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	2^238541-112723	71808	Enzo Doria	06/2014
9752	2^238529-15949	71805	Enzo Doria	04/2013
9753	9*5^102721-8	71800	Lelio R Paula	10/2014
9754	2^238494-165	71794	Lelio R Paula	02/2012
9755	18035^9562+9562^18035	71790	Hans Havermann	10/2019
9756	18390^7993+7993^18390	71771	Hans Havermann	11/2019
9757	2^238389-110905	71763	Enzo Doria	05/2014
9758	(145*10^71760-1)/9	71762	Serge Batalov	12/2014
9759	7^84913+5062	71760	Mike Oakes	02/2010
9760	21218^2409+2409^21218	71756	Hans Havermann	10/2019
9761	(F(11446)^31-F(11445)^31)/F(11444)	71753	Wayne Halsdorf	03/2012
9762	(1227^23227-1)/1226	71742	Serge Batalov	08/2020
9763	2^238268-97305	71726	Lelio R Paula	05/2012
9764	gcd(V(1330365),5F(266073)(F(266073)-1)+1)	71724	Serge Batalov	04/2015
9765	(2^238249+3770)/2	71720	Stefano Morozzi	01/2020
9766	2^238235-113247	71716	Enzo Doria	07/2014
9767	2*12^66450-5^66450	71712	Mike Oakes	11/2010
9768	(2^238213+lucasV(1,2,238213)+1)/4	71709	Mike Oakes	11/2016
9769	2^238199-111817	71706	Enzo Doria	05/2014
9770	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
9771	2^238144+98765331	71689	Jason Earls	01/2009
9772	(2^238137+2810)/2	71687	Stefano Morozzi	01/2020
9773	18^57102-4265	71679	Enzo Doria	03/2013
9774	(73*10^71670-1)/9	71671	Robert Price	01/2015
9775	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
9776	2^238067-111925	71666	Enzo Doria	05/2014
9777	(2^238024+3690)/2	71653	Stefano Morozzi	01/2020
9778	(7388^18523-1)/7387	71653	Serge Batalov	08/2020
9779	19143^5528+5528^19143	71644	Hans Havermann	10/2019
9780	65401!4+128	71638	Robert Price	09/2019
9781	36^46030+35	71637	Norbert Schneider	04/2014
9782	(74*10^71621+313)/9	71622	Robert Price	11/2017
9783	2^237905-91	71617	Lelio R Paula	02/2012
9784	(31*2^237902-1)/123	71616	Lelio R Paula	01/2014
9785	(15185*2^237866-1)/43967	71605	Lelio R Paula	04/2015
9786	16696^16957+16957^16696	71603	Norbert Schneider	09/2019
9787	(24737*2^237841+1)/25	71601	Lelio R Paula	06/2014
9788	2^237846+1299	71599	Lelio R Paula	05/2012
9789	6^92004+199801	71594	Mike Oakes	02/2011
9790	159^32516+2	71581	Lelio R Paula	05/2013
9791	2^237781+855	71580	Lelio R Paula	05/2012
9792	(2^237754+814)/2	71571	Stefano Morozzi	01/2020
9793	2^237720-4079	71561	Yves Minet	06/2011
9794	2^237698-110945	71555	Enzo Doria	05/2014
9795	2^237695-113239	71554	Enzo Doria	07/2014
9796	8*5^102362-9	71549	Lelio R Paula	10/2014
9797	(4*10^71546-31)/9	71546	Erik Branger	05/2011
9798	2^237650+37	71540	Lelio R Paula	02/2012
9799	18^56977-4391	71522	Enzo Doria	03/2013
9801	(22699*2^237565+1)/4136637	71512	Lelio R Paula	06/2014
9800	((1+sqrt(7)+sqrt(6))^48479-1)((1+sqrt(7)-sqrt(6))^48479-1)((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(7	71512	Mike Oakes	05/2009
9802	(26*10^71503+7)/3	71504	Erik Branger	11/2013
9803	(4*10^71498+173)/3	71499	Robert Price	01/2017
9804	3^149848+110	71496	Lelio R Paula	11/2014
9805	2^237498+513	71495	Lelio R Paula	05/2012
9806	2^237485+107	71491	Lelio R Paula	02/2012
9807	(2^237465+9)/2419	71481	Lelio R Paula	05/2012
9808	2^237439-112237	71477	Enzo Doria	06/2014
9809	(2^237427+2510)/2	71473	Stefano Morozzi	01/2020
9810	2^237407-9787	71467	Lelio R Paula	11/2009
9811	2^237383+72953	71460	Enzo Doria	04/2016
9812	19768^4119+4119^19768	71458	Hans Havermann	11/2019
9813	82^37337-81^37337	71457	Robert Price	01/2015
9814	(1017*2^237313-1)/19	71441	Lelio R Paula	04/2015
9815	2^237311+191	71438	Lelio R Paula	02/2012
9816	11699^17560+17560^11699	71437	Norbert Schneider	09/2019
9817	(25188^16231-1)/25187	71432	Serge Batalov	08/2020
9818	2^237280-59	71429	Lelio R Paula	02/2012
9819	(2^237275+1038)/2	71427	Stefano Morozzi	01/2020
9820	(2^237265+2774)/2	71424	Stefano Morozzi	01/2020
9821	11^68564-98	71403	Lelio R Paula	01/2015
9822	2^237173+74801	71397	Enzo Doria	04/2016
9823	(2^237150+1458)/2	71389	Stefano Morozzi	01/2020
9824	15^60697+56	71386	Lelio R Paula	01/2015
9825	2^237118+177	71380	Lelio R Paula	02/2012
9826	2^237110+69	71378	Lelio R Paula	02/2012
9827	15^60690-58	71377	Lelio R Paula	01/2015
9828	(5*2^237125-1)/599851191	71374	Lelio R Paula	01/2014
9829	20311^3262+3262^20311	71363	Hans Havermann	11/2019
9830	(3^149567+2)/539	71359	Lelio R Paula	06/2012
9831	(5*10^71357-143)/3	71358	Robert Price	04/2016
9832	2^237039-114621	71356	Enzo Doria	05/2015
9833	(2^237037+3462)/2	71355	Stefano Morozzi	01/2020
9834	12^66116-37	71352	Lelio R Paula	02/2015
9835	(3^149497+2^149497)/5	71328	Jean-Louis Charton	10/2010
9836	2^236941-66945	71327	Lelio R Paula	05/2012
9837	2^236911-1147	71318	Yves Minet	10/2009
9838	65^39337+42	71315	Lelio R Paula	01/2016
9839	(13319^17291-1)/13318	71313	Serge Batalov	08/2020
9840	(2^236863+3234)/2	71303	Stefano Morozzi	01/2020
9841	6*10^71299+7	71300	Dmitry Domanov	11/2010
9842	(25*2^236843+1)/3753	71295	Lelio R Paula	06/2012
9843	10^71291+15187	71292	Patrick De Geest	03/2016
9845	10^71291-5587309119	71291	Robert Price	03/2015
9844	10^71291-273581	71291	Patrick De Geest	03/2016
9846	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
9847	(2^236781+1514)/2	71278	Stefano Morozzi	01/2020
9848	(2^236775+2886)/2	71277	Stefano Morozzi	01/2020
9849	15105^17054+17054^15105	71271	Norbert Schneider	08/2018
9850	(2^236738+9)/13	71265	Lelio R Paula	05/2012
9851	5^101949+42	71260	Lelio R Paula	07/2014
9852	(9811^17851-1)/9810	71253	Serge Batalov	08/2020
9853	7*10^71238-39	71239	Robert Price	07/2020
9854	5*10^71237+9	71238	Dmitry Domanov	11/2010
9855	2^236634-16025	71234	Enzo Doria	04/2013
9856	71^38478+70	71233	Norbert Schneider	12/2014
9857	9*7^84280+8	71226	Lelio R Paula	10/2014
9858	(2^236603+2378)/2	71225	Stefano Morozzi	01/2020
9859	(10^71223+59)/3	71223	Serge Batalov	12/2014
9860	23260^1153+1153^23260	71219	Hans Havermann	10/2019
9861	(15185*2^236569-1)/453	71216	Lelio R Paula	04/2015
9862	51829#+(216091#)/(51829#)	71208	Makoto Morimoto	03/2016
9863	2^236528-173	71203	Lelio R Paula	02/2012
9864	3*2^236511-5	71198	Lelio R Paula	04/2014
9865	2^236477-99	71187	Lelio R Paula	02/2012
9866	11^68356-2130	71186	Enzo Doria	12/2012
9867	15128^17031+17031^15128	71186	Norbert Schneider	08/2018
9868	11^68355-3120	71185	Enzo Doria	12/2012
9869	(2^236463+998)/2	71183	Stefano Morozzi	01/2020
9870	36^45737-35^45737	71181	Robert Price	10/2012
9871	(3^149183-lucasV(1,3,149183)+1)/3	71178	Paul Vanderveen	12/2017
9872	2^236432+25	71174	Lelio R Paula	02/2012
9873	5^101818-12806	71168	Enzo Doria	02/2013
9874	(7*10^71166-457)/9	71166	Robert Price	09/2017
9875	65^39253+62	71163	Lelio R Paula	01/2016
9876	39^44718+38	71150	Norbert Schneider	05/2014
9877	18996^5557+5557^18996	71137	Hans Havermann	10/2019
9878	64983!4-256	71135	Robert Price	11/2019
9879	2^236296-407	71133	Yves Minet	02/2012
9880	2^236286-117	71130	Lelio R Paula	02/2012
9881	(2^236283+1074)/2	71128	Stefano Morozzi	01/2020
9882	2^236257-111193	71121	Enzo Doria	05/2014
9883	7^84149-36	71115	Lelio R Paula	08/2014
9885	164176#-p(164176)	71108	Henri Lifchitz	12/2018
9884	(2^236214+2934)/2	71108	Stefano Morozzi	01/2020
9886	2^236209-112123	71106	Enzo Doria	06/2014
9887	18^56644-4985	71104	Enzo Doria	03/2013
9888	(46*10^71077+521)/9	71078	Robert Price	08/2017
9889	21^53753+2	71074	Ray Chandler	08/2011
9890	(5482^19009-1)/5481	71070	Serge Batalov	08/2020
9891	(86*10^71068-311)/9	71069	Robert Price	10/2017
9892	2^236081-110923	71068	Enzo Doria	05/2014
9893	(293*27^49642-1736)/13	71058	Curtis Bright	05/2015
9894	65^39192+22	71052	Lelio R Paula	01/2016
9895	(2^236016+1246)/2	71048	Stefano Morozzi	01/2020
9896	(439#+1)^397-439#^397	71038	Mike Oakes	11/2010
9897	7^84050-2	71031	Lelio R Paula	09/2013
9898	15813^16916+16916^15813	71031	Norbert Schneider	09/2019
9899	(2^235956+3978)/2	71030	Stefano Morozzi	01/2020
9900	(3568^19993-1)/3567	71021	Serge Batalov	08/2020
9901	64877!4+128	71007	Robert Price	09/2019
9902	18562^6681+6681^18562	70997	Hans Havermann	10/2019
9903	(2^235802+474)/2	70984	Stefano Morozzi	01/2020
9904	20^54558-23	70982	Lelio R Paula	01/2015
9905	2^235793-112555	70981	Enzo Doria	06/2014
9906	49936!3-3^49936	70981	Robert Price	08/2015
9907	2^235787-78795	70979	Lelio R Paula	05/2012
9908	(2^235761+2930)/2	70971	Stefano Morozzi	01/2020
9909	Perrin(581132)	70970	Eric W. Weisstein	02/2011
9910	(2^235748+3478)/2	70967	Stefano Morozzi	01/2020
9911	14^61913-97	70961	Lelio R Paula	01/2015
9913	2^235720+16321	70959	Yves Minet	03/2010
9912	2^235718+16095	70959	Lelio R Paula	05/2012
9914	163841#+349933	70957	Nicolas PALAU	11/2016
9915	2^235710+7	70956	Lelio R Paula	02/2012
9916	(175^31627+1)/176	70939	Eric Chen	10/2017
9917	(2^235644+670)/2	70936	Stefano Morozzi	01/2020
9918	2^235635-112087	70934	Enzo Doria	06/2014
9919	153^32467+152	70931	Norbert Schneider	11/2018
9921	2^235575-1965	70916	Lelio R Paula	05/2012
9920	6^91133+101	70916	Lelio R Paula	01/2015
9922	(24755^16141-1)/24754	70914	Serge Batalov	08/2020
9923	(1102^23311-1)/1101	70914	Serge Batalov	08/2020
9924	(21181*2^235505+1)/3	70898	Lelio R Paula	06/2014
9925	(14*10^70896+211)/9	70897	Robert Price	11/2017
9926	5^101425+84	70894	Lelio R Paula	07/2014
9927	177^31536+2	70893	Lelio R Paula	05/2013
9928	43*71^38292+4	70891	Serge Batalov	03/2016
9929	(29*2^235506-1)/112029785	70888	Lelio R Paula	01/2014
9930	11^68045-1530	70862	Enzo Doria	12/2012
9931	(6969^18439-1)/6968	70861	Serge Batalov	08/2020
9932	5*10^70858+21	70859	Robert Price	01/2017
9934	2^235326+3	70841	Donovan Johnson	02/2006
9933	34523!2+4	70841	Robert Price	02/2015
9935	(31*2^235307+1)/3	70836	Lelio R Paula	06/2012
9936	(2^235310+1038)/2	70836	Stefano Morozzi	01/2020
9937	2^235308+135	70835	Lelio R Paula	02/2012
9938	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
9939	2^235274+159	70825	Lelio R Paula	02/2012
9940	3^148409+70	70810	Lelio R Paula	11/2014
9941	(19*10^70794+17)/9	70795	Robert Price	03/2015
9942	(2^235144+1350)/2	70786	Stefano Morozzi	01/2020
9943	2^235108-232709	70775	Paul Bourdelais	03/2013
9944	22995^1196+1196^22995	70773	Hans Havermann	11/2019
9945	(2^235099-2^117550+1)/5	70772		11/2006
9946	19^55325-6	70748	Lelio R Paula	08/2014
9947	257^29356+29356^257	70746	Norbert Schneider	10/2014
9948	22*10^70729+3	70731	Robert Price	10/2017
9949	2^234956+11715	70729	Lelio R Paula	05/2012
9950	(7*10^70727-43)/9	70727	Robert Price	10/2014
9951	(2^234897+3906)/2	70711	Stefano Morozzi	01/2020
9952	2^234890-30341	70709	Enzo Doria	11/2012
9953	17^57461+14	70703	Lelio R Paula	01/2015
9954	18281^7366+7366^18281	70697	Hans Havermann	09/2019
9955	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
9956	2*10^70688+51	70689	Robert Price	10/2017
9957	123^33822-122	70685	Norbert Schneider	01/2015
9958	7*10^70680-99	70681	Robert Price	11/2017
9959	(2^234784+3646)/2	70677	Stefano Morozzi	01/2020
9960	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
9961	(2^234762+1498)/2	70671	Stefano Morozzi	01/2020
9962	(24355^16111-1)/24354	70668	Serge Batalov	08/2020
9963	(2^234723+3690)/2	70659	Stefano Morozzi	01/2020
9964	(2^234718+3798)/2	70657	Stefano Morozzi	01/2020
9965	(2^234680+2902)/2	70646	Stefano Morozzi	01/2020
9966	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
9967	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
9969	2^234655-67	70639	Lelio R Paula	02/2012
9968	(79*10^70638-61)/9	70639	Robert Price	10/2015
9970	2^234652-173	70638	Lelio R Paula	02/2012
9971	2^234618-3645	70628	Lelio R Paula	05/2012
9972	(2^234610-5)/19	70624	Lelio R Paula	05/2012
9973	4*5^101038+9	70624	Lelio R Paula	10/2014
9974	2^234603+71963	70623	Enzo Doria	04/2016
9975	2^234600-113129	70622	Enzo Doria	07/2014
9976	(2^234601+1446)/2	70622	Stefano Morozzi	01/2020
9977	2^234586+9	70618	Lelio R Paula	02/2012
9978	3^148008+26	70618	Robert Price	11/2013
9979	(7*10^70616-151)/9	70616	Robert Price	09/2017
9980	65^38947+32	70608	Lelio R Paula	01/2016
9981	(2^234517+2750)/2	70597	Stefano Morozzi	01/2020
9982	18363^6988+6988^18363	70594	Hans Havermann	10/2019
9983	(2^234488-3)/11	70587	Lelio R Paula	05/2012
9984	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
9985	(8848^17881-1)/8847	70570	Serge Batalov	08/2020
9986	Phi(159495,10)	70560	Maksym Voznyy	09/2015
9987	2^234383-4035	70557	Lelio R Paula	05/2012
9988	(2^234364+3618)/2	70551	Stefano Morozzi	01/2020
9989	(2^234333+3482)/2	70541	Stefano Morozzi	01/2020
9990	2^234315-111241	70536	Enzo Doria	05/2014
9991	14^61526+97	70517	Lelio R Paula	01/2015
9992	14742^16915+16915^14742	70512	Norbert Schneider	10/2019
9993	(2^234203+3306)/2	70502	Stefano Morozzi	01/2020
9994	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
9995	51^41281-50^41281	70491	Robert Price	02/2013
9996	2^234141-112123	70484	Enzo Doria	06/2014
9997	2^234139+12285	70483	Lelio R Paula	04/2012
9998	2^234133-3163	70482	Yves Minet	04/2009
9999	2^234115+83	70476	Lelio R Paula	02/2012
10000	2^234114-1595	70476	Lelio R Paula	05/2012

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Probable Primes Top 10000

(277034 PRPs in the top)