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 ?
8501	(2^261724+60031)/13/31/7024877	78778	Tony Prest / Never Odd Or Even	04/2014
8502	(2^261724+121879)/5/789433217	78778	Tony Prest / Never Odd Or Even	04/2014
8503	(2^261724+290135)/3/3/8467/9059	78778	Tony Prest / Never Odd Or Even	04/2014
8504	(2^261724+79857)/59/3847/165331	78777	Tony Prest / Never Odd Or Even	04/2014
8505	(2^261724+22883)/3/17/23/2351/10079	78777	Tony Prest / Never Odd Or Even	04/2014
8506	(2^261724+154799)/3/5/3655653719	78777	Tony Prest / Never Odd Or Even	04/2014
8507	(2^261724+391001)/3/11/17/41/43/24071	78777	Tony Prest / Never Odd Or Even	04/2014
8508	(2^261724+622383)/34843/550717	78777	Tony Prest / Never Odd Or Even	05/2014
8509	(2^261724+302829)/5/37/37/37078147	78776	Tony Prest / Never Odd Or Even	04/2014
8510	(2^261724+315837)/43/2176136243	78776	Tony Prest / Never Odd Or Even	04/2014
8511	(2^261724+582373)/53/307/311/32117	78776	Tony Prest / Never Odd Or Even	05/2014
8512	(2^261724+295283)/3/3/3/29/43/17812273	78775	Tony Prest / Never Odd Or Even	04/2014
8513	(2^261724+27491)/3/22787/105978449	78774	Tony Prest / Never Odd Or Even	04/2014
8514	(2^261724+392751)/193813/287826689	78774	Tony Prest / Never Odd Or Even	04/2014
8515	(2^261724+328501)/7/1091/31495610519	78773	Tony Prest / Never Odd Or Even	04/2014
8516	(2^261724+111267)/19/4637/15140560427	78772	Tony Prest / Never Odd Or Even	04/2014
8517	(2^261724+572133)/127/131/73787752333	78772	Tony Prest / Never Odd Or Even	05/2014
8518	(2^261724+608733)/59/7079/18451/909151	78771	Tony Prest / Never Odd Or Even	05/2014
8519	(2^261724+255449)/3/3/5/7/1759/10177/33158869	78770	Tony Prest / Never Odd Or Even	04/2014
8520	(2^261724+99509)/3/5/5/6507271/6749659289	78769	Tony Prest / Never Odd Or Even	04/2014
8521	(2^261724+52501)/563/53939/27942831391	78769	Tony Prest / Never Odd Or Even	04/2014
8522	(2^261724+117089)/3/5/37/149/967/2027/4163741	78769	Tony Prest / Never Odd Or Even	04/2014
8523	(2^261724+372571)/1487/9209/21559/2263249	78769	Tony Prest / Never Odd Or Even	04/2014
8524	(2^261724+184549)/5/8699/44053/1409322997	78769	Tony Prest / Never Odd Or Even	04/2014
8525	(2^261724+363351)/937/159683/59523200227	78768	Tony Prest / Never Odd Or Even	04/2014
8526	(2^261724+326501)/3/43/193/263/19403/253501403	78768	Tony Prest / Never Odd Or Even	04/2014
8527	(2^261724+629477)/3/17/17/137/263/1993/16187/57347	78768	Tony Prest / Never Odd Or Even	05/2014
8528	(2^261724+94871)/3/3/13/6734017/1673425245787	78766	Tony Prest / Never Odd Or Even	04/2014
8529	(2^261724+25981)/577/1181/3643/517786334743	78766	Tony Prest / Never Odd Or Even	04/2014
8531	(23*2^261642+1)/93	78762	Lelio R Paula	10/2012
8530	(2^261724+351227)/3/3/3/3/71/13997/9595373/8193978007	78762	Tony Prest / Never Odd Or Even	04/2014
8532	(2^261724+22571)/3/7243/7321/18046081/45730741211	78761	Tony Prest / Never Odd Or Even	04/2014
8533	(2^261724+56495)/3/3/3/7/7/13/9041/512818459/23708589119	78760	Tony Prest / Never Odd Or Even	04/2014
8534	71293!4-4	78759	Robert Price	11/2019
8535	(2^261630+3582)/2	78759	Stefano Morozzi	01/2020
8536	(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/1036020834127	78750	Tony Prest / Never Odd Or Even	05/2014
8537	(2^261536+846)/2	78730	Stefano Morozzi	01/2020
8538	2^261507-2287	78722	Yves Minet	04/2009
8539	8*10^78717+39	78718	Robert Price	01/2017
8540	(78557*2^261440+1)/3	78706	Lelio R Paula	06/2014
8541	(290^31963-1)/289	78704	Serge Batalov	08/2020
8542	(21323^18181-1)/21322	78699	Serge Batalov	08/2020
8543	6^101128-16433	78693	Enzo Doria	02/2013
8544	20^60482+99	78689	Lelio R Paula	03/2015
8545	2^261348-110633	78674	Enzo Doria	05/2014
8546	191^34487+2	78666	Lelio R Paula	05/2013
8547	2^261305-110139	78661	Enzo Doria	04/2014
8548	(82*10^78635-1)/9	78636	Robert Price	12/2014
8549	10^78632+81	78633	Robert Price	03/2011
8550	10^78632-402693	78632	Patrick De Geest	07/2013
8551	3*10^78631+17	78632	Robert Price	03/2017
8552	2^261174-3911	78622	Yves Minet	04/2017
8553	2^261167+74843	78620	Enzo Doria	04/2016
8554	18810^15119+15119^18810	78617	Hans Havermann	04/2020
8555	L(376121)+F(376122)	78605	Henri Lifchitz	01/2007
8556	14^68580-29	78602	Lelio R Paula	02/2015
8557	(4270^21649-1)/4269	78592	Serge Batalov	08/2020
8558	20603^6522+6522^20603	78588	Hans Havermann	03/2020
8559	(2^261056+646)/2	78586	Stefano Morozzi	01/2020
8560	(73*10^78576-1)/9	78577	Robert Price	01/2015
8561	(2^261020+2158)/2	78575	Stefano Morozzi	01/2020
8562	(17*2^261026-1)/40451	78574	Lelio R Paula	02/2014
8563	(2415^23227-1)/2414	78572	Serge Batalov	08/2020
8565	2^261001-195	78570	Lelio R Paula	05/2012
8564	18532^17365+17365^18532	78570	Hans Havermann	02/2020
8566	5*2^260950+9	78555	Lelio R Paula	06/2014
8567	2^260931-7605	78549	Lelio R Paula	07/2013
8568	19863^9002+9002^19863	78546	Hans Havermann	02/2020
8569	15^66778-32	78538	Lelio R Paula	02/2015
8570	(11*2^260896-1)/245	78537	Lelio R Paula	02/2014
8571	30^53166+29	78533	Norbert Schneider	03/2017
8573	lucasU(2403,1,23229)-lucasU(2403,1,23228)	78529	Mike Oakes	05/2009
8572	18729^15592+15592^18729	78529	Hans Havermann	04/2020
8574	7*3^164574-2	78523	Lelio R Paula	06/2014
8575	18518^17385+17385^18518	78520	Hans Havermann	03/2020
8576	2^260830-112133	78518	Enzo Doria	06/2014
8577	13^70486+42	78518	Lelio R Paula	03/2015
8578	11^75386-7080	78507	Enzo Doria	01/2013
8580	(86^40583-1)/85	78506	Paul Bourdelais	08/2017
8579	(2^260790+1914)/2	78506	Stefano Morozzi	01/2020
8581	5*10^78504+11	78505	Robert Price	08/2019
8582	2^260711-58695	78482	Lelio R Paula	07/2013
8583	(2^260695+2258)/2	78477	Stefano Morozzi	01/2020
8584	2^260678-111065	78472	Enzo Doria	05/2014
8585	21560^4359+4359^21560	78466	Hans Havermann	02/2020
8586	18^62501-97	78456	Lelio R Paula	02/2015
8587	53^45498-2	78452	Lelio R Paula	08/2013
8588	(8890^19867-1)/8889	78449	Serge Batalov	08/2020
8589	(2^260549+642)/2	78433	Stefano Morozzi	01/2020
8590	(2^260527+3906)/2	78427	Stefano Morozzi	01/2020
8591	2^260513-111121	78423	Enzo Doria	05/2014
8592	37845!2-64	78412	Robert Price	06/2015
8593	2^260469-110695	78409	Enzo Doria	05/2014
8594	(11*10^78408-113)/3	78409	Robert Price	01/2017
8595	2^260447+8415	78403	Lelio R Paula	07/2013
8596	37837!2-64	78394	Robert Price	06/2015
8597	(19*2^260379-1)/53	78382	Lelio R Paula	02/2014
8598	2^260377-113233	78382	Enzo Doria	07/2014
8599	(2^260378+3750)/2	78382	Stefano Morozzi	01/2020
8601	9^82138+6^82138-2^82138	78380	Mike Oakes	08/2010
8600	69^42624+2	78380	Lelio R Paula	05/2013
8602	2^260369-1859713	78379	Enzo Doria	03/2016
8603	18634^16067+16067^18634	78374	Hans Havermann	02/2020
8604	14*10^78362+1089	78364	Jens K. Andersen	11/2007
8605	(2^260317+3542)/2	78363	Stefano Morozzi	01/2020
8606	(1942^23827-1)/1941	78346	Serge Batalov	08/2020
8607	5^112070-54	78334	Lelio R Paula	02/2015
8608	20120^7821+7821^20120	78333	Hans Havermann	03/2020
8609	(10^(239165+1)+5410^39165-1)/9	78331	Robert Price	04/2017
8610	(2^260195+3546)/2	78327	Stefano Morozzi	01/2020
8611	2^260182-113453	78323	Enzo Doria	07/2014
8612	f(16405)	78319	Robert Price	09/2017
8613	18547^16678+16678^18547	78309	Hans Havermann	02/2020
8614	(78557*2^260084+1)/519	78296	Lelio R Paula	06/2014
8616	10^78288+9^(78288+1)	78289	Robert Price	08/2016
8615	10^78288+39109	78289	Patrick De Geest	12/2016
8617	10^78288-216299	78288	Patrick De Geest	12/2016
8618	(2^260059+2430)/2	78286	Stefano Morozzi	01/2020
8619	(2^260056+1662)/2	78285	Stefano Morozzi	01/2020
8620	(376*70^42427-1)/3	78285	Eric Chen	10/2020
8621	5^111997+36	78283	Lelio R Paula	02/2015
8622	(2^260017+1602)/2	78273	Stefano Morozzi	01/2020
8623	(2^260017+2162)/2	78273	Stefano Morozzi	01/2020
8624	23969^1842+1842^23969	78266	Hans Havermann	05/2020
8625	19297^11370+11370^19297	78265	Hans Havermann	05/2020
8626	(21^59183+1)/22	78252	Paul Bourdelais	03/2010
8627	19090^12561+12561^19090	78251	Hans Havermann	04/2020
8628	(88*10^78242-7)/9	78243	Robert Price	11/2014
8629	2*6^100547+7	78242	Lelio R Paula	10/2014
8630	(2^259913+3470)/2	78242	Stefano Morozzi	01/2020
8631	(2^259885+3726)/2	78233	Stefano Morozzi	01/2020
8632	2^259860-111089	78226	Enzo Doria	05/2014
8633	18226^18359+18359^18226	78223	Norbert Schneider	02/2020
8634	(2^259833+3342)/2	78218	Stefano Morozzi	01/2020
8635	37^49875-2	78215	Lelio R Paula	09/2013
8636	(13*10^78213+401)/9	78214	Robert Price	10/2017
8637	7*5^111893-4	78211	Lelio R Paula	10/2014
8638	(11*2^259809-1)/1437	78209	Lelio R Paula	02/2014
8639	7^92511-6	78181	Theodore Burton	11/2005
8640	(3^163859-4)/253	78179	Lelio R Paula	10/2012
8641	(2^259689+1346)/2	78174	Stefano Morozzi	01/2020
8642	(27*2^259666-1)/625691	78163	Lelio R Paula	02/2014
8643	(2^259642+3202)/2	78160	Stefano Morozzi	01/2020
8644	(2^259624+442)/2	78155	Stefano Morozzi	01/2020
8645	3*10^78146+17	78147	Robert Price	03/2017
8646	(2^259594+1558)/2	78146	Stefano Morozzi	01/2020
8647	(576^28307+1)/577	78137	Richard Fischer	01/2018
8648	2^259503+74333	78119	Enzo Doria	04/2016
8649	(2^259503+2438)/2	78118	Stefano Morozzi	01/2020
8650	(31*2^259504-1)/13365	78116	Lelio R Paula	02/2014
8652	(58547^16384+1)/2	78111	Lelio R Paula	11/2011
8651	6^100379+13	78111	Lelio R Paula	03/2015
8653	2^259469-109909	78108	Enzo Doria	04/2014
8654	15^66413-26	78108	Lelio R Paula	02/2015
8655	18550^16229+16229^18550	78101	Hans Havermann	05/2020
8656	7^92410-9266	78096	Mike Oakes	02/2010
8657	2^259398+75799	78087	Enzo Doria	04/2016
8658	2^259394+1876189	78086	Enzo Doria	07/2016
8659	PIPrime(78073)	78073	Eric W. Weisstein	07/2006
8660	5*2^259344-7	78072	Lelio R Paula	06/2014
8661	(2^259347+990)/2	78071	Stefano Morozzi	01/2020
8662	21702^3955+3955^21702	78066	Hans Havermann	04/2020
8663	14^68097-87	78048	Lelio R Paula	02/2015
8664	2^259233-475573	78037	Paul Bourdelais	03/2013
8665	181^34554-2	78012	Lelio R Paula	10/2017
8666	3^163500-28	78010	Robert Price	12/2013
8667	(206*10^78005+7)/3	78007	Robert Price	07/2020
8668	(65*10^77992+691)/9	77993	Robert Price	08/2016
8669	(2^259035+3930)/2	77978	Stefano Morozzi	01/2020
8670	2^259013-112591	77971	Enzo Doria	06/2014
8672	7*10^77969-11	77970	Robert Price	10/2017
8671	(2^259011+2430)/2	77970	Stefano Morozzi	01/2020
8673	6^100193-100193^6	77966	Norbert Schneider	04/2017
8674	(2^258974+2638)/2	77959	Stefano Morozzi	01/2020
8675	24214^1657+1657^24214	77953	Hans Havermann	03/2020
8676	(2^258945+674)/2	77950	Stefano Morozzi	01/2020
8677	(2^258939+2450)/2	77949	Stefano Morozzi	01/2020
8678	18090^18307+18307^18090	77941	Norbert Schneider	02/2020
8679	(11259^19237-1)/11258	77935	Serge Batalov	08/2020
8680	2^258863-110235	77926	Enzo Doria	05/2014
8681	2^258852+1605	77923	Lelio R Paula	06/2013
8682	10^77919+238027	77920	Patrick De Geest	04/2020
8683	10^77919-123456789	77919	Robert Price	02/2020
8684	10^77919-25433	77919	Patrick De Geest	04/2020
8685	(11*10^77909+49)/3	77910	Robert Price	05/2016
8686	2*7^92187-9	77908	Lelio R Paula	10/2014
8687	2^258763-110155	77896	Enzo Doria	04/2014
8688	(2^258738+1062)/2	77888	Stefano Morozzi	01/2020
8689	2^258694-110387	77875	Enzo Doria	05/2014
8690	11^74773-94	77869	Lelio R Paula	02/2015
8691	6^100067+125	77868	Lelio R Paula	03/2015
8692	15^66205+8	77864	Lelio R Paula	07/2014
8693	(2^258637+17)/18605003	77851	Stefano Morozzi	03/2020
8694	5^111373-18136	77847	Enzo Doria	05/2014
8695	(2^258566+1974)/2	77836	Stefano Morozzi	01/2020
8696	2^258524-109877	77824	Enzo Doria	04/2014
8697	22828^2565+2565^22828	77823	Hans Havermann	04/2020
8698	(2^258515+3914)/2	77821	Stefano Morozzi	01/2020
8699	6^100002-16643	77817	Enzo Doria	02/2013
8700	(13*10^77811+347)/9	77812	Robert Price	10/2017
8701	19376^10365+10365^19376	77806	Hans Havermann	04/2020
8702	65^42916+28	77803	Lelio R Paula	01/2016
8703	(2^258405+3302)/2	77788	Stefano Morozzi	01/2020
8704	(89*10^77781-17)/9	77782	Robert Price	11/2015
8705	2^258382-110405	77781	Enzo Doria	05/2014
8707	5^111278-14996	77780	Enzo Doria	02/2013
8706	(2^258378+2314)/2	77780	Stefano Morozzi	01/2020
8708	14^67862+61	77779	Lelio R Paula	02/2015
8709	10^77777+48483	77778	Patrick De Geest	11/2010
8710	10^77777-183243	77777	Patrick De Geest	11/2010
8711	7((10^77777-1)/9)-814322	77777	Matt Stath	10/2020
8712	(27*2^258352+1)/43	77772	Lelio R Paula	08/2012
8713	(22329^17881-1)/22328	77758	Serge Batalov	08/2020
8714	(2^258294+2454)/2	77754	Stefano Morozzi	01/2020
8715	337^30756-10002	77740	Enzo Doria	07/2012
8716	10^77726+99	77727	Robert Price	03/2011
8717	10^77726-85947	77726	Patrick De Geest	06/2013
8718	89^39870-2	77723	Lelio R Paula	08/2013
8719	7^91966-32	77721	Lelio R Paula	02/2015
8720	35^50327+2	77709	Lelio R Paula	05/2013
8722	24^56298+23	77704	Norbert Schneider	12/2016
8721	(2^258128+3502)/2	77704	Stefano Morozzi	01/2020
8724	(2^258105+78557)/19	77697	Lelio R Paula	10/2012
8723	(2^258102+2842)/2	77697	Stefano Morozzi	01/2020
8725	2^258079+179	77690	Lelio R Paula	03/2012
8727	2^258062-113111	77685	Enzo Doria	07/2014
8726	(21752^17911-1)/21751	77685	Serge Batalov	08/2020
8728	(2^258022+2422)/2	77673	Stefano Morozzi	01/2020
8729	10^77669+123456789	77670	Robert Price	10/2019
8730	10^77669+59127	77670	Patrick De Geest	12/2019
8731	10^77669-109103	77669	Patrick De Geest	12/2019
8732	(2^258002+3822)/2	77667	Stefano Morozzi	01/2020
8733	80^40807-79	77660	Norbert Schneider	03/2015
8734	70385!4-4	77658	Robert Price	11/2019
8735	(10^77637+359)/9	77637	Serge Batalov	12/2014
8736	2^257862-165	77625	Lelio R Paula	03/2012
8737	(25*2^257853+1)/3	77623	Lelio R Paula	07/2012
8738	(2^257832+1362)/2	77615	Stefano Morozzi	01/2020
8739	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
8740	6^99728+71	77604	Lelio R Paula	01/2015
8741	2^257778-112767	77599	Enzo Doria	06/2014
8742	(31*2^257771+1)/537	77596	Lelio R Paula	07/2012
8743	(2^257762+2214)/2	77594	Stefano Morozzi	01/2020
8744	2^257729-73	77585	Lelio R Paula	03/2012
8745	(2^257728+1890)/2	77584	Stefano Morozzi	01/2020
8747	2^257689-63	77573	Lelio R Paula	03/2012
8746	(47*10^77572+493)/9	77573	Robert Price	11/2017
8748	(78557*2^257665+1)/6108725	77564	Lelio R Paula	06/2014
8749	(5570^20707-1)/5569	77562	Serge Batalov	08/2020
8750	(3^162563+8)/2885	77559	Lelio R Paula	10/2012

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