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 ?
6251	2^239356-111875	72054	Enzo Doria	05/2014
6252	(38*10^72050-119)/9	72051	Robert Price	11/2016
6253	2^239339+15015	72049	Lelio R Paula	01/2013
6254	159^32728+2	72048	Lelio R Paula	05/2013
6255	15^61259-38	72047	Lelio R Paula	01/2015
6256	92^36683-91^36683	72038	Robert Price	08/2015
6257	2^239280+54615	72031	Lelio R Paula	05/2012
6258	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015
6259	(85*10^72025-1)/3	72027	Robert Price	07/2017
6260	2^239236-97305	72018	Lelio R Paula	05/2012
6261	2^239169+59	71998	Lelio R Paula	02/2012
6262	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
6263	(15*2^239171-1)/106301	71994	Lelio R Paula	01/2014
6264	(29^49211-1)/28	71965	Robert Price	04/2012
6265	(299*10^71963+1)/3	71965	Robert Price	11/2017
6267	L(344293)	71953	Renaud Lifchitz	09/2003
6266	V(344293)	71953	Serge Batalov	03/2015
6268	6*10^71951+7	71952	Dmitry Domanov	11/2010
6269	3^150798+40	71949	Lelio R Paula	01/2015
6270	2^238961+95	71935	Lelio R Paula	02/2012
6271	2^238936-407	71927	Yves Minet	02/2012
6272	2^238923-28635	71923	Lelio R Paula	05/2012
6273	10^71910+25119	71911	Patrick De Geest	05/2016
6274	10^71910-801	71910	Robert Price	04/2016
6275	2^238845-112651	71900	Enzo Doria	06/2014
6276	2^238792-111245	71884	Enzo Doria	05/2014
6277	6*7^85059+5	71884	Lelio R Paula	10/2014
6278	2^238752-110589	71872	Enzo Doria	05/2014
6279	12^66581+7	71853	Lelio R Paula	07/2014
6280	(7*2^238691+1)/41229	71850	Lelio R Paula	06/2012
6281	4*3^150568-5	71840	Lelio R Paula	04/2014
6282	6^92301+67	71825	Lelio R Paula	01/2015
6283	2^238568+98765331	71817	Jason Earls	01/2009
6284	2^238541-112723	71808	Enzo Doria	06/2014
6285	2^238529-15949	71805	Enzo Doria	04/2013
6286	9*5^102721-8	71800	Lelio R Paula	10/2014
6287	2^238494-165	71794	Lelio R Paula	02/2012
6288	2^238389-110905	71763	Enzo Doria	05/2014
6289	(145*10^71760-1)/9	71762	Serge Batalov	12/2014
6290	7^84913+5062	71760	Mike Oakes	02/2010
6291	(F(11446)^31-F(11445)^31)/F(11444)	71753	Wayne Halsdorf	03/2012
6292	2^238268-97305	71726	Lelio R Paula	05/2012
6293	gcd(V(1330365),5F(266073)(F(266073)-1)+1)	71724	Serge Batalov	04/2015
6294	2^238235-113247	71716	Enzo Doria	07/2014
6295	2*12^66450-5^66450	71712	Mike Oakes	11/2010
6296	(2^238213+lucasV(1,2,238213)+1)/4	71709	Mike Oakes	11/2016
6297	2^238199-111817	71706	Enzo Doria	05/2014
6298	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
6299	2^238144+98765331	71689	Jason Earls	01/2009
6300	18^57102-4265	71679	Enzo Doria	03/2013
6301	(73*10^71670-1)/9	71671	Robert Price	01/2015
6302	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
6303	2^238067-111925	71666	Enzo Doria	05/2014
6304	36^46030+35	71637	Norbert Schneider	04/2014
6305	(74*10^71621+313)/9	71622	Robert Price	11/2017
6306	2^237905-91	71617	Lelio R Paula	02/2012
6307	(31*2^237902-1)/123	71616	Lelio R Paula	01/2014
6308	(15185*2^237866-1)/43967	71605	Lelio R Paula	04/2015
6309	(24737*2^237841+1)/25	71601	Lelio R Paula	06/2014
6310	2^237846+1299	71599	Lelio R Paula	05/2012
6311	6^92004+199801	71594	Mike Oakes	02/2011
6312	159^32516+2	71581	Lelio R Paula	05/2013
6313	2^237781+855	71580	Lelio R Paula	05/2012
6314	2^237720-4079	71561	Yves Minet	06/2011
6315	2^237698-110945	71555	Enzo Doria	05/2014
6316	2^237695-113239	71554	Enzo Doria	07/2014
6317	8*5^102362-9	71549	Lelio R Paula	10/2014
6318	(4*10^71546-31)/9	71546	Erik Branger	05/2011
6319	2^237650+37	71540	Lelio R Paula	02/2012
6320	18^56977-4391	71522	Enzo Doria	03/2013
6321	(22699*2^237565+1)/4136637	71512	Lelio R Paula	06/2014
6322	((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
6323	(26*10^71503+7)/3	71504	Erik Branger	11/2013
6324	(4*10^71498+173)/3	71499	Robert Price	01/2017
6325	3^149848+110	71496	Lelio R Paula	11/2014
6326	2^237498+513	71495	Lelio R Paula	05/2012
6327	2^237485+107	71491	Lelio R Paula	02/2012
6328	(2^237465+9)/2419	71481	Lelio R Paula	05/2012
6329	2^237439-112237	71477	Enzo Doria	06/2014
6330	2^237407-9787	71467	Lelio R Paula	11/2009
6331	2^237383+72953	71460	Enzo Doria	04/2016
6332	82^37337-81^37337	71457	Robert Price	01/2015
6333	(1017*2^237313-1)/19	71441	Lelio R Paula	04/2015
6334	2^237311+191	71438	Lelio R Paula	02/2012
6335	2^237280-59	71429	Lelio R Paula	02/2012
6336	11^68564-98	71403	Lelio R Paula	01/2015
6337	2^237173+74801	71397	Enzo Doria	04/2016
6338	15^60697+56	71386	Lelio R Paula	01/2015
6339	2^237118+177	71380	Lelio R Paula	02/2012
6340	2^237110+69	71378	Lelio R Paula	02/2012
6341	15^60690-58	71377	Lelio R Paula	01/2015
6342	(5*2^237125-1)/599851191	71374	Lelio R Paula	01/2014
6343	(3^149567+2)/539	71359	Lelio R Paula	06/2012
6344	(5*10^71357-143)/3	71358	Robert Price	04/2016
6345	2^237039-114621	71356	Enzo Doria	05/2015
6346	12^66116-37	71352	Lelio R Paula	02/2015
6347	(3^149497+2^149497)/5	71328	Jean-Louis Charton	10/2010
6348	2^236941-66945	71327	Lelio R Paula	05/2012
6349	2^236911-1147	71318	Yves Minet	10/2009
6350	65^39337+42	71315	Lelio R Paula	01/2016
6351	6*10^71299+7	71300	Dmitry Domanov	11/2010
6352	(25*2^236843+1)/3753	71295	Lelio R Paula	06/2012
6353	10^71291+15187	71292	Patrick De Geest	03/2016
6355	10^71291-5587309119	71291	Robert Price	03/2015
6354	10^71291-273581	71291	Patrick De Geest	03/2016
6356	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
6357	(2^236738+9)/13	71265	Lelio R Paula	05/2012
6358	5^101949+42	71260	Lelio R Paula	07/2014
6359	5*10^71237+9	71238	Dmitry Domanov	11/2010
6360	2^236634-16025	71234	Enzo Doria	04/2013
6361	71^38478+70	71233	Norbert Schneider	12/2014
6362	9*7^84280+8	71226	Lelio R Paula	10/2014
6363	(10^71223+59)/3	71223	Serge Batalov	12/2014
6364	(15185*2^236569-1)/453	71216	Lelio R Paula	04/2015
6365	51829#+(216091#)/(51829#)	71208	Makoto Morimoto	03/2016
6366	2^236528-173	71203	Lelio R Paula	02/2012
6367	3*2^236511-5	71198	Lelio R Paula	04/2014
6368	2^236477-99	71187	Lelio R Paula	02/2012
6369	11^68356-2130	71186	Enzo Doria	12/2012
6370	11^68355-3120	71185	Enzo Doria	12/2012
6371	36^45737-35^45737	71181	Robert Price	10/2012
6372	(3^149183-lucasV(1,3,149183)+1)/3	71178	Paul Vanderveen	12/2017
6373	2^236432+25	71174	Lelio R Paula	02/2012
6374	5^101818-12806	71168	Enzo Doria	02/2013
6375	(7*10^71166-457)/9	71166	Robert Price	09/2017
6376	65^39253+62	71163	Lelio R Paula	01/2016
6377	39^44718+38	71150	Norbert Schneider	05/2014
6378	2^236296-407	71133	Yves Minet	02/2012
6379	2^236286-117	71130	Lelio R Paula	02/2012
6380	2^236257-111193	71121	Enzo Doria	05/2014
6381	7^84149-36	71115	Lelio R Paula	08/2014
6382	2^236209-112123	71106	Enzo Doria	06/2014
6383	18^56644-4985	71104	Enzo Doria	03/2013
6384	(46*10^71077+521)/9	71078	Robert Price	08/2017
6385	21^53753+2	71074	Ray Chandler	08/2011
6386	(86*10^71068-311)/9	71069	Robert Price	10/2017
6387	2^236081-110923	71068	Enzo Doria	05/2014
6388	(293*27^49642-1736)/13	71058	Curtis Bright	05/2015
6389	65^39192+22	71052	Lelio R Paula	01/2016
6390	(439#+1)^397-439#^397	71038	Mike Oakes	11/2010
6391	7^84050-2	71031	Lelio R Paula	09/2013
6392	20^54558-23	70982	Lelio R Paula	01/2015
6393	2^235793-112555	70981	Enzo Doria	06/2014
6394	49936!3-3^49936	70981	Robert Price	08/2015
6395	2^235787-78795	70979	Lelio R Paula	05/2012
6396	Perrin(581132)	70970	Eric W. Weisstein	02/2011
6397	14^61913-97	70961	Lelio R Paula	01/2015
6398	2^235720+16321	70959	Yves Minet	03/2010
6399	2^235718+16095	70959	Lelio R Paula	05/2012
6400	163841#+349933	70957	Nicolas PALAU	11/2016
6401	2^235710+7	70956	Lelio R Paula	02/2012
6402	(175^31627+1)/176	70939	Eric Chen	10/2017
6403	2^235635-112087	70934	Enzo Doria	06/2014
6405	2^235575-1965	70916	Lelio R Paula	05/2012
6404	6^91133+101	70916	Lelio R Paula	01/2015
6406	(21181*2^235505+1)/3	70898	Lelio R Paula	06/2014
6407	(14*10^70896+211)/9	70897	Robert Price	11/2017
6408	5^101425+84	70894	Lelio R Paula	07/2014
6409	177^31536+2	70893	Lelio R Paula	05/2013
6410	43*71^38292+4	70891	Serge Batalov	03/2016
6411	(29*2^235506-1)/112029785	70888	Lelio R Paula	01/2014
6412	11^68045-1530	70862	Enzo Doria	12/2012
6413	5*10^70858+21	70859	Robert Price	01/2017
6414	2^235326+3	70841	Donovan Johnson	02/2006
6415	34523!2+4	70841	Robert Price	02/2015
6416	(31*2^235307+1)/3	70836	Lelio R Paula	06/2012
6417	2^235308+135	70835	Lelio R Paula	02/2012
6418	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
6419	2^235274+159	70825	Lelio R Paula	02/2012
6420	3^148409+70	70810	Lelio R Paula	11/2014
6421	(19*10^70794+17)/9	70795	Robert Price	03/2015
6422	2^235108-232709	70775	Paul Bourdelais	03/2013
6423	(2^235099-2^117550+1)/5	70772		11/2006
6424	19^55325-6	70748	Lelio R Paula	08/2014
6425	257^29356+29356^257	70746	Norbert Schneider	10/2014
6426	22*10^70729+3	70731	Robert Price	10/2017
6427	2^234956+11715	70729	Lelio R Paula	05/2012
6428	(7*10^70727-43)/9	70727	Robert Price	10/2014
6429	2^234890-30341	70709	Enzo Doria	11/2012
6430	17^57461+14	70703	Lelio R Paula	01/2015
6431	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
6432	2*10^70688+51	70689	Robert Price	10/2017
6433	123^33822-122	70685	Norbert Schneider	01/2015
6434	7*10^70680-99	70681	Robert Price	11/2017
6435	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
6436	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
6437	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
6439	2^234655-67	70639	Lelio R Paula	02/2012
6438	(79*10^70638-61)/9	70639	Robert Price	10/2015
6440	2^234652-173	70638	Lelio R Paula	02/2012
6441	2^234618-3645	70628	Lelio R Paula	05/2012
6442	(2^234610-5)/19	70624	Lelio R Paula	05/2012
6443	4*5^101038+9	70624	Lelio R Paula	10/2014
6444	2^234603+71963	70623	Enzo Doria	04/2016
6445	2^234600-113129	70622	Enzo Doria	07/2014
6446	2^234586+9	70618	Lelio R Paula	02/2012
6447	3^148008+26	70618	Robert Price	11/2013
6448	(7*10^70616-151)/9	70616	Robert Price	09/2017
6449	65^38947+32	70608	Lelio R Paula	01/2016
6450	(2^234488-3)/11	70587	Lelio R Paula	05/2012
6451	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
6452	Phi(159495,10)	70560	Maksym Voznyy	09/2015
6453	2^234383-4035	70557	Lelio R Paula	05/2012
6454	2^234315-111241	70536	Enzo Doria	05/2014
6455	14^61526+97	70517	Lelio R Paula	01/2015
6456	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
6457	51^41281-50^41281	70491	Robert Price	02/2013
6458	2^234141-112123	70484	Enzo Doria	06/2014
6459	2^234139+12285	70483	Lelio R Paula	04/2012
6460	2^234133-3163	70482	Yves Minet	04/2009
6461	2^234115+83	70476	Lelio R Paula	02/2012
6462	2^234114-1595	70476	Lelio R Paula	05/2012
6463	24^51061-23^51061	70475	Robert Price	07/2012
6464	19471^16428-2	70467	Faysal YAtim	09/2005
6465	7^83381+12	70466	Robert Price	01/2014
6466	2^234067-111427	70462	Enzo Doria	05/2014
6467	(266*10^70457+1)/3	70459	Robert Price	02/2016
6468	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
6469	2^234026+12909	70449	Lelio R Paula	04/2012
6470	2^233965-19	70431	Lelio R Paula	02/2012
6471	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
6472	2^233908-17109	70414	Enzo Doria	05/2013
6473	695^24772+24772^695	70402	Norbert Schneider	09/2016
6474	3*5^100719-2	70401	Lelio R Paula	10/2014
6475	2^233829-111355	70390	Enzo Doria	05/2014
6476	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
6477	7*3^147519+8	70386	Lelio R Paula	04/2014
6478	141^32749-2	70385	Lelio R Paula	10/2017
6479	5*7^83265+2	70368	Lelio R Paula	10/2014
6480	(23*10^70363+97)/3	70364	Robert Price	02/2017
6481	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
6482	5^100652-13916	70353	Enzo Doria	02/2013
6483	45^42555-2	70353	Lelio R Paula	08/2013
6484	2^233661-61	70339	Lelio R Paula	02/2012
6485	2^233523-112249	70298	Enzo Doria	06/2014
6486	5*3^147324-8	70293	Lelio R Paula	04/2014
6487	2^233488-13065	70287	Enzo Doria	11/2012
6488	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
6489	(22*10^70259+161)/3	70260	Robert Price	02/2017
6490	2^233388+465	70257	Lelio R Paula	11/2012
6491	14^61299+59	70257	Lelio R Paula	01/2015
6492	2^233383+94065	70256	Lelio R Paula	04/2012
6493	49471!3-6561	70253	Robert Price	11/2015
6494	7^83121+6^(83121-1)	70246	Robert Price	03/2016
6495	(197*10^70241-11)/3	70243	Robert Price	10/2017
6496	23*10^70240-7	70242	Robert Price	03/2016
6497	(71*10^70227-53)/9	70228	Robert Price	10/2015
6498	(2^233247-9)/17	70214	Lelio R Paula	05/2012
6499	(11^67421-2^67421)/9	70211	Robert Price	01/2013
6500	(23*10^70209-41)/9	70210	Robert Price	03/2015

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Probable Primes Top 10000

(212140 PRPs in the top)