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 ?
8002	2^263032+87517	79181	Yves Minet	11/2010
8001	6^101755+95	79181	Lelio R Paula	03/2015
8003	(2^263010+1738)/2	79174	Stefano Morozzi	01/2020
8004	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
8005	5*7^93674+8	79165	Lelio R Paula	10/2014
8006	(2^262939+1326)/2	79153	Stefano Morozzi	01/2020
8007	(2^262941+926)/2	79153	Stefano Morozzi	01/2020
8008	lucasU(486,25,29457)-5*lucasU(486,25,29456)	79137	Mike Oakes	05/2009
8009	260^32768+179^32768	79134	Serge Batalov	03/2018
8010	11^75978-42	79123	Lelio R Paula	02/2015
8011	8*5^113180+9	79111	Lelio R Paula	10/2014
8012	(2^262757+3222)/2	79098	Stefano Morozzi	01/2020
8013	(6883*2^262741-1)/4835	79094	Lelio R Paula	04/2015
8014	(9*2^262745+1)/137	79093	Lelio R Paula	10/2012
8015	12^73285+85	79088	Lelio R Paula	02/2015
8016	19^61840+52	79079	Lelio R Paula	03/2015
8018	(10^79067+77)/3	79067	Robert Price	01/2017
8017	(2^262655+678)/2	79067	Stefano Morozzi	01/2020
8019	(1017*2^262640-1)/11557	79062	Lelio R Paula	04/2015
8020	(2^262634+1674)/2	79061	Stefano Morozzi	01/2020
8021	10^79040+137949	79041	Patrick De Geest	02/2016
8023	10^79040-1007297	79040	Robert Price	02/2015
8022	10^79040-77427	79040	Patrick De Geest	02/2016
8024	2^262551-17295	79036	Lelio R Paula	07/2013
8025	(22973^18121-1)/22972	79026	Serge Batalov	08/2020
8026	3^165597+340	79010	Lelio R Paula	02/2015
8027	19620^10633+10633^19620	79003	Hans Havermann	02/2020
8028	(23*2^262435+1)/55	79001	Lelio R Paula	10/2012
8029	11^75860-2100	79001	Enzo Doria	12/2012
8030	8*7^93463+9	78987	Lelio R Paula	10/2014
8031	(2^262376+3942)/2	78983	Stefano Morozzi	01/2020
8032	67^43240-2	78960	Lelio R Paula	09/2013
8033	1000001^13159-1000000^13159	78953	Jean-Louis Charton	10/2003
8034	(2^262263+3410)/2	78949	Stefano Morozzi	01/2020
8035	2^262199-110287	78930	Enzo Doria	05/2014
8036	(19*2^262180-1)/177	78924	Lelio R Paula	02/2014
8037	(3^165403+4)/7	78917	Lelio R Paula	10/2012
8038	2^21068*(2^241076+1)-1	78914	Makoto Morimoto	03/2014
8039	2^29258*(2^232886+1)-1	78914	Makoto Morimoto	03/2014
8041	2^262144+18531	78914	Makoto Morimoto	12/2015
8040	2^262144-231425	78914	Matthias Baur	03/2020
8042	(2^262137+1730)/2	78911	Stefano Morozzi	01/2020
8043	(2^(2^18)+2450)/(23^2137*577)	78908	Makoto Morimoto	08/2017
8044	(2^(2^18)-5719)/(35993623)	78907	Makoto Morimoto	08/2017
8045	14^68837+75	78897	Lelio R Paula	02/2015
8046	(2^262055+1806)/2	78887	Stefano Morozzi	01/2020
8047	(20450^18301-1)/20449	78886	Serge Batalov	08/2020
8048	(2^262049+1406)/2	78885	Stefano Morozzi	01/2020
8049	106^38949+105	78884	Norbert Schneider	12/2016
8050	(2^262010+3778)/2	78873	Stefano Morozzi	01/2020
8051	18683^16636+16636^18683	78862	Hans Havermann	03/2020
8052	(2^261964+1450)/2	78859	Stefano Morozzi	01/2020
8053	23288^2433+2433^23288	78857	Hans Havermann	03/2020
8054	(70^42737+1)/71	78853	Paul Bourdelais	08/2017
8055	(2^261919+2474)/2	78846	Stefano Morozzi	01/2020
8056	(25*2^261917-1)/20927	78842	Lelio R Paula	02/2014
8057	2^261881-1859713	78835	Enzo Doria	03/2016
8059	2^261874+1915	78832	Lelio R Paula	07/2013
8058	(2^261872+1582)/2	78832	Stefano Morozzi	01/2020
8060	2^261856+98765331	78827	Jason Earls	01/2009
8061	(5*2^261857-1)/20501277	78821	Lelio R Paula	02/2014
8062	(10493^19603-1)/10492	78818	Serge Batalov	08/2020
8063	24586^1605+1605^24586	78810	Hans Havermann	02/2020
8064	(2^261786+3538)/2	78806	Stefano Morozzi	01/2020
8065	(2^261780+2290)/2	78804	Stefano Morozzi	01/2020
8066	2^261724+92691	78787	Tony Prest / Never Odd Or Even	03/2014
8067	2^261724+285111	78787	Tony Prest / Never Odd Or Even	04/2014
8068	2^261724+293713	78787	Tony Prest / Never Odd Or Even	04/2014
8069	(2^261724+381949)/5	78787	Tony Prest / Never Odd Or Even	04/2014
8070	2^261724+572971	78787	Tony Prest / Never Odd Or Even	05/2014
8071	(2^261724+392705)/3/7	78786	Tony Prest / Never Odd Or Even	04/2014
8072	(2^261724+629709)/5/5	78786	Tony Prest / Never Odd Or Even	05/2014
8073	(2^261724+67397)/3/103	78785	Tony Prest / Never Odd Or Even	04/2014
8074	(2^261724+323043)/11/103	78784	Tony Prest / Never Odd Or Even	04/2014
8075	(2^261724+370143)/1289	78784	Tony Prest / Never Odd Or Even	04/2014
8076	(2^261724+560259)/5/5/73	78784	Tony Prest / Never Odd Or Even	05/2014
8077	(2^261724+64109)/3/3/3/5/5/19	78783	Tony Prest / Never Odd Or Even	04/2014
8078	(2^261724+394491)/55787	78783	Tony Prest / Never Odd Or Even	04/2014
8079	(2^261724+625897)/23/883	78783	Tony Prest / Never Odd Or Even	05/2014
8080	19473^11110+11110^19473	78783	Hans Havermann	04/2020
8081	(2^261724+292471)/13/97/151	78782	Tony Prest / Never Odd Or Even	04/2014
8082	(2^261724+154303)/11/67/127	78782	Tony Prest / Never Odd Or Even	04/2014
8083	(2^261724+313319)/3/3/3/3/5/11/113	78782	Tony Prest / Never Odd Or Even	04/2014
8084	(2^261724+383949)/5/41/43/83	78781	Tony Prest / Never Odd Or Even	04/2014
8085	(2^261724+626567)/3/331/631	78781	Tony Prest / Never Odd Or Even	05/2014
8086	(2^261724+32987)/3/3/19/223/1031	78780	Tony Prest / Never Odd Or Even	04/2014
8087	(2^261724+5813)/3/5991397	78780	Tony Prest / Never Odd Or Even	04/2014
8088	(2^261724+13481)/3/11/239/2087	78780	Tony Prest / Never Odd Or Even	04/2014
8089	(2^261724+103399)/5/13/37/10607	78780	Tony Prest / Never Odd Or Even	04/2014
8090	(2^261724+18477)/367/65111	78780	Tony Prest / Never Odd Or Even	04/2014
8091	(2^261724+121285)/167/227/1217	78780	Tony Prest / Never Odd Or Even	04/2014
8092	(2^261724+262037)/3/3/11/23/18517	78780	Tony Prest / Never Odd Or Even	04/2014
8093	(2^261724+586157)/3/7/457/1259	78780	Tony Prest / Never Odd Or Even	05/2014
8094	(2^261724+315287)/3/45822541	78779	Tony Prest / Never Odd Or Even	04/2014
8095	(2^261724+605675)/3/3/3/103/207481	78779	Tony Prest / Never Odd Or Even	05/2014
8096	(2^261724+60031)/13/31/7024877	78778	Tony Prest / Never Odd Or Even	04/2014
8097	(2^261724+121879)/5/789433217	78778	Tony Prest / Never Odd Or Even	04/2014
8098	(2^261724+290135)/3/3/8467/9059	78778	Tony Prest / Never Odd Or Even	04/2014
8099	(2^261724+79857)/59/3847/165331	78777	Tony Prest / Never Odd Or Even	04/2014
8100	(2^261724+22883)/3/17/23/2351/10079	78777	Tony Prest / Never Odd Or Even	04/2014
8101	(2^261724+154799)/3/5/3655653719	78777	Tony Prest / Never Odd Or Even	04/2014
8102	(2^261724+391001)/3/11/17/41/43/24071	78777	Tony Prest / Never Odd Or Even	04/2014
8103	(2^261724+622383)/34843/550717	78777	Tony Prest / Never Odd Or Even	05/2014
8104	(2^261724+302829)/5/37/37/37078147	78776	Tony Prest / Never Odd Or Even	04/2014
8105	(2^261724+315837)/43/2176136243	78776	Tony Prest / Never Odd Or Even	04/2014
8106	(2^261724+582373)/53/307/311/32117	78776	Tony Prest / Never Odd Or Even	05/2014
8107	(2^261724+295283)/3/3/3/29/43/17812273	78775	Tony Prest / Never Odd Or Even	04/2014
8108	(2^261724+27491)/3/22787/105978449	78774	Tony Prest / Never Odd Or Even	04/2014
8109	(2^261724+392751)/193813/287826689	78774	Tony Prest / Never Odd Or Even	04/2014
8110	(2^261724+328501)/7/1091/31495610519	78773	Tony Prest / Never Odd Or Even	04/2014
8111	(2^261724+111267)/19/4637/15140560427	78772	Tony Prest / Never Odd Or Even	04/2014
8112	(2^261724+572133)/127/131/73787752333	78772	Tony Prest / Never Odd Or Even	05/2014
8113	(2^261724+608733)/59/7079/18451/909151	78771	Tony Prest / Never Odd Or Even	05/2014
8114	(2^261724+255449)/3/3/5/7/1759/10177/33158869	78770	Tony Prest / Never Odd Or Even	04/2014
8115	(2^261724+99509)/3/5/5/6507271/6749659289	78769	Tony Prest / Never Odd Or Even	04/2014
8116	(2^261724+52501)/563/53939/27942831391	78769	Tony Prest / Never Odd Or Even	04/2014
8117	(2^261724+117089)/3/5/37/149/967/2027/4163741	78769	Tony Prest / Never Odd Or Even	04/2014
8118	(2^261724+372571)/1487/9209/21559/2263249	78769	Tony Prest / Never Odd Or Even	04/2014
8119	(2^261724+184549)/5/8699/44053/1409322997	78769	Tony Prest / Never Odd Or Even	04/2014
8120	(2^261724+363351)/937/159683/59523200227	78768	Tony Prest / Never Odd Or Even	04/2014
8121	(2^261724+326501)/3/43/193/263/19403/253501403	78768	Tony Prest / Never Odd Or Even	04/2014
8122	(2^261724+629477)/3/17/17/137/263/1993/16187/57347	78768	Tony Prest / Never Odd Or Even	05/2014
8123	(2^261724+94871)/3/3/13/6734017/1673425245787	78766	Tony Prest / Never Odd Or Even	04/2014
8124	(2^261724+25981)/577/1181/3643/517786334743	78766	Tony Prest / Never Odd Or Even	04/2014
8126	(23*2^261642+1)/93	78762	Lelio R Paula	10/2012
8125	(2^261724+351227)/3/3/3/3/71/13997/9595373/8193978007	78762	Tony Prest / Never Odd Or Even	04/2014
8127	(2^261724+22571)/3/7243/7321/18046081/45730741211	78761	Tony Prest / Never Odd Or Even	04/2014
8128	(2^261724+56495)/3/3/3/7/7/13/9041/512818459/23708589119	78760	Tony Prest / Never Odd Or Even	04/2014
8129	71293!4-4	78759	Robert Price	11/2019
8130	(2^261630+3582)/2	78759	Stefano Morozzi	01/2020
8131	(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/1036020834127	78750	Tony Prest / Never Odd Or Even	05/2014
8132	(2^261536+846)/2	78730	Stefano Morozzi	01/2020
8133	2^261507-2287	78722	Yves Minet	04/2009
8134	8*10^78717+39	78718	Robert Price	01/2017
8135	(78557*2^261440+1)/3	78706	Lelio R Paula	06/2014
8136	(290^31963-1)/289	78704	Serge Batalov	08/2020
8137	(21323^18181-1)/21322	78699	Serge Batalov	08/2020
8138	6^101128-16433	78693	Enzo Doria	02/2013
8139	20^60482+99	78689	Lelio R Paula	03/2015
8140	2^261348-110633	78674	Enzo Doria	05/2014
8141	191^34487+2	78666	Lelio R Paula	05/2013
8142	2^261305-110139	78661	Enzo Doria	04/2014
8143	(82*10^78635-1)/9	78636	Robert Price	12/2014
8144	10^78632+81	78633	Robert Price	03/2011
8145	10^78632-402693	78632	Patrick De Geest	07/2013
8146	3*10^78631+17	78632	Robert Price	03/2017
8147	2^261174-3911	78622	Yves Minet	04/2017
8148	2^261167+74843	78620	Enzo Doria	04/2016
8149	18810^15119+15119^18810	78617	Hans Havermann	04/2020
8150	L(376121)+F(376122)	78605	Henri Lifchitz	01/2007
8151	14^68580-29	78602	Lelio R Paula	02/2015
8152	(4270^21649-1)/4269	78592	Serge Batalov	08/2020
8153	20603^6522+6522^20603	78588	Hans Havermann	03/2020
8154	(2^261056+646)/2	78586	Stefano Morozzi	01/2020
8155	(73*10^78576-1)/9	78577	Robert Price	01/2015
8156	(2^261020+2158)/2	78575	Stefano Morozzi	01/2020
8157	(17*2^261026-1)/40451	78574	Lelio R Paula	02/2014
8158	(2415^23227-1)/2414	78572	Serge Batalov	08/2020
8160	2^261001-195	78570	Lelio R Paula	05/2012
8159	18532^17365+17365^18532	78570	Hans Havermann	02/2020
8161	5*2^260950+9	78555	Lelio R Paula	06/2014
8162	2^260931-7605	78549	Lelio R Paula	07/2013
8163	19863^9002+9002^19863	78546	Hans Havermann	02/2020
8164	15^66778-32	78538	Lelio R Paula	02/2015
8165	(11*2^260896-1)/245	78537	Lelio R Paula	02/2014
8166	30^53166+29	78533	Norbert Schneider	03/2017
8168	lucasU(2403,1,23229)-lucasU(2403,1,23228)	78529	Mike Oakes	05/2009
8167	18729^15592+15592^18729	78529	Hans Havermann	04/2020
8169	7*3^164574-2	78523	Lelio R Paula	06/2014
8170	18518^17385+17385^18518	78520	Hans Havermann	03/2020
8171	2^260830-112133	78518	Enzo Doria	06/2014
8172	13^70486+42	78518	Lelio R Paula	03/2015
8173	11^75386-7080	78507	Enzo Doria	01/2013
8175	(86^40583-1)/85	78506	Paul Bourdelais	08/2017
8174	(2^260790+1914)/2	78506	Stefano Morozzi	01/2020
8176	5*10^78504+11	78505	Robert Price	08/2019
8177	2^260711-58695	78482	Lelio R Paula	07/2013
8178	(2^260695+2258)/2	78477	Stefano Morozzi	01/2020
8179	2^260678-111065	78472	Enzo Doria	05/2014
8180	21560^4359+4359^21560	78466	Hans Havermann	02/2020
8181	18^62501-97	78456	Lelio R Paula	02/2015
8182	53^45498-2	78452	Lelio R Paula	08/2013
8183	(8890^19867-1)/8889	78449	Serge Batalov	08/2020
8184	(2^260549+642)/2	78433	Stefano Morozzi	01/2020
8185	(2^260527+3906)/2	78427	Stefano Morozzi	01/2020
8186	2^260513-111121	78423	Enzo Doria	05/2014
8187	37845!2-64	78412	Robert Price	06/2015
8188	2^260469-110695	78409	Enzo Doria	05/2014
8189	(11*10^78408-113)/3	78409	Robert Price	01/2017
8190	2^260447+8415	78403	Lelio R Paula	07/2013
8191	37837!2-64	78394	Robert Price	06/2015
8192	(19*2^260379-1)/53	78382	Lelio R Paula	02/2014
8193	2^260377-113233	78382	Enzo Doria	07/2014
8194	(2^260378+3750)/2	78382	Stefano Morozzi	01/2020
8196	9^82138+6^82138-2^82138	78380	Mike Oakes	08/2010
8195	69^42624+2	78380	Lelio R Paula	05/2013
8197	2^260369-1859713	78379	Enzo Doria	03/2016
8198	18634^16067+16067^18634	78374	Hans Havermann	02/2020
8199	14*10^78362+1089	78364	Jens K. Andersen	11/2007
8200	(2^260317+3542)/2	78363	Stefano Morozzi	01/2020
8201	(1942^23827-1)/1941	78346	Serge Batalov	08/2020
8202	5^112070-54	78334	Lelio R Paula	02/2015
8203	20120^7821+7821^20120	78333	Hans Havermann	03/2020
8204	(10^(239165+1)+5410^39165-1)/9	78331	Robert Price	04/2017
8205	(2^260195+3546)/2	78327	Stefano Morozzi	01/2020
8206	2^260182-113453	78323	Enzo Doria	07/2014
8207	f(16405)	78319	Robert Price	09/2017
8208	18547^16678+16678^18547	78309	Hans Havermann	02/2020
8209	(78557*2^260084+1)/519	78296	Lelio R Paula	06/2014
8211	10^78288+9^(78288+1)	78289	Robert Price	08/2016
8210	10^78288+39109	78289	Patrick De Geest	12/2016
8212	10^78288-216299	78288	Patrick De Geest	12/2016
8213	(2^260059+2430)/2	78286	Stefano Morozzi	01/2020
8214	(2^260056+1662)/2	78285	Stefano Morozzi	01/2020
8215	5^111997+36	78283	Lelio R Paula	02/2015
8216	(2^260017+1602)/2	78273	Stefano Morozzi	01/2020
8217	(2^260017+2162)/2	78273	Stefano Morozzi	01/2020
8218	23969^1842+1842^23969	78266	Hans Havermann	05/2020
8219	19297^11370+11370^19297	78265	Hans Havermann	05/2020
8220	(21^59183+1)/22	78252	Paul Bourdelais	03/2010
8221	19090^12561+12561^19090	78251	Hans Havermann	04/2020
8222	(88*10^78242-7)/9	78243	Robert Price	11/2014
8223	2*6^100547+7	78242	Lelio R Paula	10/2014
8224	(2^259913+3470)/2	78242	Stefano Morozzi	01/2020
8225	(2^259885+3726)/2	78233	Stefano Morozzi	01/2020
8226	2^259860-111089	78226	Enzo Doria	05/2014
8227	18226^18359+18359^18226	78223	Norbert Schneider	02/2020
8228	(2^259833+3342)/2	78218	Stefano Morozzi	01/2020
8229	37^49875-2	78215	Lelio R Paula	09/2013
8230	(13*10^78213+401)/9	78214	Robert Price	10/2017
8231	7*5^111893-4	78211	Lelio R Paula	10/2014
8232	(11*2^259809-1)/1437	78209	Lelio R Paula	02/2014
8233	7^92511-6	78181	Theodore Burton	11/2005
8234	(3^163859-4)/253	78179	Lelio R Paula	10/2012
8235	(2^259689+1346)/2	78174	Stefano Morozzi	01/2020
8236	(27*2^259666-1)/625691	78163	Lelio R Paula	02/2014
8237	(2^259642+3202)/2	78160	Stefano Morozzi	01/2020
8238	(2^259624+442)/2	78155	Stefano Morozzi	01/2020
8239	3*10^78146+17	78147	Robert Price	03/2017
8240	(2^259594+1558)/2	78146	Stefano Morozzi	01/2020
8241	(576^28307+1)/577	78137	Richard Fischer	01/2018
8242	2^259503+74333	78119	Enzo Doria	04/2016
8243	(2^259503+2438)/2	78118	Stefano Morozzi	01/2020
8244	(31*2^259504-1)/13365	78116	Lelio R Paula	02/2014
8246	(58547^16384+1)/2	78111	Lelio R Paula	11/2011
8245	6^100379+13	78111	Lelio R Paula	03/2015
8247	2^259469-109909	78108	Enzo Doria	04/2014
8248	15^66413-26	78108	Lelio R Paula	02/2015
8249	18550^16229+16229^18550	78101	Hans Havermann	05/2020
8250	7^92410-9266	78096	Mike Oakes	02/2010

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Probable Primes Top 10000

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