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 (> 50000)	Who ?	When ?
9501	2^215789-18825	64959	Lelio R Paula	09/2011
9502	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
9504	U(315311)	64954	Serge Batalov	03/2015
9503	(2^215773+3530)/2	64954	Stefano Morozzi	12/2019
9505	46072!3-59049	64951	Robert Price	12/2015
9506	2^215750-5955	64948	Lelio R Paula	09/2011
9507	(2^215743+2234)/2	64945	Stefano Morozzi	12/2019
9508	13^58281+46	64922	Lelio R Paula	07/2013
9509	15633^14212+14212^15633	64919	Hans Havermann	07/2019
9510	2^215623+183	64909	Lelio R Paula	08/2011
9511	(2^215611+3326)/2	64906	Stefano Morozzi	12/2019
9512	(46*10^64904+521)/9	64905	Robert Price	08/2017
9513	(2^215606+862)/2	64904	Stefano Morozzi	12/2019
9514	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
9515	5*2^215554+3	64889	Lelio R Paula	04/2014
9516	(2^215553+3690)/2	64888	Stefano Morozzi	12/2019
9517	2^215541-112075	64885	Enzo Doria	06/2014
9518	2*10^64882-3	64883	Dmitry Domanov	11/2010
9520	16592^8121+8121^16592	64869	Hans Havermann	07/2019
9519	(2^215490+2602)/2	64869	Stefano Morozzi	12/2019
9521	10^64862+342339	64863	Patrick De Geest	05/2013
9522	10^64862-47	64862	Robert Price	05/2011
9523	19^50718-84	64856	Lelio R Paula	08/2013
9524	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
9525	86413!6-12	64846	Robert Price	08/2018
9527	10^64843+4278697839	64844	Robert Price	05/2015
9526	10^64843+21967	64844	Patrick De Geest	03/2016
9528	10^64843-340073	64843	Patrick De Geest	03/2016
9529	11^62254+70	64831	Lelio R Paula	07/2013
9530	2^215351-111925	64828	Enzo Doria	05/2014
9531	(2^215331+3906)/2	64821	Stefano Morozzi	12/2019
9532	2^215310-117	64815	Lelio R Paula	08/2011
9533	(2^215307+1554)/2	64814	Stefano Morozzi	12/2019
9534	124^30958-123	64809	Norbert Schneider	02/2015
9535	(7*10^64807+17)/3	64808	Erik Branger	03/2014
9536	59703!4-256	64806	Robert Price	11/2019
9537	(2^215277+2522)/2	64805	Stefano Morozzi	12/2019
9538	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
9539	2^215243-15949	64795	Enzo Doria	04/2013
9540	23^47581-22^47581	64793	Robert Price	08/2012
9541	(62*10^64783-17)/9	64784	Robert Price	09/2015
9542	10^64770+987654321	64771	Robert Price	12/2019
9543	10^64770+164451	64771	Patrick De Geest	02/2020
9544	10^64770-478179	64770	Patrick De Geest	02/2020
9545	5*3^135747-4	64769	Lelio R Paula	04/2014
9546	(59*10^64767-41)/9	64768	Robert Price	09/2015
9549	(2^215140+3)/19	64763	Lelio R Paula	04/2012
9548	2^215135-17169	64763	Enzo Doria	05/2013
9547	(2^215141+6)/38	64763	Stefano Morozzi	03/2020
9550	16078^10665+10665^16078	64762	Hans Havermann	07/2019
9551	2^215115-111277	64757	Enzo Doria	05/2014
9552	9*5^92641+2	64755	Lelio R Paula	09/2014
9553	(2^215069+414)/2	64742	Stefano Morozzi	12/2019
9554	(2^215036+2638)/2	64732	Stefano Morozzi	12/2019
9555	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
9556	(2^215017+762)/2	64727	Stefano Morozzi	12/2019
9557	14073^15602-15602^14073	64724	Norbert Schneider	12/2019
9558	(2^215008+2958)/2	64724	Stefano Morozzi	12/2019
9559	5791^17200+17200^5791	64720	Norbert Schneider	12/2018
9560	(5*10^64715-23)/9	64715	Robert Price	11/2014
9561	(2^214941+2754)/2	64704	Stefano Morozzi	12/2019
9562	2^214938-1781	64703	Yves Minet	03/2013
9563	(2^214914+2202)/2	64696	Stefano Morozzi	12/2019
9564	21003^1202+1202^21003	64688	Hans Havermann	07/2019
9565	11^62111-420	64682	Enzo Doria	08/2012
9566	18870^2677+2677^18870	64680	Hans Havermann	07/2019
9567	5^92525+42	64673	Lelio R Paula	06/2013
9568	2^214824+71893	64669	Enzo Doria	04/2016
9570	19157^2374+2374^19157	64665	Hans Havermann	08/2019
9569	(2^214812+3162)/2	64665	Stefano Morozzi	12/2019
9571	2^214799-2221	64661	Yves Minet	08/2013
9572	18393^3274+3274^18393	64653	Hans Havermann	07/2019
9573	(2^214766+2562)/2	64651	Stefano Morozzi	12/2019
9574	(2^214746+1242)/2	64645	Stefano Morozzi	12/2019
9575	(2^214740+1846)/2	64643	Stefano Morozzi	12/2019
9576	5939^17128+17128^5939	64637	Norbert Schneider	10/2018
9577	(2^214703+2594)/2	64632	Stefano Morozzi	12/2019
9578	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
9579	92^32907+32907^92	64623	Serge Batalov	05/2014
9580	17650^4579+4579^17650	64613	Hans Havermann	07/2019
9581	(89*10^64608-539)/9	64609	Robert Price	11/2017
9582	6^83013+101	64597	Lelio R Paula	07/2013
9583	p(13775)#/2+8	64594	Robert Price	01/2017
9584	(2^214528+3378)/2	64580	Stefano Morozzi	12/2019
9585	(7*10^64568-43)/9	64568	Robert Price	10/2014
9586	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
9587	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
9588	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
9589	2^214458+54615	64559	Lelio R Paula	10/2011
9590	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
9591	(2^214445+3282)/2	64555	Stefano Morozzi	12/2019
9592	(2^214443+2558)/2	64554	Stefano Morozzi	12/2019
9593	(2^214442+3738)/2	64554	Stefano Morozzi	12/2019
9594	(2^214406+3550)/2	64543	Stefano Morozzi	12/2019
9595	2^214389-683113	64538	Paul Bourdelais	03/2013
9596	(76*10^64534+113)/9	64535	Robert Price	11/2017
9597	2^214369-111241	64532	Enzo Doria	05/2014
9598	(19^50461+3^50461)/22	64526	Robert Price	07/2013
9599	11^61954-3660	64519	Enzo Doria	12/2012
9600	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
9601	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
9602	2^214300-4547	64511	Yves Minet	03/2019
9603	35^41779-34	64510	Norbert Schneider	04/2014
9604	(159^29303+1)/160	64506	Eric Chen	12/2017
9605	(89*10^64504-179)/9	64505	Robert Price	11/2017
9606	11^61939-5220	64503	Enzo Doria	01/2013
9607	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
9608	L(308604)+P(308604)	64495	Robert Price	12/2017
9609	126^30706-125	64494	Norbert Schneider	02/2015
9610	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
9611	13661^15594-15594^13661	64489	Norbert Schneider	12/2019
9612	(2^214219+1014)/2	64487	Stefano Morozzi	12/2019
9613	2^214215+12909	64486	Lelio R Paula	10/2011
9614	(2^214206+1458)/2	64483	Stefano Morozzi	12/2019
9615	16581^7738+7738^16581	64478	Hans Havermann	07/2019
9616	5^92225+66	64463	Lelio R Paula	06/2013
9617	2^214126-240551	64459	Paul Bourdelais	03/2013
9618	8*6^82827+5	64453	Lelio R Paula	09/2014
9619	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
9620	(2^214092+3966)/2	64448	Stefano Morozzi	12/2019
9621	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
9622	14^56227+89	64444	Lelio R Paula	08/2013
9625	2^214055-159	64437	Lelio R Paula	08/2011
9623	10^64436+2667	64437	Patrick De Geest	05/2013
9624	65^35543-64^35543	64437	Robert Price	08/2013
9626	10^64436-53	64436	Robert Price	05/2011
9627	(3^135043-lucasV(1,3,135043)+1)/3	64432	Paul Vanderveen	11/2017
9628	(2^214030+1722)/2	64430	Stefano Morozzi	12/2019
9629	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
9630	3^135027+100	64425	Lelio R Paula	05/2013
9631	(3^134972-7)/2	64398	Lelio R Paula	04/2012
9632	6*10^64387+7	64388	Dmitry Domanov	11/2010
9633	2^213864-18377	64380	Enzo Doria	05/2013
9634	17929^3892+3892^17929	64369	Hans Havermann	06/2019
9635	(2^213821+9)/209	64365	Lelio R Paula	04/2012
9636	(2^213799+3650)/2	64360	Stefano Morozzi	12/2019
9637	2^213788+135	64357	Lelio R Paula	08/2011
9638	17703^4316+4316^17703	64352	Hans Havermann	06/2019
9639	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
9640	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
9641	(11^61781+2^61781)/13	64338	Robert Price	02/2013
9642	6^82670+37	64330	Lelio R Paula	07/2013
9643	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012
9644	(22*10^64326+161)/3	64327	Robert Price	02/2017
9645	11^61767-4050	64324	Enzo Doria	12/2012
9646	2^213645-114853	64314	Enzo Doria	05/2015
9647	(2^213641+1794)/2	64313	Stefano Morozzi	12/2019
9648	13^57733+18	64312	Lelio R Paula	07/2013
9649	2^213621+72707	64307	Enzo Doria	04/2016
9650	10^64305+136791	64306	Patrick De Geest	05/2011
9651	10^64305-9	64305	Alexander Gramolin	01/2011
9652	V(307652)	64295	Serge Batalov	03/2015
9653	4*10^64286-89	64287	Robert Price	08/2017
9654	(2^213552+3082)/2	64286	Stefano Morozzi	12/2019
9655	(2^213546-5)/2221	64281	Lelio R Paula	04/2012
9656	(2^213473+702)/2	64262	Stefano Morozzi	12/2019
9658	2^213438-58695	64252	Lelio R Paula	10/2011
9657	(2^213439+1170)/2	64252	Stefano Morozzi	12/2019
9659	(2^213398+2094)/2	64239	Stefano Morozzi	12/2019
9660	2^213367-105	64230	Lelio R Paula	08/2011
9661	595^23148+23148^595	64225	Norbert Schneider	07/2016
9663	3^134601+8680	64221	Lelio R Paula	05/2013
9662	(26*10^64220+61)/3	64221	Robert Price	06/2017
9664	500^23793+23793^500	64217	Norbert Schneider	08/2016
9665	179^28504-2	64216	Lelio R Paula	10/2017
9667	2^213314-455	64214	Yves Minet	02/2012
9666	39^40359-38	64214	Norbert Schneider	05/2014
9668	2^213292-16085	64208	Enzo Doria	04/2013
9669	(2^213282+3922)/2	64204	Stefano Morozzi	12/2019
9670	(72524!5+1)/25	64203	Joe McLean	10/2018
9671	2^213274-77	64202	Lelio R Paula	08/2011
9672	19^50203+78	64198	Lelio R Paula	08/2013
9673	(44*10^64192-233)/9	64193	Robert Price	10/2017
9674	2^213240-112865	64192	Enzo Doria	06/2014
9675	(2^213196+3186)/2	64179	Stefano Morozzi	12/2019
9676	2^213190-112391	64177	Enzo Doria	06/2014
9677	(2^213209+11)/18230777	64176	Stefano Morozzi	03/2020
9678	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
9679	14^55991+27	64173	Lelio R Paula	07/2013
9680	2^213158-112581	64167	Enzo Doria	06/2014
9681	2^213148+91	64164	Lelio R Paula	08/2011
9682	(96^32369+1)/97	64163	Paul Bourdelais	08/2017
9684	6^82439+125	64151	Lelio R Paula	07/2013
9683	7*2^213102+9	64151	Lelio R Paula	04/2014
9685	(2^213063+3186)/2	64139	Stefano Morozzi	12/2019
9686	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
9687	15621^12736+12736^15621	64125	Hans Havermann	07/2019
9688	15633^12622+12622^15633	64113	Hans Havermann	07/2019
9689	610^23017+23017^610	64110	Norbert Schneider	07/2016
9690	2^212950-64875	64105	Lelio R Paula	10/2011
9691	(266*10^64102-17)/3	64104	Robert Price	06/2016
9692	p(13679)#/2+64	64097	Robert Price	03/2017
9693	19^50119+94	64090	Lelio R Paula	08/2013
9694	2^212880-147	64084	Lelio R Paula	08/2011
9695	(2^212876+2826)/2	64082	Stefano Morozzi	12/2019
9696	11^61523-4590	64070	Enzo Doria	01/2013
9697	5^91663+38	64070	Lelio R Paula	05/2013
9698	5^91650+52	64061	Lelio R Paula	05/2013
9699	(2^212801+2822)/2	64060	Stefano Morozzi	12/2019
9700	(2^212798+2442)/2	64059	Stefano Morozzi	12/2019
9701	(2^212795+1734)/2	64058	Stefano Morozzi	12/2019
9702	2^212770+69	64051	Lelio R Paula	08/2011
9703	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
9704	(2*10^64041-17)/3	64041	Robert Price	08/2014
9705	(15^54449+1)/16	64036	Paul Bourdelais	03/2010
9706	(29*10^64027+91)/3	64028	Robert Price	03/2016
9707	(lucasV(1,2,425405)+2)/(17*89)	64027	Mike Oakes	03/2017
9708	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
9709	15862^10863+10863^15862	64019	Hans Havermann	06/2019
9710	2^212663+53	64018	Lelio R Paula	08/2011
9711	(4*10^64014+197)/3	64015	Robert Price	03/2017
9712	85402!6-3	64014	Robert Price	08/2018
9713	(140^29819+1)/141	63994	Richard Fischer	05/2018
9714	15313^15094+15094^15313	63991	Hans Havermann	06/2019
9715	10^63986+63	63987	Robert Price	01/2011
9716	10^63986-31557	63986	Patrick De Geest	05/2013
9717	15699^11900+11900^15699	63983	Hans Havermann	07/2019
9718	31487!2-2^31487	63982	Robert Price	09/2015
9719	(2^212539+3950)/2	63981	Stefano Morozzi	12/2019
9720	(21*2^212522-1)/1416323	63971	Lelio R Paula	01/2014
9721	5^91517+98	63968	Lelio R Paula	04/2013
9722	(2^212486+2874)/2	63965	Stefano Morozzi	12/2019
9723	(19*10^63960-43)/3	63961	Robert Price	10/2017
9724	(62*10^63954-17)/9	63955	Robert Price	09/2015
9726	5^91493-4^91493	63951	Predrag Minovic	04/2004
9725	V(364793)	63951	Serge Batalov	03/2015
9727	19^50004+58	63943	Lelio R Paula	05/2013
9728	5*6^82172-7	63943	Lelio R Paula	09/2014
9729	(56*10^63942+223)/9	63943	Robert Price	07/2016
9730	19^50000-24	63938	Lelio R Paula	05/2013
9731	(23*2^212374-1)/27019	63928	Lelio R Paula	01/2014
9732	(9*2^212355-1)/761	63924	Lelio R Paula	01/2014
9734	2^212344-183	63922	Lelio R Paula	08/2011
9733	(58695*2^212336-1)/379	63922	Lelio R Paula	04/2015
9735	10^63916+79	63917	Robert Price	01/2011
9736	10^63916-76823	63916	Patrick De Geest	05/2013
9737	(2^212318+462)/2	63914	Stefano Morozzi	12/2019
9738	2^212295-25	63908	Lelio R Paula	08/2011
9739	2^212285-2383	63905	Yves Minet	10/2013
9740	267^26336+26336^267	63905	Norbert Schneider	09/2014
9741	(-lucasV(1,2,424552)-2)/1601	63899	Mike Oakes	03/2017
9743	19^49962+60	63890	Lelio R Paula	05/2013
9742	3^133906-113056	63890	Enzo Doria	07/2014
9744	7933^16384+7932^16384	63889	Richard Fischer	09/2019
9745	(lucasV(1,2,424451)+2)/3	63886	Mike Oakes	03/2017
9746	3*6^82092+5	63881	Lelio R Paula	09/2014
9747	15441^13706+13706^15441	63879	Hans Havermann	02/2017
9748	2^212154-776351	63865	Paul Bourdelais	03/2013
9749	35^41359+2	63862	Lelio R Paula	05/2013
9750	(61*10^63857-43)/9	63858	Robert Price	09/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)