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 ?
8251	19807^10954+10954^19807	80012	Hans Havermann	04/2020
8252	3^167687-104	80008	Lelio R Paula	02/2015
8253	11^76826-5790	80007	Enzo Doria	01/2013
8254	10^80000+85731	80001	Patrick De Geest	10/2009
8255	10^80000-7169	80000	Patrick De Geest	09/2009
8256	10^79999+22399	80000	Patrick De Geest	09/2009
8257	10^79999-74873	79999	Patrick De Geest	09/2009
8258	3^167668+58	79998	Lelio R Paula	02/2015
8259	(2^265728+3742)/2	79992	Stefano Morozzi	01/2020
8260	18780^18137+18137^18780	79976	Hans Havermann	04/2020
8261	19190^14709+14709^19190	79976	Hans Havermann	04/2020
8262	155^36506-2	79961	Lelio R Paula	10/2017
8263	(2^265621+3882)/2	79960	Stefano Morozzi	01/2020
8265	2^265612+4257	79958	Lelio R Paula	07/2013
8264	(2^265613+1470)/2	79958	Stefano Morozzi	01/2020
8266	5*3^167577+4	79956	Lelio R Paula	06/2014
8267	(9179*2^265593-1)/9	79955	Lelio R Paula	04/2015
8268	6^102723-43	79935	Lelio R Paula	04/2015
8269	21052^6261+6261^21052	79927	Hans Havermann	03/2020
8270	11^76748-3360	79925	Enzo Doria	12/2012
8271	19430^12981+12981^19430	79922	Hans Havermann	03/2020
8272	(2^265490+870)/2	79921	Stefano Morozzi	01/2020
8273	(13*2^265498-1)/187119	79919	Lelio R Paula	02/2014
8274	(2^265438+3978)/2	79905	Stefano Morozzi	01/2020
8275	(2^265409+1250)/2	79896	Stefano Morozzi	01/2020
8276	2^265399-109855	79894	Enzo Doria	04/2014
8277	(2^265380+3930)/2	79888	Stefano Morozzi	01/2020
8278	(20^61403-1)/19	79886	Paul Bourdelais	03/2010
8279	(2^265368+2970)/2	79884	Stefano Morozzi	01/2020
8280	18^63635+59	79880	Lelio R Paula	02/2015
8281	(11*10^79867-107)/3	79868	Robert Price	11/2016
8282	3^167375+80	79859	Lelio R Paula	02/2015
8283	5^114240-14486	79851	Enzo Doria	02/2013
8284	49^47238+48	79842	Norbert Schneider	07/2014
8285	2^265212-3779	79837	Yves Minet	04/2017
8286	(2^265201+2790)/2	79834	Stefano Morozzi	01/2020
8287	91^40746+40746^91	79824	Norbert Schneider	12/2014
8288	(68*10^79813-257)/9	79814	Robert Price	06/2017
8289	(13063^19391-1)/13062	79811	Serge Batalov	08/2020
8290	(5*2^265118-1)/61	79808	Lelio R Paula	02/2014
8291	(2^265102+1462)/2	79804	Stefano Morozzi	01/2020
8292	2^265074+28425	79796	Lelio R Paula	07/2013
8293	2^265072+1185	79795	Lelio R Paula	07/2013
8295	p(16682)#/2-128	79771	Robert Price	05/2017
8294	(2^264994+1714)/2	79771	Stefano Morozzi	01/2020
8297	3^167167-34	79759	Robert Price	11/2013
8296	(2^264952+3258)/2	79759	Stefano Morozzi	01/2020
8298	12^73906+29	79758	Lelio R Paula	02/2015
8299	2^264934+255	79754	Lelio R Paula	07/2013
8300	4*10^79729-87	79730	Robert Price	03/2017
8301	2^264846-111701	79727	Enzo Doria	05/2014
8302	2^264831-112041	79723	Enzo Doria	06/2014
8303	2^264816-455	79718	Yves Minet	03/2012
8304	(55*10^79711+89)/9	79712	Robert Price	09/2017
8305	47^47667-46	79704	Theodore Burton	02/2007
8306	13^71547+96	79700	Lelio R Paula	03/2015
8307	2^264752-112883	79699	Enzo Doria	06/2014
8308	(2^264748+1978)/2	79697	Stefano Morozzi	01/2020
8309	(185*10^79694-11)/3	79696	Robert Price	10/2020
8310	2^264732+133	79693	Lelio R Paula	05/2012
8311	8*3^167010+7	79685	Lelio R Paula	06/2014
8312	42^49087-41	79681	Norbert Schneider	06/2014
8313	(26*10^79678-119)/3	79679	Robert Price	07/2016
8314	2^264683-21	79678	Lelio R Paula	05/2012
8315	7^94279+18	79675	Lelio R Paula	02/2015
8317	2^264655-127	79670	Lelio R Paula	02/2012
8316	(2^264658+3102)/2	79670	Stefano Morozzi	01/2020
8318	(2^264637+1682)/2	79664	Stefano Morozzi	01/2020
8319	2^264597-459043	79652	Enzo Doria	05/2015
8320	(21*2^264566+1)/5	79643	Lelio R Paula	10/2012
8321	2^264536+1870021	79634	Enzo Doria	05/2016
8322	(17*2^264512-1)/359	79625	Lelio R Paula	02/2014
8323	19957^9762+9762^19957	79620	Hans Havermann	03/2020
8324	2^264477-109783	79616	Enzo Doria	04/2014
8325	18^63419-1333	79609	Enzo Doria	03/2013
8326	13^71451-36	79593	Lelio R Paula	03/2015
8327	23314^2593+2593^23314	79590	Hans Havermann	03/2020
8328	(2^264410-5)/128002609121	79585	Lelio R Paula	10/2012
8329	19^62234+90	79582	Lelio R Paula	03/2015
8330	(2^264276+2866)/2	79555	Stefano Morozzi	01/2020
8331	12^73714+49	79551	Lelio R Paula	02/2015
8332	(2^264213+1442)/2	79536	Stefano Morozzi	01/2020
8333	(3*2^264184-1)/1433339	79522	Lelio R Paula	02/2014
8334	(2^264160+1590)/2	79520	Stefano Morozzi	01/2020
8335	(29*10^79510-107)/3	79511	Robert Price	08/2020
8336	(9363^20021-1)/9362	79508	Serge Batalov	08/2020
8337	2^264103-112531	79503	Enzo Doria	06/2014
8338	19^62170+78	79501	Lelio R Paula	03/2015
8339	11^76340-2580	79500	Enzo Doria	12/2012
8340	(2^264084+858)/2	79497	Stefano Morozzi	01/2020
8341	(5652^21187-1)/5651	79495	Serge Batalov	08/2020
8342	(23*10^79492-11)/3	79493	Robert Price	10/2015
8343	((2^132049+13650)^2+(2^132049+13650)+41)/2003/23841473	79491	Makoto Morimoto	05/2016
8344	2^264060-112133	79490	Enzo Doria	06/2014
8346	((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/10426147	79488	Makoto Morimoto	05/2016
8345	20158^8775+8775^20158	79488	Hans Havermann	02/2020
8347	9^83298+6^83298-2^83298	79487	Mike Oakes	08/2010
8348	18^63319+35	79483	Lelio R Paula	02/2015
8349	(10011^19867-1)/10010	79474	Serge Batalov	08/2020
8350	2*10^79468+77	79469	Robert Price	08/2020
8351	22479^3428+3428^22479	79465	Hans Havermann	04/2020
8352	38303!2+256	79461	Robert Price	01/2015
8353	(29*10^79445+61)/9	79446	Robert Price	04/2015
8354	2^263902-195	79443	Lelio R Paula	05/2012
8355	3^166499-112696	79441	Enzo Doria	06/2014
8356	11^76279-2760	79437	Enzo Doria	12/2012
8357	18907^15894+15894^18907	79433	Hans Havermann	03/2020
8358	6^102077-25	79432	Lelio R Paula	03/2015
8359	2^263852-1017	79428	Lelio R Paula	07/2013
8360	2^263842-33	79425	Lelio R Paula	05/2012
8361	(2^263814+3582)/2	79416	Stefano Morozzi	01/2020
8362	12^73584-55	79411	Lelio R Paula	02/2015
8363	(2^263783+3558)/2	79407	Stefano Morozzi	01/2020
8364	2^263772-185	79404	Lelio R Paula	05/2012
8365	(15^67489+1)/16	79373	Paul Bourdelais	03/2010
8366	2^263664+15015	79371	Lelio R Paula	07/2013
8367	(2^263643+1206)/2	79365	Stefano Morozzi	01/2020
8368	(2^263642+3082)/2	79364	Stefano Morozzi	01/2020
8369	(3319^22541-1)/3318	79364	Serge Batalov	08/2020
8370	10^79362+3^79363	79363	Mike Oakes	06/2010
8371	(2^263591+2910)/2	79349	Stefano Morozzi	01/2020
8372	(2^263589+1922)/2	79348	Stefano Morozzi	01/2020
8373	Phi(163244,10)/2448661/6856249	79331	Maksym Voznyy	11/2015
8374	3^166262+44	79328	Lelio R Paula	02/2015
8375	4*10^79327-63	79328	Robert Price	12/2016
8376	2^263486+513	79318	Lelio R Paula	07/2013
8377	(2^263458+1282)/2	79309	Stefano Morozzi	01/2020
8378	(2^263456+1558)/2	79308	Stefano Morozzi	01/2020
8379	2^263448-519509	79306	Paul Bourdelais	03/2013
8380	(18926^18541-1)/18925	79297	Serge Batalov	08/2020
8381	69153^16384+2	79296	Matt Stath	01/2019
8382	21^59971-20^59971	79295	Robert Price	05/2012
8383	2^263372+123	79283	Lelio R Paula	05/2012
8384	(2^263366+1974)/2	79281	Stefano Morozzi	01/2020
8385	17^64429+84	79277	Lelio R Paula	03/2015
8386	11^76124-11430	79275	Enzo Doria	12/2012
8387	19294^12845+12845^19294	79274	Hans Havermann	03/2020
8388	(206*10^79268-17)/9	79270	Robert Price	03/2017
8389	13^71157+18	79265	Lelio R Paula	03/2015
8390	2^263297+65835	79261	Lelio R Paula	07/2013
8391	19^61980-18	79258	Theodore Burton	12/2005
8392	(2^263259+2970)/2	79249	Stefano Morozzi	01/2020
8393	2*10^79242+93	79243	Robert Price	07/2016
8394	(2^263226+1074)/2	79239	Stefano Morozzi	01/2020
8395	(88^40751-1)/87	79238	Paul Bourdelais	08/2017
8396	(103*29^54179-39)/4	79233	Curtis Bright	05/2015
8397	9^83024-83024^9	79226	Norbert Schneider	08/2017
8398	17^64382-26	79219	Lelio R Paula	03/2015
8399	7^93733-74	79214	Lelio R Paula	02/2015
8400	15^67352+38	79213	Lelio R Paula	02/2015
8401	2^263135-110235	79212	Enzo Doria	05/2014
8402	(2^263080+3658)/2	79195	Stefano Morozzi	01/2020
8403	2^263044+4257	79185	Lelio R Paula	07/2013
8404	(2^263039+3554)/2	79183	Stefano Morozzi	01/2020
8406	2^263032+87517	79181	Yves Minet	11/2010
8405	6^101755+95	79181	Lelio R Paula	03/2015
8407	(2^263010+1738)/2	79174	Stefano Morozzi	01/2020
8408	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
8409	5*7^93674+8	79165	Lelio R Paula	10/2014
8410	(2^262939+1326)/2	79153	Stefano Morozzi	01/2020
8411	(2^262941+926)/2	79153	Stefano Morozzi	01/2020
8412	lucasU(486,25,29457)-5*lucasU(486,25,29456)	79137	Mike Oakes	05/2009
8413	260^32768+179^32768	79134	Serge Batalov	03/2018
8414	11^75978-42	79123	Lelio R Paula	02/2015
8415	8*5^113180+9	79111	Lelio R Paula	10/2014
8416	(2^262757+3222)/2	79098	Stefano Morozzi	01/2020
8417	(6883*2^262741-1)/4835	79094	Lelio R Paula	04/2015
8418	(9*2^262745+1)/137	79093	Lelio R Paula	10/2012
8419	12^73285+85	79088	Lelio R Paula	02/2015
8420	19^61840+52	79079	Lelio R Paula	03/2015
8422	(10^79067+77)/3	79067	Robert Price	01/2017
8421	(2^262655+678)/2	79067	Stefano Morozzi	01/2020
8423	(1017*2^262640-1)/11557	79062	Lelio R Paula	04/2015
8424	(2^262634+1674)/2	79061	Stefano Morozzi	01/2020
8425	10^79040+137949	79041	Patrick De Geest	02/2016
8427	10^79040-1007297	79040	Robert Price	02/2015
8426	10^79040-77427	79040	Patrick De Geest	02/2016
8428	2^262551-17295	79036	Lelio R Paula	07/2013
8429	(22973^18121-1)/22972	79026	Serge Batalov	08/2020
8430	3^165597+340	79010	Lelio R Paula	02/2015
8431	19620^10633+10633^19620	79003	Hans Havermann	02/2020
8432	(23*2^262435+1)/55	79001	Lelio R Paula	10/2012
8433	11^75860-2100	79001	Enzo Doria	12/2012
8434	8*7^93463+9	78987	Lelio R Paula	10/2014
8435	(2^262376+3942)/2	78983	Stefano Morozzi	01/2020
8436	67^43240-2	78960	Lelio R Paula	09/2013
8437	1000001^13159-1000000^13159	78953	Jean-Louis Charton	10/2003
8438	(2^262263+3410)/2	78949	Stefano Morozzi	01/2020
8439	2^262199-110287	78930	Enzo Doria	05/2014
8440	(19*2^262180-1)/177	78924	Lelio R Paula	02/2014
8441	(3^165403+4)/7	78917	Lelio R Paula	10/2012
8442	2^21068*(2^241076+1)-1	78914	Makoto Morimoto	03/2014
8443	2^29258*(2^232886+1)-1	78914	Makoto Morimoto	03/2014
8445	2^262144+18531	78914	Makoto Morimoto	12/2015
8444	2^262144-231425	78914	Matthias Baur	03/2020
8446	(2^262137+1730)/2	78911	Stefano Morozzi	01/2020
8447	(2^(2^18)+2450)/(23^2137*577)	78908	Makoto Morimoto	08/2017
8448	(2^(2^18)-5719)/(35993623)	78907	Makoto Morimoto	08/2017
8449	14^68837+75	78897	Lelio R Paula	02/2015
8450	(2^262055+1806)/2	78887	Stefano Morozzi	01/2020
8451	(20450^18301-1)/20449	78886	Serge Batalov	08/2020
8452	(2^262049+1406)/2	78885	Stefano Morozzi	01/2020
8453	106^38949+105	78884	Norbert Schneider	12/2016
8454	(2^262010+3778)/2	78873	Stefano Morozzi	01/2020
8455	(14*10^78863-191)/3	78864	Robert Price	10/2020
8456	18683^16636+16636^18683	78862	Hans Havermann	03/2020
8457	(2^261964+1450)/2	78859	Stefano Morozzi	01/2020
8458	23288^2433+2433^23288	78857	Hans Havermann	03/2020
8459	(70^42737+1)/71	78853	Paul Bourdelais	08/2017
8460	(2^261919+2474)/2	78846	Stefano Morozzi	01/2020
8461	(25*2^261917-1)/20927	78842	Lelio R Paula	02/2014
8462	2^261881-1859713	78835	Enzo Doria	03/2016
8464	2^261874+1915	78832	Lelio R Paula	07/2013
8463	(2^261872+1582)/2	78832	Stefano Morozzi	01/2020
8465	2^261856+98765331	78827	Jason Earls	01/2009
8466	(5*2^261857-1)/20501277	78821	Lelio R Paula	02/2014
8467	(10493^19603-1)/10492	78818	Serge Batalov	08/2020
8468	24586^1605+1605^24586	78810	Hans Havermann	02/2020
8469	(2^261786+3538)/2	78806	Stefano Morozzi	01/2020
8470	(2^261780+2290)/2	78804	Stefano Morozzi	01/2020
8471	2^261724+92691	78787	Tony Prest / Never Odd Or Even	03/2014
8472	2^261724+285111	78787	Tony Prest / Never Odd Or Even	04/2014
8473	2^261724+293713	78787	Tony Prest / Never Odd Or Even	04/2014
8474	(2^261724+381949)/5	78787	Tony Prest / Never Odd Or Even	04/2014
8475	2^261724+572971	78787	Tony Prest / Never Odd Or Even	05/2014
8476	(2^261724+392705)/3/7	78786	Tony Prest / Never Odd Or Even	04/2014
8477	(2^261724+629709)/5/5	78786	Tony Prest / Never Odd Or Even	05/2014
8478	(2^261724+67397)/3/103	78785	Tony Prest / Never Odd Or Even	04/2014
8479	(2^261724+323043)/11/103	78784	Tony Prest / Never Odd Or Even	04/2014
8480	(2^261724+370143)/1289	78784	Tony Prest / Never Odd Or Even	04/2014
8481	(2^261724+560259)/5/5/73	78784	Tony Prest / Never Odd Or Even	05/2014
8482	(2^261724+64109)/3/3/3/5/5/19	78783	Tony Prest / Never Odd Or Even	04/2014
8483	(2^261724+394491)/55787	78783	Tony Prest / Never Odd Or Even	04/2014
8484	(2^261724+625897)/23/883	78783	Tony Prest / Never Odd Or Even	05/2014
8485	19473^11110+11110^19473	78783	Hans Havermann	04/2020
8486	(2^261724+292471)/13/97/151	78782	Tony Prest / Never Odd Or Even	04/2014
8487	(2^261724+154303)/11/67/127	78782	Tony Prest / Never Odd Or Even	04/2014
8488	(2^261724+313319)/3/3/3/3/5/11/113	78782	Tony Prest / Never Odd Or Even	04/2014
8489	(2^261724+383949)/5/41/43/83	78781	Tony Prest / Never Odd Or Even	04/2014
8490	(2^261724+626567)/3/331/631	78781	Tony Prest / Never Odd Or Even	05/2014
8491	(2^261724+32987)/3/3/19/223/1031	78780	Tony Prest / Never Odd Or Even	04/2014
8492	(2^261724+5813)/3/5991397	78780	Tony Prest / Never Odd Or Even	04/2014
8493	(2^261724+13481)/3/11/239/2087	78780	Tony Prest / Never Odd Or Even	04/2014
8494	(2^261724+103399)/5/13/37/10607	78780	Tony Prest / Never Odd Or Even	04/2014
8495	(2^261724+18477)/367/65111	78780	Tony Prest / Never Odd Or Even	04/2014
8496	(2^261724+121285)/167/227/1217	78780	Tony Prest / Never Odd Or Even	04/2014
8497	(2^261724+262037)/3/3/11/23/18517	78780	Tony Prest / Never Odd Or Even	04/2014
8498	(2^261724+586157)/3/7/457/1259	78780	Tony Prest / Never Odd Or Even	05/2014
8499	(2^261724+315287)/3/45822541	78779	Tony Prest / Never Odd Or Even	04/2014
8500	(2^261724+605675)/3/3/3/103/207481	78779	Tony Prest / Never Odd Or Even	05/2014

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Probable Primes Top 10000

(277054 PRPs in the top)