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 ?
9751	(21323^18181-1)/21322	78699	Serge Batalov	08/2020
9752	6^101128-16433	78693	Enzo Doria	02/2013
9753	20^60482+99	78689	Lelio R Paula	03/2015
9754	2^261348-110633	78674	Enzo Doria	05/2014
9755	191^34487+2	78666	Lelio R Paula	05/2013
9756	2^261305-110139	78661	Enzo Doria	04/2014
9757	(682*10^78656-7)/9	78658	Robert Price	08/2021
9758	(82*10^78635-1)/9	78636	Robert Price	12/2014
9759	10^78632+81	78633	Robert Price	03/2011
9760	10^78632-402693	78632	Patrick De Geest	07/2013
9761	3*10^78631+17	78632	Robert Price	03/2017
9762	2^261174-3911	78622	Yves Minet	04/2017
9763	2^261167+74843	78620	Enzo Doria	04/2016
9764	18810^15119+15119^18810	78617	Hans Havermann	04/2020
9765	L(376121)+F(376122)	78605	Henri Lifchitz	01/2007
9766	14^68580-29	78602	Lelio R Paula	02/2015
9767	(4270^21649-1)/4269	78592	Serge Batalov	08/2020
9768	20603^6522+6522^20603	78588	Hans Havermann	03/2020
9769	(2^261056+646)/2	78586	Stefano Morozzi	01/2020
9770	(73*10^78576-1)/9	78577	Robert Price	01/2015
9771	(2^261020+2158)/2	78575	Stefano Morozzi	01/2020
9772	(17*2^261026-1)/40451	78574	Lelio R Paula	02/2014
9773	(2415^23227-1)/2414	78572	Serge Batalov	08/2020
9775	2^261001-195	78570	Lelio R Paula	05/2012
9774	18532^17365+17365^18532	78570	Hans Havermann	02/2020
9776	5*2^260950+9	78555	Lelio R Paula	06/2014
9777	2^260931-7605	78549	Lelio R Paula	07/2013
9778	19863^9002+9002^19863	78546	Hans Havermann	02/2020
9779	15^66778-32	78538	Lelio R Paula	02/2015
9780	(11*2^260896-1)/245	78537	Lelio R Paula	02/2014
9781	30^53166+29	78533	Norbert Schneider	03/2017
9782	lucasU(2403,1,23229)-lucasU(2403,1,23228)	78529	Mike Oakes	05/2009
9783	18729^15592+15592^18729	78529	Hans Havermann	04/2020
9784	7*3^164574-2	78523	Lelio R Paula	06/2014
9785	18518^17385+17385^18518	78520	Hans Havermann	03/2020
9786	2^260830-112133	78518	Enzo Doria	06/2014
9787	13^70486+42	78518	Lelio R Paula	03/2015
9788	11^75386-7080	78507	Enzo Doria	01/2013
9790	(86^40583-1)/85	78506	Paul Bourdelais	08/2017
9789	(2^260790+1914)/2	78506	Stefano Morozzi	01/2020
9791	5*10^78504+11	78505	Robert Price	08/2019
9792	2^260711-58695	78482	Lelio R Paula	07/2013
9793	(2^260695+2258)/2	78477	Stefano Morozzi	01/2020
9794	2^260678-111065	78472	Enzo Doria	05/2014
9795	21560^4359+4359^21560	78466	Hans Havermann	02/2020
9796	18^62501-97	78456	Lelio R Paula	02/2015
9797	53^45498-2	78452	Lelio R Paula	08/2013
9798	(8890^19867-1)/8889	78449	Serge Batalov	08/2020
9799	(2^260549+642)/2	78433	Stefano Morozzi	01/2020
9800	(2^260527+3906)/2	78427	Stefano Morozzi	01/2020
9801	2^260513-111121	78423	Enzo Doria	05/2014
9802	37845!2-64	78412	Robert Price	06/2015
9803	2^260469-110695	78409	Enzo Doria	05/2014
9804	(11*10^78408-113)/3	78409	Robert Price	01/2017
9805	2^260447+8415	78403	Lelio R Paula	07/2013
9806	5*10^78395-69	78396	Robert Price	02/2021
9807	37837!2-64	78394	Robert Price	06/2015
9808	2^260410-111546435	78392	Paul Bourdelais	10/2021
9810	(19*2^260379-1)/53	78382	Lelio R Paula	02/2014
9811	2^260377-113233	78382	Enzo Doria	07/2014
9809	(2^260378+3750)/2	78382	Stefano Morozzi	01/2020
9813	9^82138+6^82138-2^82138	78380	Mike Oakes	08/2010
9812	69^42624+2	78380	Lelio R Paula	05/2013
9814	2^260369-1859713	78379	Enzo Doria	03/2016
9815	18634^16067+16067^18634	78374	Hans Havermann	02/2020
9816	14*10^78362+1089	78364	Jens K. Andersen	11/2007
9817	(2^260317+3542)/2	78363	Stefano Morozzi	01/2020
9818	(1942^23827-1)/1941	78346	Serge Batalov	08/2020
9819	5^112070-54	78334	Lelio R Paula	02/2015
9820	20120^7821+7821^20120	78333	Hans Havermann	03/2020
9821	(10^(239165+1)+5410^39165-1)/9	78331	Robert Price	04/2017
9822	(2^260195+3546)/2	78327	Stefano Morozzi	01/2020
9823	2^260182-113453	78323	Enzo Doria	07/2014
9824	f(16405)	78319	Robert Price	09/2017
9825	18547^16678+16678^18547	78309	Hans Havermann	02/2020
9826	(78557*2^260084+1)/519	78296	Lelio R Paula	06/2014
9828	10^78288+9^(78288+1)	78289	Robert Price	08/2016
9827	10^78288+39109	78289	Patrick De Geest	12/2016
9829	10^78288-216299	78288	Patrick De Geest	12/2016
9830	(2^260059+2430)/2	78286	Stefano Morozzi	01/2020
9831	(2^260056+1662)/2	78285	Stefano Morozzi	01/2020
9832	(376*70^42427-1)/3	78285	Eric Chen	10/2020
9833	5^111997+36	78283	Lelio R Paula	02/2015
9834	(2^260017+1602)/2	78273	Stefano Morozzi	01/2020
9835	(2^260017+2162)/2	78273	Stefano Morozzi	01/2020
9836	23969^1842+1842^23969	78266	Hans Havermann	05/2020
9837	19297^11370+11370^19297	78265	Hans Havermann	05/2020
9838	(21^59183+1)/22	78252	Paul Bourdelais	03/2010
9839	19090^12561+12561^19090	78251	Hans Havermann	04/2020
9840	(88*10^78242-7)/9	78243	Robert Price	11/2014
9841	2*6^100547+7	78242	Lelio R Paula	10/2014
9842	(2^259913+3470)/2	78242	Stefano Morozzi	01/2020
9843	(2^259885+3726)/2	78233	Stefano Morozzi	01/2020
9844	2^259860-111089	78226	Enzo Doria	05/2014
9845	18226^18359+18359^18226	78223	Norbert Schneider	02/2020
9846	(2^259833+3342)/2	78218	Stefano Morozzi	01/2020
9847	37^49875-2	78215	Lelio R Paula	09/2013
9848	(13*10^78213+401)/9	78214	Robert Price	10/2017
9849	7*5^111893-4	78211	Lelio R Paula	10/2014
9850	(11*2^259809-1)/1437	78209	Lelio R Paula	02/2014
9851	7^92511-6	78181	Theodore Burton	11/2005
9852	(3^163859-4)/253	78179	Lelio R Paula	10/2012
9853	(2^259689+1346)/2	78174	Stefano Morozzi	01/2020
9854	(27*2^259666-1)/625691	78163	Lelio R Paula	02/2014
9855	(2^259642+3202)/2	78160	Stefano Morozzi	01/2020
9856	(2^259624+442)/2	78155	Stefano Morozzi	01/2020
9857	3*10^78146+17	78147	Robert Price	03/2017
9858	(2^259594+1558)/2	78146	Stefano Morozzi	01/2020
9859	(576^28307+1)/577	78137	Richard Fischer	01/2018
9860	2^259503+74333	78119	Enzo Doria	04/2016
9861	(2^259503+2438)/2	78118	Stefano Morozzi	01/2020
9862	(31*2^259504-1)/13365	78116	Lelio R Paula	02/2014
9864	(58547^16384+1)/2	78111	Lelio R Paula	11/2011
9863	6^100379+13	78111	Lelio R Paula	03/2015
9865	2^259469-109909	78108	Enzo Doria	04/2014
9866	15^66413-26	78108	Lelio R Paula	02/2015
9867	18550^16229+16229^18550	78101	Hans Havermann	05/2020
9868	7^92410-9266	78096	Mike Oakes	02/2010
9869	2^259398+75799	78087	Enzo Doria	04/2016
9870	2^259394+1876189	78086	Enzo Doria	07/2016
9871	PIPrime(78073)	78073	Eric W. Weisstein	07/2006
9872	5*2^259344-7	78072	Lelio R Paula	06/2014
9873	(2^259347+990)/2	78071	Stefano Morozzi	01/2020
9874	21702^3955+3955^21702	78066	Hans Havermann	04/2020
9875	14^68097-87	78048	Lelio R Paula	02/2015
9876	2^259233-475573	78037	Paul Bourdelais	03/2013
9877	181^34554-2	78012	Lelio R Paula	10/2017
9878	3^163500-28	78010	Robert Price	12/2013
9879	(206*10^78005+7)/3	78007	Robert Price	07/2020
9880	(65*10^77992+691)/9	77993	Robert Price	08/2016
9881	(2^259035+3930)/2	77978	Stefano Morozzi	01/2020
9882	2^259013-112591	77971	Enzo Doria	06/2014
9883	7*10^77969-11	77970	Robert Price	10/2017
9884	(2^259011+2430)/2	77970	Stefano Morozzi	01/2020
9885	6^100193-100193^6	77966	Norbert Schneider	04/2017
9886	(2^258974+2638)/2	77959	Stefano Morozzi	01/2020
9887	24214^1657+1657^24214	77953	Hans Havermann	03/2020
9888	(2^258945+674)/2	77950	Stefano Morozzi	01/2020
9889	(2^258939+2450)/2	77949	Stefano Morozzi	01/2020
9890	18090^18307+18307^18090	77941	Norbert Schneider	02/2020
9891	(11259^19237-1)/11258	77935	Serge Batalov	08/2020
9892	2^258863-110235	77926	Enzo Doria	05/2014
9893	2^258852+1605	77923	Lelio R Paula	06/2013
9894	10^77919+238027	77920	Patrick De Geest	04/2020
9895	10^77919-123456789	77919	Robert Price	02/2020
9896	10^77919-25433	77919	Patrick De Geest	04/2020
9897	(11*10^77909+49)/3	77910	Robert Price	05/2016
9898	2*7^92187-9	77908	Lelio R Paula	10/2014
9899	2^258763-110155	77896	Enzo Doria	04/2014
9900	(2^258738+1062)/2	77888	Stefano Morozzi	01/2020
9901	2^258694-110387	77875	Enzo Doria	05/2014
9902	11^74773-94	77869	Lelio R Paula	02/2015
9903	6^100067+125	77868	Lelio R Paula	03/2015
9904	15^66205+8	77864	Lelio R Paula	07/2014
9905	(2^258637+17)/18605003	77851	Stefano Morozzi	03/2020
9906	5^111373-18136	77847	Enzo Doria	05/2014
9907	(2^258566+1974)/2	77836	Stefano Morozzi	01/2020
9908	2^258524-109877	77824	Enzo Doria	04/2014
9909	22828^2565+2565^22828	77823	Hans Havermann	04/2020
9910	(2^258515+3914)/2	77821	Stefano Morozzi	01/2020
9911	6^100002-16643	77817	Enzo Doria	02/2013
9912	(13*10^77811+347)/9	77812	Robert Price	10/2017
9913	11*10^77807+3	77809	Robert Price	07/2021
9914	19376^10365+10365^19376	77806	Hans Havermann	04/2020
9915	(29*10^77803+31)/3	77804	Robert Price	04/2021
9916	65^42916+28	77803	Lelio R Paula	01/2016
9917	(2^258405+3302)/2	77788	Stefano Morozzi	01/2020
9918	(89*10^77781-17)/9	77782	Robert Price	11/2015
9919	2^258382-110405	77781	Enzo Doria	05/2014
9920	5^111278-14996	77780	Enzo Doria	02/2013
9921	(2^258378+2314)/2	77780	Stefano Morozzi	01/2020
9922	14^67862+61	77779	Lelio R Paula	02/2015
9923	10^77777+48483	77778	Patrick De Geest	11/2010
9924	10^77777-183243	77777	Patrick De Geest	11/2010
9925	7((10^77777-1)/9)-814322	77777	Matt Stath	10/2020
9926	(27*2^258352+1)/43	77772	Lelio R Paula	08/2012
9927	(22329^17881-1)/22328	77758	Serge Batalov	08/2020
9928	(2^258294+2454)/2	77754	Stefano Morozzi	01/2020
9929	337^30756-10002	77740	Enzo Doria	07/2012
9930	10^77726+99	77727	Robert Price	03/2011
9931	10^77726-85947	77726	Patrick De Geest	06/2013
9932	89^39870-2	77723	Lelio R Paula	08/2013
9933	7^91966-32	77721	Lelio R Paula	02/2015
9934	35^50327+2	77709	Lelio R Paula	05/2013
9936	24^56298+23	77704	Norbert Schneider	12/2016
9935	(2^258128+3502)/2	77704	Stefano Morozzi	01/2020
9937	(2^258105+78557)/19	77697	Lelio R Paula	10/2012
9938	(2^258102+2842)/2	77697	Stefano Morozzi	01/2020
9939	2^258079+179	77690	Lelio R Paula	03/2012
9940	2^258062-113111	77685	Enzo Doria	07/2014
9941	(21752^17911-1)/21751	77685	Serge Batalov	08/2020
9942	(2^258022+2422)/2	77673	Stefano Morozzi	01/2020
9943	10^77669+123456789	77670	Robert Price	10/2019
9944	10^77669+59127	77670	Patrick De Geest	12/2019
9945	10^77669-109103	77669	Patrick De Geest	12/2019
9946	(2^258002+3822)/2	77667	Stefano Morozzi	01/2020
9947	80^40807-79	77660	Norbert Schneider	03/2015
9948	70385!4-4	77658	Robert Price	11/2019
9949	(10^77637+359)/9	77637	Serge Batalov	12/2014
9950	(10^77650+7)/29/89489773/108148639	77633	Alfred Reich	06/2021
9951	2^257862-165	77625	Lelio R Paula	03/2012
9952	(25*2^257853+1)/3	77623	Lelio R Paula	07/2012
9953	(2^257832+1362)/2	77615	Stefano Morozzi	01/2020
9954	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
9955	6^99728+71	77604	Lelio R Paula	01/2015
9956	2^257778-112767	77599	Enzo Doria	06/2014
9957	(31*2^257771+1)/537	77596	Lelio R Paula	07/2012
9958	(2^257762+2214)/2	77594	Stefano Morozzi	01/2020
9959	2^257729-73	77585	Lelio R Paula	03/2012
9960	(2^257728+1890)/2	77584	Stefano Morozzi	01/2020
9961	2^257689-63	77573	Lelio R Paula	03/2012
9962	(47*10^77572+493)/9	77573	Robert Price	11/2017
9963	91*10^77563-9	77565	Robert Price	06/2021
9964	(78557*2^257665+1)/6108725	77564	Lelio R Paula	06/2014
9965	(5570^20707-1)/5569	77562	Serge Batalov	08/2020
9966	2^257650+111546435	77561	Paul Bourdelais	10/2021
9967	(3^162563+8)/2885	77559	Lelio R Paula	10/2012
9968	2^257636-110235	77557	Enzo Doria	05/2014
9969	(23*10^77556+97)/3	77557	Robert Price	02/2017
9970	(2^257639+2630)/2	77557	Stefano Morozzi	01/2020
9971	(2^257625+3354)/2	77553	Stefano Morozzi	01/2020
9972	2^257621-110071	77552	Enzo Doria	04/2014
9973	19580^9129+9129^19580	77546	Hans Havermann	03/2020
9974	2^257567-64875	77536	Lelio R Paula	06/2013
9975	(18098^18211-1)/18097	77532	Serge Batalov	08/2020
9976	(2^257429+2394)/2	77494	Stefano Morozzi	01/2020
9977	(2^257373+1206)/2	77477	Stefano Morozzi	01/2020
9978	2*7^91674+9	77474	Lelio R Paula	10/2014
9979	(2^257248+2442)/2	77440	Stefano Morozzi	01/2020
9980	(17*10^77427-47)/3	77428	Robert Price	05/2017
9981	10^77418+841683	77419	Patrick De Geest	06/2013
9982	10^77418-33	77418	Robert Price	05/2011
9983	19^60539-36	77415	Lelio R Paula	03/2015
9984	(9562^19447-1)/9561	77406	Serge Batalov	08/2020
9985	37401!!-1024	77397	Robert Price	11/2015
9986	(2^257095+1410)/2	77394	Stefano Morozzi	01/2020
9987	11^74313-18750	77390	Enzo Doria	12/2012
9988	2^257044-112883	77378	Enzo Doria	06/2014
9989	8*10^77377+51	77378	Robert Price	05/2017
9990	Phi(258121,2)/719	77375	Jeppe Stig Nielsen	09/2020
9991	2*7^91553+9	77372	Lelio R Paula	10/2014
9992	713^27118+27118^713	77371	Norbert Schneider	12/2016
9993	(22711^17761-1)/22710	77367	Serge Batalov	08/2020
9994	18652^14043+14043^18652	77359	Hans Havermann	03/2020
9995	(11391^19069-1)/11390	77351	Serge Batalov	08/2020
9996	6*10^77346-29	77347	Robert Price	08/2020
9997	2^256920-111155	77341	Enzo Doria	05/2014
9998	2^256896-6555	77334	Lelio R Paula	06/2013
9999	(52*10^77322-7)/9	77323	Robert Price	12/2014
10000	2^256849-112939	77320	Enzo Doria	06/2014

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PRP Records

Probable Primes Top 10000

(288515 PRPs in the top)