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 (> 30000)	Who ?	When ?
8251	Phi(61456,109)	59526	Enzo Doria	05/2012
8252	(59^33613+1)/60	59522	Paul Bourdelais	08/2017
8253	3^124747+94	59520	Lelio R Paula	10/2012
8254	17^48370+18	59517	Lelio R Paula	03/2013
8255	20^45740-1523	59510	Enzo Doria	03/2013
8256	(47*10^59509+493)/9	59510	Robert Price	11/2017
8257	(7*2^197642-1)/3051	59494	Lelio R Paula	01/2014
8258	18^47390-1853	59488	Enzo Doria	03/2013
8259	(2^197581-7)/1915	59475	Lelio R Paula	02/2012
8260	(24737*2^197559+1)/77	59474	Lelio R Paula	06/2014
8261	2^197540-2459	59466	Yves Minet	07/2014
8262	(44*10^59454+1)/9	59455	Serge Batalov	11/2010
8263	2^197494-17805	59452	Enzo Doria	05/2013
8264	2^197482-16821	59449	Enzo Doria	05/2013
8265	2^197485+75767	59449	Enzo Doria	04/2016
8266	(3*2^197483+1)/25	59448	Lelio R Paula	07/2012
8267	2^197466-1868351	59444	Enzo Doria	04/2016
8268	2^197411-17781	59427	Enzo Doria	05/2013
8269	(F(142164)^3-F(142163)^3)/F(142162)	59421	Wayne Halsdorf	03/2012
8270	2^197392-114629	59421	Enzo Doria	05/2015
8271	2^197355-157	59410	Lelio R Paula	04/2011
8272	5^84992-84	59407	Lelio R Paula	10/2012
8273	2*3^124504-5	59404	Lelio R Paula	04/2014
8274	2^197307-19165	59396	Enzo Doria	05/2013
8276	2^197303+32769	59395	Lelio R Paula	05/2011
8275	2*10^59394-69	59395	Robert Price	07/2017
8277	(53*10^59389+1)/9	59390	Serge Batalov	11/2010
8278	6^76316-35	59386	Lelio R Paula	10/2012
8279	2^197259-2929	59381	Yves Minet	09/2014
8280	lucasU(46,1,35715)-lucasU(46,1,35714)	59377	Mike Oakes	04/2009
8281	17^48253-6	59373	Lelio R Paula	03/2013
8282	2^197156-15837	59350	Enzo Doria	04/2013
8283	2^197152-4295	59349	Yves Minet	08/2018
8284	2^197149-18481	59348	Enzo Doria	05/2013
8285	2^197142-17157	59346	Enzo Doria	05/2013
8287	(F(6)^65707-F(5)^65707)/F(4)	59339	Wayne Halsdorf	04/2010
8286	(8^65707-5^65707)/3	59339	Robert Price	12/2012
8288	(2*14283^14283+1)/7925497975	59334	David Broadhurst	09/2010
8289	2^197012-111719	59307	Enzo Doria	05/2014
8290	2^196975+513	59296	Lelio R Paula	05/2011
8291	(61*10^59294+119)/9	59295	Robert Price	09/2017
8292	4*10^59292+39	59293	Robert Price	11/2017
8293	2^196960+97	59291	Lelio R Paula	04/2011
8294	9^62116+8^(62116-1)	59274	Robert Price	03/2016
8295	2^196900-97305	59273	Lelio R Paula	09/2011
8296	5*6^76155+7	59261	Lelio R Paula	09/2014
8297	15^50385-14	59258	Wojciech Florek	06/2006
8298	(136777#-1)/8823581477	59254	Donovan Johnson	05/2006
8299	(2^196744-3)*6-7	59227	Gilbert Mozzo	05/2016
8300	(67607*2^196696+1)/3	59216	Lelio R Paula	05/2014
8301	2^196696-112967	59212	Enzo Doria	06/2014
8302	20^45508-4223	59208	Enzo Doria	03/2013
8303	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
8304	14^51651-81	59199	Lelio R Paula	03/2013
8305	2^196650-1451	59198	Yves Minet	08/2012
8306	2^196636-2797799	59194	Enzo Doria	04/2016
8307	1111*2^196610-555	59189	Henri Lifchitz	04/2005
8308	3^124041+658	59183	Lelio R Paula	10/2012
8309	2^196590-111797	59180	Enzo Doria	05/2014
8310	(10^59174-13)/3	59174	Robert Price	02/2017
8311	(2*10^59174-113)/3	59174	Robert Price	09/2017
8312	(9179*2^196533-1)/783	59164	Lelio R Paula	04/2015
8313	379*10^59152+9	59155	Arkadiusz Wesolowski	10/2011
8314	(404*10^59149-53)/9	59151	Robert Price	11/2017
8315	13^53095+40	59145	Lelio R Paula	03/2013
8316	2*F(282999)-1	59144	Henri Lifchitz	12/2009
8317	4*7^69984+3	59144	Lelio R Paula	09/2014
8318	(5*10^59142+1)/3	59143	Erik Branger	12/2013
8319	2^196463+5711	59142	Lelio R Paula	10/2011
8320	2^196453-97305	59139	Lelio R Paula	09/2011
8321	(28*10^59135+53)/9	59136	Serge Batalov	11/2008
8322	(28*10^59133+113)/3	59134	Robert Price	03/2016
8323	2^196434+7	59133	Lelio R Paula	04/2011
8324	(8*10^59127-29)/3	59128	Robert Price	05/2016
8325	2^196414+255	59127	Lelio R Paula	05/2011
8326	5^84586-92	59124	Lelio R Paula	10/2012
8327	2^196388-17177	59119	Enzo Doria	05/2013
8328	79427!6-6	59119	Robert Price	08/2018
8329	3^123890+20	59111	Lelio R Paula	10/2012
8330	2^196355-1021777	59109	Paul Bourdelais	11/2012
8331	11^56754-1410	59104	Enzo Doria	11/2012
8332	(7*2^196297-1)/1200407	59087	Lelio R Paula	01/2014
8333	(16*10^59062-19)/3	59063	Robert Price	03/2016
8334	35^38249-1228	59060	Enzo Doria	03/2013
8335	5^84475-18	59046	Lelio R Paula	10/2012
8336	2^196123-17701	59039	Enzo Doria	05/2013
8337	12^54702-31	59034	Lelio R Paula	03/2013
8338	2^196101-175	59033	Lelio R Paula	04/2011
8339	2^196085+5775	59028	Lelio R Paula	05/2011
8340	2^196034+11715	59013	Lelio R Paula	05/2011
8341	2^196018-18485	59008	Enzo Doria	05/2013
8342	2^195984-2163	58998	Yves Minet	08/2013
8343	3^123645-16	58994	Lelio R Paula	10/2012
8344	39^37078-38	58994	Norbert Schneider	05/2014
8345	2^195958-16853	58990	Enzo Doria	05/2013
8346	2^195930-3071	58981	Yves Minet	10/2014
8347	2^195924+513	58980	Lelio R Paula	05/2011
8348	2^195863+155	58961	Lelio R Paula	04/2011
8349	(28*10^58956+113)/3	58957	Robert Price	03/2016
8350	11^56612-9300	58956	Enzo Doria	02/2013
8351	2^195833-17173	58952	Enzo Doria	05/2013
8352	(27*2^195833-1)/53	58952	Lelio R Paula	01/2014
8353	(13*2^195821-1)/122425	58945	Lelio R Paula	01/2014
8354	139^27504-138	58942	Norbert Schneider	10/2015
8355	(418*10^58923+23)/9	58925	Robert Price	08/2017
8356	3^123495+44	58923	Lelio R Paula	10/2012
8357	2^195737-18565	58923	Enzo Doria	05/2013
8358	79185!6-16	58921	Robert Price	08/2018
8359	14^51407+47	58920	Lelio R Paula	03/2013
8360	2^195691-99	58909	Lelio R Paula	04/2011
8361	2^195667-1859827	58902	Enzo Doria	04/2016
8363	2^195642+75499	58895	Enzo Doria	04/2016
8362	(299*10^58893+1)/3	58895	Robert Price	11/2017
8364	8*6^75678+5	58890	Lelio R Paula	09/2014
8365	2^195618+73189	58887	Enzo Doria	04/2016
8366	(3928^20480+1)/(3928^4096+1)	58887	Serge Batalov	01/2017
8367	t(197953)	58881	Robert Price	12/2014
8368	2^195581-16105	58876	Enzo Doria	04/2013
8369	(8*10^58872+67)/3	58873	Robert Price	01/2017
8370	7*2^195542-5	58865	Lelio R Paula	03/2014
8371	2*10^58861+9^58861	58862	Mike Oakes	04/2011
8372	11^56513-1620	58853	Enzo Doria	11/2012
8373	2^195496+165	58851	Lelio R Paula	04/2011
8374	5^84187+66	58845	Lelio R Paula	10/2012
8375	(28*10^58843-43)/3	58844	Robert Price	04/2016
8376	2^195462-17565	58840	Enzo Doria	05/2013
8377	2^195449-4171	58837	Yves Minet	02/2018
8378	2^195435+59273	58832	Yves Minet	01/2011
8379	2^195424-18605	58829	Enzo Doria	05/2013
8380	2^195385-111	58817	Lelio R Paula	04/2011
8381	7*10^58815-83	58816	Robert Price	09/2017
8382	2^195357-4303	58809	Yves Minet	08/2018
8383	(47*2^195254+1)/268821	58774	Lelio R Paula	03/2015
8384	2^195207-18109	58764	Enzo Doria	05/2013
8385	2^195199-1567	58761	Yves Minet	08/2012
8386	2^195190+73759	58759	Enzo Doria	04/2016
8387	9*7^69525-4	58757	Lelio R Paula	09/2014
8388	2^195170-18045	58753	Enzo Doria	05/2013
8389	2^195166-165	58751	Lelio R Paula	04/2011
8390	(754*10^58748-7)/9	58750	Robert Price	11/2017
8391	(22699*2^195140+1)/175	58746	Lelio R Paula	05/2014
8392	7*3^123109-2	58739	Lelio R Paula	04/2014
8393	(8*10^58738-611)/9	58738	Robert Price	11/2017
8394	18^46790+77	58735	Lelio R Paula	03/2013
8396	2^195095-337297	58730	Gary Barnes	09/2009
8395	(14*10^58729+31)/9	58730	Robert Price	02/2015
8397	99^29424+98	58720	Norbert Schneider	07/2013
8398	(15185*2^195039-1)/219	58715	Lelio R Paula	04/2015
8399	2^195001-69	58702	Lelio R Paula	04/2011
8400	2^194978-487811	58695	Gary Barnes	09/2009
8401	163^26530+26530^163	58690	Serge Batalov	05/2014
8402	2^194940-194940+1	58683	Robert Price	10/2014
8403	(76*10^58669+41)/9	58670	Robert Price	10/2015
8404	14^51186+87	58666	Lelio R Paula	03/2013
8405	2^194878-97305	58665	Lelio R Paula	09/2011
8406	5^83927-18136	58663	Enzo Doria	05/2014
8407	(24737*2^194865+1)/1085	58662	Lelio R Paula	06/2014
8408	7^69411+40	58660	Lelio R Paula	10/2012
8409	6^75382-79	58659	Lelio R Paula	10/2012
8410	2^194854+27	58657	Lelio R Paula	04/2011
8411	2^194801+29835	58641	Lelio R Paula	10/2012
8412	2^194752+195	58627	Lelio R Paula	04/2011
8413	7^69371-6^69371	58626	Predrag Minovic	08/2004
8414	2^194747-112519	58625	Enzo Doria	06/2014
8415	(15*2^194737+1)/59	58622	Lelio R Paula	07/2012
8416	(23*2^194700+1)/3	58612	Lelio R Paula	02/2012
8417	10^58608+55273	58609	Patrick De Geest	07/2017
8418	10^58608-800001	58608	Robert Price	06/2017
8419	10^58608-60119	58608	Patrick De Geest	07/2017
8420	5^83836+76	58599	Lelio R Paula	10/2012
8421	18^46664+31	58577	Lelio R Paula	03/2013
8422	(34*10^58577-7)/9/19/463	58574	Makoto Morimoto	04/2016
8423	2^194574+165	58573	Lelio R Paula	04/2011
8426	2^194569-12211	58572	Enzo Doria	06/2014
8424	10^58571+5^58571+2^58571	58572	Robert Price	12/2016
8425	10^58571+202837	58572	Patrick De Geest	02/2017
8427	(10^58571+41)/3	58571	Robert Price	01/2017
8428	10^58571-343629	58571	Patrick De Geest	02/2017
8429	(43*10^58563-403)/9	58564	Robert Price	04/2017
8430	11^56235-7950	58563	Enzo Doria	02/2013
8431	(14*10^58550+211)/9	58551	Robert Price	11/2017
8432	2^194479-113239	58545	Enzo Doria	07/2014
8433	2^194455-112249	58537	Enzo Doria	06/2014
8434	2^194405-111919	58522	Enzo Doria	05/2014
8435	(4*10^58521-19)/3	58522	Robert Price	06/2017
8437	(7^69247-4^69247)/3	58521	Robert Price	06/2012
8436	5*7^69246+8	58521	Lelio R Paula	09/2014
8438	2^194358-1167	58508	Lelio R Paula	05/2011
8439	(2^194366+7)/1373	58507	Lelio R Paula	02/2012
8440	(493*10^58486-7)/9	58488	Robert Price	07/2016
8441	3^122579-340	58486	Lelio R Paula	10/2012
8442	(11*10^58458-149)/3	58459	Robert Price	01/2017
8443	(47*10^58456+133)/9	58457	Robert Price	04/2017
8444	2^194186+85	58456	Lelio R Paula	04/2011
8445	3^122506-2^(122506-1)	58451	Robert Price	01/2016
8446	(74^31267-1)/73	58444	Paul Bourdelais	08/2017
8447	177^25998-2	58443	Lelio R Paula	10/2017
8448	15^49690-26	58440	Lelio R Paula	03/2013
8449	10^58437+110721	58438	Patrick De Geest	12/2012
8450	10^58437-11	58437	Robert Price	05/2011
8451	2^194095+69	58429	Lelio R Paula	04/2011
8452	(29*10^58417-77)/3	58418	Robert Price	01/2017
8453	2^194034+177	58411	Lelio R Paula	04/2011
8454	789^20158+20158^789	58400	Norbert Schneider	06/2016
8455	14^50949+75	58395	Lelio R Paula	03/2013
8456	2^193974-114761	58392	Enzo Doria	05/2015
8457	2^193965+5	58390	Henri Lifchitz	12/2002
8458	(5*10^58384-29)/3	58385	Robert Price	02/2017
8459	3^122360+80	58381	Lelio R Paula	10/2012
8460	10103^14577-114	58373	Enzo Doria	07/2012
8461	(22699*2^193883+1)/21	58368	Lelio R Paula	06/2014
8462	(31*2^193886+1)/140765	58362	Lelio R Paula	07/2012
8463	11^56041-1560	58361	Enzo Doria	11/2012
8464	(2^193881+9)/17699	58360	Lelio R Paula	02/2012
8465	3^122313+58	58359	Lelio R Paula	10/2012
8466	6^74996-119	58359	Lelio R Paula	10/2012
8467	(11*2^193859+1)/13	58358	Lelio R Paula	07/2012
8468	2^193861-112255	58358	Enzo Doria	06/2014
8469	(22699*2^193854+1)/4927	58357	Lelio R Paula	06/2014
8470	18^46487+37	58354	Lelio R Paula	03/2013
8471	17^47419+54	58347	Lelio R Paula	03/2013
8472	(31*2^193791+1)/3	58338	Lelio R Paula	02/2012
8473	(27*2^193805-1)/982249	58337	Lelio R Paula	01/2014
8474	3^122219-2^122219	58314	Mike Oakes	09/2003
8475	(199*10^58306+11)/3	58308	Robert Price	05/2017
8476	2^193674-18825	58302	Lelio R Paula	05/2011
8477	5*10^58275+3	58276	Dmitry Domanov	11/2010
8478	2^193578-112913	58273	Enzo Doria	06/2014
8479	2^193541+1299	58262	Lelio R Paula	05/2011
8480	10^58250+93	58251	Robert Price	01/2011
8481	10^58250-175607	58250	Patrick De Geest	12/2012
8482	(107^28703+1)/108	58248	Richard Fischer	05/2018
8483	2^193492+8415	58247	Lelio R Paula	10/2012
8484	2^193444+157	58233	Lelio R Paula	04/2011
8485	Phi(28754,28754)	58231	Henri Lifchitz	08/2013
8486	2^193430-111881	58229	Enzo Doria	05/2014
8487	10^58225+124579	58226	Patrick De Geest	12/2012
8488	10^58225-93	58225	Robert Price	05/2011
8489	2^193375-295	58212	Yves Minet	05/2013
8490	2^193345+77267	58203	Enzo Doria	05/2016
8491	21^44017-20^44017	58201	Robert Price	05/2012
8492	(17*2^193329-1)/9	58199	Lelio R Paula	01/2014
8493	17^47291+20	58190	Lelio R Paula	03/2013
8494	p(12528)#/2-128	58170	Robert Price	05/2017
8495	2^193214-135	58164	Lelio R Paula	04/2011
8496	19^45483-80	58162	Lelio R Paula	03/2013
8497	(4*10^58155+83)/3	58156	Robert Price	01/2017
8498	14^50739-13	58154	Lelio R Paula	03/2013
8499	(1017*2^193184-1)/4823	58154	Lelio R Paula	04/2015
8500	(2*10^58151+457)/9	58151	Robert Price	01/2017

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Probable Primes Top 10000

(218736 PRPs in the top)