466	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
8467	23839^14802+14802^23839	99417	Hans Havermann	02/2018
8468	(2*10^99408+529)/9	99408	Robert Price	01/2017
8469	(2^330216+3510)/2	99405	Stefano Morozzi	09/2020
8470	53^57646-2	99398	Lelio R Paula	09/2013
8471	2^330165+1870025	99390	Enzo Doria	05/2016
8472	7*10^99383+97	99384	Robert Price	09/2021
8473	2^330142-155	99383	Lelio R Paula	12/2012
8474	2^330088-115259	99367	Enzo Doria	06/2015
8475	24216^12671+12671^24216	99354	Hans Havermann	01/2018
8476	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
8477	(746*10^99303+1)/9	99305	Robert Price	02/2017
8478	3^208107+40	99293	Lelio R Paula	08/2016
8479	(3939^27617-1)/3938	99291	Serge Batalov	06/2022
8480	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
8481	8*3^208093+5	99287	Lelio R Paula	08/2014
8482	5^142043+56	99284	Lelio R Paula	08/2016
8483	(13*10^99282-157)/9	99283	Robert Price	05/2021
8484	(10^99284+7)/53/67	99281	Alfred Reich	06/2021
8485	22*10^99275+7	99277	Robert Price	04/2016
8486	2^329778+1876189	99274	Enzo Doria	07/2016
8487	(6580^25997-1)/6579	99259	Serge Batalov	06/2022
8488	(2249^29611-1)/2248	99253	Serge Batalov	06/2022
8489	(10^99239-13)/3	99239	Robert Price	02/2017
8490	(1199^32233-1)/1198	99237	Serge Batalov	06/2022
8492	3^207987+62	99236	Lelio R Paula	08/2016
8491	(62*10^99235+91)/9	99236	Robert Price	07/2021
8493	2^329638+49	99231	Lelio R Paula	12/2012
8494	7^117413-18	99226	Lelio R Paula	08/2016
8495	2^329586-458903	99216	Enzo Doria	04/2015
8496	(6290^26119-1)/6289	99214	Serge Batalov	06/2022
8498	2^329553+101	99206	Lelio R Paula	12/2012
8497	(21297^22921-1)/21296	99206	Serge Batalov	06/2022
8499	2^329551-112897	99205	Enzo Doria	06/2014
8500	(3^207925+7)/50	99204	Lelio R Paula	09/2013

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PRP Records

Probable Primes Top 10000

(293016 PRPs in the top)