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	(35*10^59584-197)/9	59585	Robert Kinser	10/2017
8502	2^197932-3959	59584	Yves Minet	04/2017
8503	2^197909-18961	59577	Enzo Doria	05/2013
8504	(3^124871+2)/45031	59574	Lelio R Paula	04/2012
8505	2^197872+81	59566	Henri Lifchitz	10/2005
8506	2^197873-18469	59566	Enzo Doria	05/2013
8507	(22*10^59558-31)/9	59559	Robert Price	04/2015
8509	2^197840-465	59556	Lelio R Paula	05/2011
8508	(31*2^197856-1)/3889605	59556	Lelio R Paula	01/2014
8510	2^197808-17805	59547	Enzo Doria	05/2013
8511	2^197781-17905	59539	Enzo Doria	05/2013
8512	2^197777-17473	59537	Enzo Doria	05/2013
8513	6^76507-149	59535	Lelio R Paula	10/2012
8515	Phi(61456,109)	59526	Enzo Doria	05/2012
8514	18^47420+23	59526	Lelio R Paula	03/2013
8516	(59^33613+1)/60	59522	Paul Bourdelais	08/2017
8517	3^124747+94	59520	Lelio R Paula	10/2012
8518	17^48370+18	59517	Lelio R Paula	03/2013
8519	20^45740-1523	59510	Enzo Doria	03/2013
8520	(47*10^59509+493)/9	59510	Robert Price	11/2017
8521	(7*2^197642-1)/3051	59494	Lelio R Paula	01/2014
8522	18^47390-1853	59488	Enzo Doria	03/2013
8523	(2^197581-7)/1915	59475	Lelio R Paula	02/2012
8524	(24737*2^197559+1)/77	59474	Lelio R Paula	06/2014
8525	2^197540-2459	59466	Yves Minet	07/2014
8526	(44*10^59454+1)/9	59455	Serge Batalov	11/2010
8527	2^197494-17805	59452	Enzo Doria	05/2013
8528	2^197482-16821	59449	Enzo Doria	05/2013
8529	2^197485+75767	59449	Enzo Doria	04/2016
8530	(3*2^197483+1)/25	59448	Lelio R Paula	07/2012
8531	2^197466-1868351	59444	Enzo Doria	04/2016
8532	2^197411-17781	59427	Enzo Doria	05/2013
8533	(F(142164)^3-F(142163)^3)/F(142162)	59421	Wayne Halsdorf	03/2012
8534	2^197392-114629	59421	Enzo Doria	05/2015
8535	2^197355-157	59410	Lelio R Paula	04/2011
8536	5^84992-84	59407	Lelio R Paula	10/2012
8537	2*3^124504-5	59404	Lelio R Paula	04/2014
8538	2^197307-19165	59396	Enzo Doria	05/2013
8540	2^197303+32769	59395	Lelio R Paula	05/2011
8539	2*10^59394-69	59395	Robert Price	07/2017
8541	(53*10^59389+1)/9	59390	Serge Batalov	11/2010
8542	6^76316-35	59386	Lelio R Paula	10/2012
8543	2^197259-2929	59381	Yves Minet	09/2014
8544	lucasU(46,1,35715)-lucasU(46,1,35714)	59377	Mike Oakes	04/2009
8545	17^48253-6	59373	Lelio R Paula	03/2013
8546	2^197156-15837	59350	Enzo Doria	04/2013
8547	2^197152-4295	59349	Yves Minet	08/2018
8548	2^197149-18481	59348	Enzo Doria	05/2013
8549	2^197142-17157	59346	Enzo Doria	05/2013
8551	(F(6)^65707-F(5)^65707)/F(4)	59339	Wayne Halsdorf	04/2010
8550	(8^65707-5^65707)/3	59339	Robert Price	12/2012
8552	(2*14283^14283+1)/7925497975	59334	David Broadhurst	09/2010
8553	2^197012-111719	59307	Enzo Doria	05/2014
8554	2^196975+513	59296	Lelio R Paula	05/2011
8555	(61*10^59294+119)/9	59295	Robert Price	09/2017
8556	4*10^59292+39	59293	Robert Price	11/2017
8557	2^196960+97	59291	Lelio R Paula	04/2011
8558	9^62116+8^(62116-1)	59274	Robert Price	03/2016
8559	2^196900-97305	59273	Lelio R Paula	09/2011
8560	5*6^76155+7	59261	Lelio R Paula	09/2014
8561	15^50385-14	59258	Wojciech Florek	06/2006
8562	(136777#-1)/8823581477	59254	Donovan Johnson	05/2006
8563	(2^196744-3)*6-7	59227	Gilbert Mozzo	05/2016
8564	(67607*2^196696+1)/3	59216	Lelio R Paula	05/2014
8565	2^196696-112967	59212	Enzo Doria	06/2014
8566	20^45508-4223	59208	Enzo Doria	03/2013
8567	gcd(Phi(325820,10),(10^16291+1)^3(10^16291+1-10^8146)+(10^32582+10^16291)(10^8146+1)+10^48873)	59201	Serge Batalov	04/2015
8568	14^51651-81	59199	Lelio R Paula	03/2013
8569	2^196650-1451	59198	Yves Minet	08/2012
8570	2^196636-2797799	59194	Enzo Doria	04/2016
8571	1111*2^196610-555	59189	Henri Lifchitz	04/2005
8572	3^124041+658	59183	Lelio R Paula	10/2012
8573	2^196590-111797	59180	Enzo Doria	05/2014
8574	(10^59174-13)/3	59174	Robert Price	02/2017
8575	(2*10^59174-113)/3	59174	Robert Price	09/2017
8576	(9179*2^196533-1)/783	59164	Lelio R Paula	04/2015
8577	379*10^59152+9	59155	Arkadiusz Wesolowski	10/2011
8578	(404*10^59149-53)/9	59151	Robert Price	11/2017
8579	13^53095+40	59145	Lelio R Paula	03/2013
8581	2*F(282999)-1	59144	Henri Lifchitz	12/2009
8580	4*7^69984+3	59144	Lelio R Paula	09/2014
8582	(5*10^59142+1)/3	59143	Erik Branger	12/2013
8583	2^196463+5711	59142	Lelio R Paula	10/2011
8584	2^196453-97305	59139	Lelio R Paula	09/2011
8585	(28*10^59135+53)/9	59136	Serge Batalov	11/2008
8586	(28*10^59133+113)/3	59134	Robert Price	03/2016
8587	2^196434+7	59133	Lelio R Paula	04/2011
8588	(8*10^59127-29)/3	59128	Robert Price	05/2016
8589	2^196414+255	59127	Lelio R Paula	05/2011
8590	5^84586-92	59124	Lelio R Paula	10/2012
8591	2^196388-17177	59119	Enzo Doria	05/2013
8592	79427!6-6	59119	Robert Price	08/2018
8593	3^123890+20	59111	Lelio R Paula	10/2012
8594	2^196355-1021777	59109	Paul Bourdelais	11/2012
8595	11^56754-1410	59104	Enzo Doria	11/2012
8596	(7*2^196297-1)/1200407	59087	Lelio R Paula	01/2014
8597	(16*10^59062-19)/3	59063	Robert Price	03/2016
8598	35^38249-1228	59060	Enzo Doria	03/2013
8599	5^84475-18	59046	Lelio R Paula	10/2012
8600	2^196123-17701	59039	Enzo Doria	05/2013
8601	12^54702-31	59034	Lelio R Paula	03/2013
8602	2^196101-175	59033	Lelio R Paula	04/2011
8603	2^196085+5775	59028	Lelio R Paula	05/2011
8604	2^196034+11715	59013	Lelio R Paula	05/2011
8605	2^196018-18485	59008	Enzo Doria	05/2013
8606	2^195984-2163	58998	Yves Minet	08/2013
8607	3^123645-16	58994	Lelio R Paula	10/2012
8608	39^37078-38	58994	Norbert Schneider	05/2014
8609	2^195958-16853	58990	Enzo Doria	05/2013
8610	2^195930-3071	58981	Yves Minet	10/2014
8611	2^195924+513	58980	Lelio R Paula	05/2011
8612	2^195863+155	58961	Lelio R Paula	04/2011
8613	(28*10^58956+113)/3	58957	Robert Price	03/2016
8614	11^56612-9300	58956	Enzo Doria	02/2013
8615	2^195833-17173	58952	Enzo Doria	05/2013
8616	(27*2^195833-1)/53	58952	Lelio R Paula	01/2014
8617	(13*2^195821-1)/122425	58945	Lelio R Paula	01/2014
8618	139^27504-138	58942	Norbert Schneider	10/2015
8619	(418*10^58923+23)/9	58925	Robert Price	08/2017
8620	3^123495+44	58923	Lelio R Paula	10/2012
8621	2^195737-18565	58923	Enzo Doria	05/2013
8622	79185!6-16	58921	Robert Price	08/2018
8623	14^51407+47	58920	Lelio R Paula	03/2013
8624	2^195691-99	58909	Lelio R Paula	04/2011
8625	2^195667-1859827	58902	Enzo Doria	04/2016
8627	2^195642+75499	58895	Enzo Doria	04/2016
8626	(299*10^58893+1)/3	58895	Robert Price	11/2017
8628	8*6^75678+5	58890	Lelio R Paula	09/2014
8629	2^195618+73189	58887	Enzo Doria	04/2016
8630	(3928^20480+1)/(3928^4096+1)	58887	Serge Batalov	01/2017
8631	t(197953)	58881	Robert Price	12/2014
8632	2^195581-16105	58876	Enzo Doria	04/2013
8633	(8*10^58872+67)/3	58873	Robert Price	01/2017
8634	7*2^195542-5	58865	Lelio R Paula	03/2014
8635	2*10^58861+9^58861	58862	Mike Oakes	04/2011
8636	11^56513-1620	58853	Enzo Doria	11/2012
8637	2^195496+165	58851	Lelio R Paula	04/2011
8638	5^84187+66	58845	Lelio R Paula	10/2012
8639	(28*10^58843-43)/3	58844	Robert Price	04/2016
8640	2^195462-17565	58840	Enzo Doria	05/2013
8641	2^195449-4171	58837	Yves Minet	02/2018
8642	2^195435+59273	58832	Yves Minet	01/2011
8643	2^195424-18605	58829	Enzo Doria	05/2013
8644	2^195385-111	58817	Lelio R Paula	04/2011
8645	7*10^58815-83	58816	Robert Price	09/2017
8646	2^195357-4303	58809	Yves Minet	08/2018
8647	(47*2^195254+1)/268821	58774	Lelio R Paula	03/2015
8648	2^195207-18109	58764	Enzo Doria	05/2013
8649	2^195199-1567	58761	Yves Minet	08/2012
8650	2^195190+73759	58759	Enzo Doria	04/2016
8651	9*7^69525-4	58757	Lelio R Paula	09/2014
8652	2^195170-18045	58753	Enzo Doria	05/2013
8653	2^195166-165	58751	Lelio R Paula	04/2011
8654	(754*10^58748-7)/9	58750	Robert Price	11/2017
8655	(22699*2^195140+1)/175	58746	Lelio R Paula	05/2014
8656	7*3^123109-2	58739	Lelio R Paula	04/2014
8657	(8*10^58738-611)/9	58738	Robert Price	11/2017
8658	18^46790+77	58735	Lelio R Paula	03/2013
8660	2^195095-337297	58730	Gary Barnes	09/2009
8659	(14*10^58729+31)/9	58730	Robert Price	02/2015
8661	99^29424+98	58720	Norbert Schneider	07/2013
8662	(15185*2^195039-1)/219	58715	Lelio R Paula	04/2015
8663	2^195001-69	58702	Lelio R Paula	04/2011
8664	2^194978-487811	58695	Gary Barnes	09/2009
8665	163^26530+26530^163	58690	Serge Batalov	05/2014
8666	2^194940-194940+1	58683	Robert Price	10/2014
8667	(76*10^58669+41)/9	58670	Robert Price	10/2015
8668	14^51186+87	58666	Lelio R Paula	03/2013
8669	2^194878-97305	58665	Lelio R Paula	09/2011
8670	5^83927-18136	58663	Enzo Doria	05/2014
8671	(24737*2^194865+1)/1085	58662	Lelio R Paula	06/2014
8672	7^69411+40	58660	Lelio R Paula	10/2012
8673	6^75382-79	58659	Lelio R Paula	10/2012
8674	2^194854+27	58657	Lelio R Paula	04/2011
8675	2^194801+29835	58641	Lelio R Paula	10/2012
8676	2^194752+195	58627	Lelio R Paula	04/2011
8677	7^69371-6^69371	58626	Predrag Minovic	08/2004
8678	2^194747-112519	58625	Enzo Doria	06/2014
8679	(15*2^194737+1)/59	58622	Lelio R Paula	07/2012
8680	(23*2^194700+1)/3	58612	Lelio R Paula	02/2012
8681	10^58608+55273	58609	Patrick De Geest	07/2017
8682	10^58608-800001	58608	Robert Price	06/2017
8683	10^58608-60119	58608	Patrick De Geest	07/2017
8684	5^83836+76	58599	Lelio R Paula	10/2012
8685	18^46664+31	58577	Lelio R Paula	03/2013
8686	(34*10^58577-7)/9/19/463	58574	Makoto Morimoto	04/2016
8687	2^194574+165	58573	Lelio R Paula	04/2011
8690	2^194569-12211	58572	Enzo Doria	06/2014
8688	10^58571+5^58571+2^58571	58572	Robert Price	12/2016
8689	10^58571+202837	58572	Patrick De Geest	02/2017
8691	(10^58571+41)/3	58571	Robert Price	01/2017
8692	10^58571-343629	58571	Patrick De Geest	02/2017
8693	(43*10^58563-403)/9	58564	Robert Price	04/2017
8695	11^56235-7950	58563	Enzo Doria	02/2013
8694	145^27095-144	58563	Norbert Schneider	11/2018
8696	(14*10^58550+211)/9	58551	Robert Price	11/2017
8697	2^194479-113239	58545	Enzo Doria	07/2014
8698	2^194455-112249	58537	Enzo Doria	06/2014
8699	2^194405-111919	58522	Enzo Doria	05/2014
8700	(4*10^58521-19)/3	58522	Robert Price	06/2017
8702	(7^69247-4^69247)/3	58521	Robert Price	06/2012
8701	5*7^69246+8	58521	Lelio R Paula	09/2014
8703	2^194358-1167	58508	Lelio R Paula	05/2011
8704	(2^194366+7)/1373	58507	Lelio R Paula	02/2012
8705	(493*10^58486-7)/9	58488	Robert Price	07/2016
8706	3^122579-340	58486	Lelio R Paula	10/2012
8707	(11*10^58458-149)/3	58459	Robert Price	01/2017
8708	(47*10^58456+133)/9	58457	Robert Price	04/2017
8709	2^194186+85	58456	Lelio R Paula	04/2011
8710	3^122506-2^(122506-1)	58451	Robert Price	01/2016
8711	(74^31267-1)/73	58444	Paul Bourdelais	08/2017
8712	177^25998-2	58443	Lelio R Paula	10/2017
8713	15^49690-26	58440	Lelio R Paula	03/2013
8714	10^58437+110721	58438	Patrick De Geest	12/2012
8715	10^58437-11	58437	Robert Price	05/2011
8716	2^194095+69	58429	Lelio R Paula	04/2011
8717	(29*10^58417-77)/3	58418	Robert Price	01/2017
8718	2^194034+177	58411	Lelio R Paula	04/2011
8719	789^20158+20158^789	58400	Norbert Schneider	06/2016
8720	14^50949+75	58395	Lelio R Paula	03/2013
8721	2^193974-114761	58392	Enzo Doria	05/2015
8722	2^193965+5	58390	Henri Lifchitz	12/2002
8723	(5*10^58384-29)/3	58385	Robert Price	02/2017
8724	3^122360+80	58381	Lelio R Paula	10/2012
8725	10103^14577-114	58373	Enzo Doria	07/2012
8726	(22699*2^193883+1)/21	58368	Lelio R Paula	06/2014
8727	(31*2^193886+1)/140765	58362	Lelio R Paula	07/2012
8728	11^56041-1560	58361	Enzo Doria	11/2012
8729	(2^193881+9)/17699	58360	Lelio R Paula	02/2012
8730	3^122313+58	58359	Lelio R Paula	10/2012
8731	6^74996-119	58359	Lelio R Paula	10/2012
8732	(11*2^193859+1)/13	58358	Lelio R Paula	07/2012
8733	2^193861-112255	58358	Enzo Doria	06/2014
8734	(22699*2^193854+1)/4927	58357	Lelio R Paula	06/2014
8735	18^46487+37	58354	Lelio R Paula	03/2013
8736	17^47419+54	58347	Lelio R Paula	03/2013
8737	(31*2^193791+1)/3	58338	Lelio R Paula	02/2012
8738	(27*2^193805-1)/982249	58337	Lelio R Paula	01/2014
8739	144^27025-143	58330	Norbert Schneider	11/2018
8740	3^122219-2^122219	58314	Mike Oakes	09/2003
8741	(199*10^58306+11)/3	58308	Robert Price	05/2017
8742	2^193674-18825	58302	Lelio R Paula	05/2011
8743	5*10^58275+3	58276	Dmitry Domanov	11/2010
8744	2^193578-112913	58273	Enzo Doria	06/2014
8745	2^193541+1299	58262	Lelio R Paula	05/2011
8746	10^58250+93	58251	Robert Price	01/2011
8747	10^58250-175607	58250	Patrick De Geest	12/2012
8748	(107^28703+1)/108	58248	Richard Fischer	05/2018
8749	2^193492+8415	58247	Lelio R Paula	10/2012
8750	2^193444+157	58233	Lelio R Paula	04/2011

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PRP Records

Probable Primes Top 10000

(252402 PRPs in the top)