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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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 (> 30000)	Who ?	When ?
9751	2003^14821-102	48935	Enzo Doria	06/2012
9752	7^57901+82	48933	Lelio R Paula	06/2012
9753	t(166683)	48933	Robert Price	10/2014
9754	11^46985-18	48930	Lelio R Paula	10/2012
9755	2^162521+98765331	48924	Jason Earls	12/2008
9756	V(380406)	48914	Serge Batalov	03/2015
9757	2^162482+65835	48912	Lelio R Paula	10/2011
9758	12^45317+7	48906	Lelio R Paula	10/2012
9759	(4^81223+3^81223)/7	48901	Jean-Louis Charton	03/2011
9760	(2^162474-5)/1353094831	48901	Lelio R Paula	01/2012
9761	3^102477+2660	48894	Lelio R Paula	07/2012
9762	2^162412+29835	48891	Lelio R Paula	10/2011
9763	9*6^62820+7	48885	Lelio R Paula	09/2014
9764	(169^21943+1)/170	48885	Richard Fischer	11/2015
9765	(11987^11987+3067)/2/3/5^2/11/13/2857	48884	Makoto Morimoto	07/2016
9766	13^43881-50	48881	Lelio R Paula	11/2012
9767	8173^12492-12492^8173	48874	Norbert Schneider	05/2013
9768	20^37563-1363	48871	Enzo Doria	03/2013
9770	(923522^8192+1)/114689	48864	Lelio R Paula	11/2014
9769	13137^5242+5242^13137	48864	Hans Havermann	04/2016
9771	15^41545+92	48861	Lelio R Paula	11/2012
9772	(11981^11981+632)/97/1709	48860	Makoto Morimoto	07/2016
9773	(919695^8192+1)/131074	48850	Lelio R Paula	12/2014
9774	(917697^8192+1)/2	48847	Lelio R Paula	12/2014
9775	(12^45259-5^45259)/7	48842	Robert Price	03/2013
9776	9*5^69862+8	48833	Lelio R Paula	09/2014
9777	12^45244-95	48827	Lelio R Paula	10/2012
9778	(29*2^162182-1)/5	48823	Lelio R Paula	01/2014
9779	(2^162167-3)6+10^4881813803-7	48823	Gilbert Mozzo	11/2016
9780	(2^162167-3)*6-7	48818	Gilbert Mozzo	03/2016
9781	7*10^48816-69	48817	Robert Price	01/2017
9782	(11971^11971+3180)/103/7577	48814	Makoto Morimoto	07/2016
9783	2^162143-51	48810	Lelio R Paula	08/2010
9784	2^162136-284519	48808	Gary Barnes	08/2009
9785	5^69828-15386	48808	Enzo Doria	02/2013
9786	5^69826-3*4^69826	48807	Mike Oakes	02/2010
9787	2^162123+74063	48804	Enzo Doria	04/2016
9788	21001^11289-104	48794	Enzo Doria	07/2012
9789	5^69802-32	48790	Lelio R Paula	05/2012
9790	(902939^8192+1)/2	48789	Lelio R Paula	12/2014
9791	(2^162059+78557)/35	48784	Lelio R Paula	05/2012
9792	(900239^8192+1)/2	48778	Lelio R Paula	12/2014
9793	138^22794-137	48777	Norbert Schneider	10/2015
9794	2^162033+76757	48777	Enzo Doria	05/2016
9795	18^38850-37	48768	Lelio R Paula	11/2012
9796	(898286^8192+1)/786433	48765	Lelio R Paula	11/2014
9797	68^26610+67	48764	Norbert Schneider	10/2012
9798	2^161987+15015	48763	Lelio R Paula	10/2011
9799	(11959^11959+6523)/2/5581	48762	Makoto Morimoto	07/2016
9800	3^102198-86	48761	Lelio R Paula	06/2012
9801	(13224!+1)/221497	48755	Donovan Johnson	04/2006
9802	18^38838-13	48753	Lelio R Paula	11/2012
9803	161923*2^161923+161923+2	48749	Robert Price	05/2016
9804	(892493^8192+1)/131074	48743	Lelio R Paula	12/2014
9805	(11953^11953+133)/2/46861	48734	Makoto Morimoto	06/2016
9806	2^161881-14941	48732	Enzo Doria	04/2013
9807	(888215^8192+1)/2	48730	Lelio R Paula	12/2014
9808	-lucasV(1,2,323749)-2	48730	Mike Oakes	02/2017
9809	10268^12147+12147^10268	48728	Norbert Schneider	11/2013
9811	(26*10^48726-11)/3	48727	Erik Branger	05/2013
9810	3*6^62618-7	48727	Lelio R Paula	09/2014
9813	2^161857-45	48724	Lelio R Paula	08/2010
9812	(889160^8192+1)/73283633153	48724	Lelio R Paula	11/2014
9814	2^161837+467	48718	Lelio R Paula	11/2007
9815	3^102102+10	48716	Lelio R Paula	01/2007
9816	2^161806-8295	48709	Lelio R Paula	04/2009
9817	(25*2^161811-1)/457	48709	Lelio R Paula	01/2014
9818	13311^4558+4558^13311	48702	Hans Havermann	05/2016
9819	24^35284-457	48700	Enzo Doria	03/2013
9820	3^102058+8680	48695	Lelio R Paula	06/2012
9821	13537^3948+3948^13537	48685	Hans Havermann	05/2016
9822	(11941^11941+6414)/5	48684	Makoto Morimoto	07/2016
9823	2^161719-15097	48683	Enzo Doria	04/2013
9824	(41*10^48678+373)/9	48679	Robert Price	04/2017
9825	3*10^48668-7^48668	48669	Mike Oakes	01/2010
9826	13201!+13201!2+13201#-2	48666	Joe McLean	10/2007
9827	2*3^101994-5	48664	Lelio R Paula	03/2014
9828	(11939^11939+2801)/2^2/5/19/307/2210473	48664	Makoto Morimoto	07/2016
9829	11933^11933+1316	48648	Makoto Morimoto	07/2016
9830	(-lucasV(1,2,323096)+2)/(3*193)	48629	Mike Oakes	02/2017
9831	(lucasV(1,2,323208)-2)/(3^3571137173320111660317957*80803)	48622	Mike Oakes	02/2017
9832	95^24584+94	48621	Norbert Schneider	05/2013
9833	(11927^11927+2091)/2/2273/62683	48613	Makoto Morimoto	07/2016
9834	(10^48604-31)/3	48604	Serge Batalov	12/2014
9835	Phi(11923,11925)	48600	Henri Lifchitz	11/2003
9836	(11923^11923+3199)/2/42649	48598	Makoto Morimoto	07/2016
9837	75^25915-2	48593	Lelio R Paula	08/2013
9838	3^101816-104	48579	Lelio R Paula	07/2012
9839	(852175^8192+1)/327682	48578	Lelio R Paula	12/2014
9840	numbpart(61681*61682/2)	48578	Serge Batalov	04/2017
9841	132^22904+131	48570	Norbert Schneider	03/2015
9842	2^161333-114871	48567	Enzo Doria	05/2015
9843	13889^3138+3138^13889	48566	Hans Havermann	05/2016
9844	13174^4857+4857^13174	48565	Hans Havermann	05/2016
9845	2^161326+7969	48564	Yves Minet	02/2010
9846	(2^161330-5)/29	48564	Lelio R Paula	01/2012
9847	(848412^8192+1)/786433	48562	Lelio R Paula	11/2014
9848	(847181^8192+1)/2	48562	Lelio R Paula	12/2014
9849	4*10^48548+79	48549	Robert Price	01/2017
9851	(13*10^48547+11)/3	48548	Erik Branger	05/2013
9850	(9913*2^161263-1)/17	48548	Lelio R Paula	03/2015
9852	2^161258+63439	48544	Yves Minet	11/2010
9853	2^161238-459491	48538	Enzo Doria	05/2015
9854	(11909^11909+305)/2/157771	48535	Makoto Morimoto	07/2016
9855	2^161226+66615	48534	Lelio R Paula	12/2008
9856	2^161205-5955	48528	Lelio R Paula	04/2009
9857	10^48526+13	48527	Jason Earls	02/2008
9858	10^48526-41441	48526	Patrick De Geest	06/2009
9859	2^161199-14569	48526	Enzo Doria	04/2013
9860	9*2^161190-7	48524	Lelio R Paula	02/2014
9861	(3^101708+7)/53384	48523	Lelio R Paula	03/2012
9862	(2^161187+78557)/236155	48517	Lelio R Paula	05/2012
9863	(19*2^161174-1)/5685	48516	Lelio R Paula	01/2014
9864	(835525^8192+1)/2	48513	Lelio R Paula	12/2014
9865	20^37287-61	48512	Lelio R Paula	11/2012
9866	2^161143-14089	48509	Enzo Doria	04/2013
9867	(11903^11903+3950)/7/563	48509	Makoto Morimoto	07/2016
9868	(8*10^48507+49)/3	48508	Robert Price	03/2016
9869	2^161106-246581	48498	Gary Barnes	08/2009
9870	2^161098+18915	48496	Lelio R Paula	10/2011
9871	(832081^8192+1)/1474562	48492	Lelio R Paula	12/2014
9872	8*10^48490+21	48491	Robert Price	02/2017
9873	7^57369+22	48483	Lelio R Paula	06/2012
9874	3^101615+2660	48483	Lelio R Paula	06/2012
9875	(11897^11897+3419)/2^2/593	48483	Makoto Morimoto	07/2016
9876	7337^12542-12542^7337	48482	Norbert Schneider	11/2016
9878	(828754^8192+1)/638977	48478	Lelio R Paula	11/2014
9877	3*10^48477+13	48478	Robert Price	08/2017
9879	(265*10^48474+11)/3	48476	Robert Price	03/2017
9880	13260^4523+4523^13260	48471	Hans Havermann	05/2016
9881	2^161003-113059	48467	Enzo Doria	07/2014
9882	(73*10^48461+53)/9	48462	Erik Branger	05/2013
9883	(822278^8192+1)/65537	48452	Syoichiro Yamada	05/2008
9884	10^48449+112501	48450	Patrick De Geest	05/2007
9885	10^48449-48449	48449	Henri Lifchitz	07/2002
9886	10^48442+57	48443	Robert Price	01/2011
9887	2^160922-869688105	48443	Lelio R Paula	10/2011
9888	10^48442-33533	48442	Patrick De Geest	01/2012
9889	5101^13065-110	48441	Enzo Doria	07/2012
9890	(818917^8192+1)/2	48441	Lelio R Paula	12/2014
9891	(11887^11887+7018)/19/31/327319	48433	Makoto Morimoto	07/2016
9892	2^160883+76763	48431	Enzo Doria	05/2016
9893	2^160873+18915	48428	Lelio R Paula	10/2011
9894	13206^4645+4645^13206	48427	Hans Havermann	04/2016
9895	10^48420+6139	48421	Patrick De Geest	05/2016
9897	10^48420-2*10^1592-1	48420	Serge Batalov	01/2015
9896	10^48420-29273	48420	Patrick De Geest	03/2016
9899	2^160822-2163	48413	Yves Minet	08/2013
9898	(lucasV(1,2,321685)+2)/(571*911)	48413	Mike Oakes	02/2017
9901	10^48410+9^(48410-1)	48411	Robert Price	03/2016
9900	10^48410+90163	48411	Patrick De Geest	12/2016
9904	(3^101473+4)/264481	48410	Lelio R Paula	03/2012
9903	9*2^160811+7	48410	Lelio R Paula	02/2014
9902	10^48410-3287	48410	Patrick De Geest	12/2016
9905	(22699*2^160806+1)/1573	48409	Lelio R Paula	05/2014
9906	3*7^57278-8	48407	Lelio R Paula	09/2014
9907	2^160789-113215	48403	Enzo Doria	07/2014
9908	6900^12607-12607^6900	48397	Norbert Schneider	12/2016
9909	3^101404+2	48383	Mike Oakes	11/2009
9910	3^101395-110	48378	Lelio R Paula	06/2012
9911	2^160701+191	48376	Lelio R Paula	01/2011
9912	6*F(231436)+1	48368	Gilbert Mozzo	06/2015
9913	2^160654-15	48362	Lelio R Paula	08/2010
9914	20^37167+53	48356	Lelio R Paula	11/2012
9915	(799247^8192+1)/2	48355	Lelio R Paula	12/2014
9916	(238*10^48352-1)/3	48354	Robert Price	05/2016
9917	18661^390+390^18661	48352	Anatoly F. Selevich	01/2007
9918	21^36566+2	48349	Ray Chandler	08/2011
9919	7^57208-92	48347	Lelio R Paula	06/2012
9920	5^69165-2^69166	48345	Mike Oakes	10/2010
9921	(11867^11867+2981)/2^3/111341	48345	Makoto Morimoto	07/2016
9922	(3^101331-4)/4679	48344	Lelio R Paula	03/2012
9923	13^43396-24	48341	Lelio R Paula	10/2012
9924	Phi(85113,10)/170227/340453/2080331947/20239360723/577232068985083	48339	Serge Batalov	06/2011
9925	7*2^160574-9	48339	Lelio R Paula	02/2014
9926	lucasU(42,1,29781)+lucasU(42,1,29780)	48334	Mike Oakes	04/2009
9927	3^101296-19318	48331	Enzo Doria	02/2013
9928	(lucasV(1,2,321119)+2)/(5*53)	48331	Mike Oakes	01/2017
9930	(11863^11863+2822)/3/140681/148483	48322	Makoto Morimoto	07/2016
9929	5970^12797-12797^5970	48322	Norbert Schneider	03/2017
9931	17^39270+52	48320	Lelio R Paula	11/2012
9932	(791013^8192+1)/2	48318	Lelio R Paula	12/2014
9933	10^48314+71469	48315	Patrick De Geest	06/2016
9936	11^46393-7950	48314	Enzo Doria	02/2013
9935	10^48314-2*10^4988-1	48314	Serge Batalov	01/2015
9934	10^48314-423797	48314	Patrick De Geest	03/2016
9937	2^160491+87713	48313	Yves Minet	03/2010
9938	8*6^62084-7	48312	Lelio R Paula	09/2014
9939	2^160477+72977	48309	Enzo Doria	04/2016
9940	2^160471+99	48307	Lelio R Paula	07/2009
9941	(9913*2^160481-1)/4191875	48307	Lelio R Paula	03/2015
9943	(43^29573+1)/44	48305	Robert Price	11/2013
9942	2^160463-2907	48305	Yves Minet	09/2014
9944	(68*10^48304-257)/9	48305	Robert Price	06/2017
9945	Phi(77061,10)/4151276071/15207988351	48301	Maksym Voznyy	02/2010
9946	5^69098-14576	48298	Enzo Doria	02/2013
9947	(2*10^48297-17)/3	48297	Erik Branger	03/2013
9948	10^48292+104707	48293	Patrick De Geest	06/2016
9949	10^48292-2*10^392-1	48292	Serge Batalov	01/2015
9950	10^48292-66803	48292	Patrick De Geest	03/2016
9951	45709!4+2	48291	Robert Price	03/2017
9952	2^160402-1127	48286	Yves Minet	05/2013
9953	2^160398-1451	48285	Yves Minet	08/2012
9954	11^46365+26	48285	Lelio R Paula	10/2012
9955	t(160462)	48285	Robert Price	05/2015
9956	(3^50599-75)^2-77	48284	Jorge Menendez	02/2017
9957	2^160387-3721	48282	Yves Minet	04/2017
9958	3^101192+2^101193	48281	Mike Oakes	10/2009
9959	5^69063-18	48273	Lelio R Paula	05/2012
9960	5^69060-15416	48271	Enzo Doria	02/2013
9961	2^160343-667	48269	Yves Minet	01/2012
9962	2^160302-2145	48256	Lelio R Paula	04/2009
9963	12^44705-85	48245	Lelio R Paula	10/2012
9964	(58695*2^160249-1)/149	48243	Lelio R Paula	03/2015
9965	2^160218+12705	48231	Lelio R Paula	10/2011
9966	(F(14425)^17-F(14424)^17)/F(14423)	48230	Wayne Halsdorf	02/2010
9967	(771035^8192+1)/2	48227	Lelio R Paula	12/2014
9969	18348^425+425^18348	48226	Anatoly F. Selevich	12/2006
9968	(29*2^160204-1)/67	48226	Lelio R Paula	01/2014
9970	2^160166+5775	48215	Lelio R Paula	04/2009
9971	11875^11478+11478^11875	48211	Anatoly F. Selevich	10/2009
9972	17^39177-40	48206	Lelio R Paula	11/2012
9973	(5*2^160135-1)/4290399	48200	Lelio R Paula	01/2014
9974	(763957^8192+1)/2	48194	Lelio R Paula	12/2014
9975	(11833^11833+1278)/7/89/107	48193	Makoto Morimoto	06/2016
9976	gcd(V(576505),5F(115301)(F(115301)+1)+1)	48192	Serge Batalov	04/2015
9977	8788^12217+12217^8788	48183	Norbert Schneider	01/2014
9978	(11831^11831+1584)/5/23/97/1409	48181	Makoto Morimoto	07/2016
9979	(760473^8192+1)/2	48178	Lelio R Paula	12/2014
9980	-lucasV(-1,2,320104)/31	48178	Mike Oakes	01/2017
9981	gcd(V(864525),5F(172905)(F(172905)-1)+1)	48176	Serge Batalov	04/2015
9982	(760135^8192+1)/294914	48171	Lelio R Paula	12/2014
9984	4357^13236-110	48169	Enzo Doria	06/2012
9983	(11827^11827+4120)/17	48169	Makoto Morimoto	07/2016
9985	(3*2^160013-1)/2425	48166	Lelio R Paula	01/2014
9986	13^43238+82	48165	Lelio R Paula	11/2012
9987	2^159992+657	48163	Lelio R Paula	02/2013
9988	2^159984-383009	48160	Gary Barnes	08/2009
9989	2^159958-58695	48153	Lelio R Paula	03/2009
9990	471^18014-18014^471	48152	Norbert Schneider	08/2017
9991	6408*10^48143+11821^11821-24	48147	Gilbert Mozzo	12/2012
9992	(755045^8192+1)/229378	48147	Lelio R Paula	12/2014
9993	11821^11821-24	48143	Henri Lifchitz	10/2011
9994	(33*2^159934+1)/1936969	48141	Michael Porter	10/2015
9995	(11821^11821+1240)/19/13789	48138	Makoto Morimoto	06/2016
9996	20^36997-51	48135	Lelio R Paula	11/2012
9997	(3^100895+7)/24321775034	48129	Lelio R Paula	03/2012
9998	(15185*2^159869-1)/1827	48127	Lelio R Paula	03/2015
9999	3*7^56945+8	48125	Lelio R Paula	09/2014
10000	(749655^8192+1)/131074	48122	Lelio R Paula	12/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(181746 PRPs in the top)