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	(4*10^71498+173)/3	71499	Robert Price	01/2017
6252	3^149848+110	71496	Lelio R Paula	11/2014
6253	2^237498+513	71495	Lelio R Paula	05/2012
6254	2^237485+107	71491	Lelio R Paula	02/2012
6255	(2^237465+9)/2419	71481	Lelio R Paula	05/2012
6256	2^237439-112237	71477	Enzo Doria	06/2014
6257	2^237407-9787	71467	Lelio R Paula	11/2009
6258	2^237383+72953	71460	Enzo Doria	04/2016
6259	82^37337-81^37337	71457	Robert Price	01/2015
6260	(1017*2^237313-1)/19	71441	Lelio R Paula	04/2015
6261	2^237311+191	71438	Lelio R Paula	02/2012
6262	2^237280-59	71429	Lelio R Paula	02/2012
6263	11^68564-98	71403	Lelio R Paula	01/2015
6264	2^237173+74801	71397	Enzo Doria	04/2016
6265	15^60697+56	71386	Lelio R Paula	01/2015
6266	2^237118+177	71380	Lelio R Paula	02/2012
6267	2^237110+69	71378	Lelio R Paula	02/2012
6268	15^60690-58	71377	Lelio R Paula	01/2015
6269	(5*2^237125-1)/599851191	71374	Lelio R Paula	01/2014
6270	(3^149567+2)/539	71359	Lelio R Paula	06/2012
6271	(5*10^71357-143)/3	71358	Robert Price	04/2016
6272	2^237039-114621	71356	Enzo Doria	05/2015
6273	12^66116-37	71352	Lelio R Paula	02/2015
6274	(3^149497+2^149497)/5	71328	Jean-Louis Charton	10/2010
6275	2^236941-66945	71327	Lelio R Paula	05/2012
6276	2^236911-1147	71318	Yves Minet	10/2009
6277	65^39337+42	71315	Lelio R Paula	01/2016
6278	6*10^71299+7	71300	Dmitry Domanov	11/2010
6279	(25*2^236843+1)/3753	71295	Lelio R Paula	06/2012
6280	10^71291+15187	71292	Patrick De Geest	03/2016
6282	10^71291-5587309119	71291	Robert Price	03/2015
6281	10^71291-273581	71291	Patrick De Geest	03/2016
6283	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
6284	(2^236738+9)/13	71265	Lelio R Paula	05/2012
6285	5^101949+42	71260	Lelio R Paula	07/2014
6286	5*10^71237+9	71238	Dmitry Domanov	11/2010
6287	2^236634-16025	71234	Enzo Doria	04/2013
6288	71^38478+70	71233	Norbert Schneider	12/2014
6289	9*7^84280+8	71226	Lelio R Paula	10/2014
6290	(10^71223+59)/3	71223	Serge Batalov	12/2014
6291	(15185*2^236569-1)/453	71216	Lelio R Paula	04/2015
6292	51829#+(216091#)/(51829#)	71208	Makoto Morimoto	03/2016
6293	2^236528-173	71203	Lelio R Paula	02/2012
6294	3*2^236511-5	71198	Lelio R Paula	04/2014
6295	2^236477-99	71187	Lelio R Paula	02/2012
6296	11^68356-2130	71186	Enzo Doria	12/2012
6297	11^68355-3120	71185	Enzo Doria	12/2012
6298	36^45737-35^45737	71181	Robert Price	10/2012
6299	(3^149183-lucasV(1,3,149183)+1)/3	71178	Paul Vanderveen	12/2017
6300	2^236432+25	71174	Lelio R Paula	02/2012
6301	5^101818-12806	71168	Enzo Doria	02/2013
6302	(7*10^71166-457)/9	71166	Robert Price	09/2017
6303	65^39253+62	71163	Lelio R Paula	01/2016
6304	39^44718+38	71150	Norbert Schneider	05/2014
6305	2^236296-407	71133	Yves Minet	02/2012
6306	2^236286-117	71130	Lelio R Paula	02/2012
6307	2^236257-111193	71121	Enzo Doria	05/2014
6308	7^84149-36	71115	Lelio R Paula	08/2014
6309	2^236209-112123	71106	Enzo Doria	06/2014
6310	18^56644-4985	71104	Enzo Doria	03/2013
6311	(46*10^71077+521)/9	71078	Robert Price	08/2017
6312	21^53753+2	71074	Ray Chandler	08/2011
6313	(86*10^71068-311)/9	71069	Robert Price	10/2017
6314	2^236081-110923	71068	Enzo Doria	05/2014
6315	(293*27^49642-1736)/13	71058	Curtis Bright	05/2015
6316	65^39192+22	71052	Lelio R Paula	01/2016
6317	(439#+1)^397-439#^397	71038	Mike Oakes	11/2010
6318	7^84050-2	71031	Lelio R Paula	09/2013
6319	20^54558-23	70982	Lelio R Paula	01/2015
6320	2^235793-112555	70981	Enzo Doria	06/2014
6321	49936!3-3^49936	70981	Robert Price	08/2015
6322	2^235787-78795	70979	Lelio R Paula	05/2012
6323	Perrin(581132)	70970	Eric W. Weisstein	02/2011
6324	14^61913-97	70961	Lelio R Paula	01/2015
6325	2^235720+16321	70959	Yves Minet	03/2010
6326	2^235718+16095	70959	Lelio R Paula	05/2012
6327	163841#+349933	70957	Nicolas PALAU	11/2016
6328	2^235710+7	70956	Lelio R Paula	02/2012
6329	(175^31627+1)/176	70939	Eric Chen	10/2017
6330	2^235635-112087	70934	Enzo Doria	06/2014
6332	2^235575-1965	70916	Lelio R Paula	05/2012
6331	6^91133+101	70916	Lelio R Paula	01/2015
6333	(21181*2^235505+1)/3	70898	Lelio R Paula	06/2014
6334	(14*10^70896+211)/9	70897	Robert Price	11/2017
6335	5^101425+84	70894	Lelio R Paula	07/2014
6336	177^31536+2	70893	Lelio R Paula	05/2013
6337	43*71^38292+4	70891	Serge Batalov	03/2016
6338	(29*2^235506-1)/112029785	70888	Lelio R Paula	01/2014
6339	11^68045-1530	70862	Enzo Doria	12/2012
6340	5*10^70858+21	70859	Robert Price	01/2017
6342	2^235326+3	70841	Donovan Johnson	02/2006
6341	34523!2+4	70841	Robert Price	02/2015
6343	(31*2^235307+1)/3	70836	Lelio R Paula	06/2012
6344	2^235308+135	70835	Lelio R Paula	02/2012
6345	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
6346	2^235274+159	70825	Lelio R Paula	02/2012
6347	3^148409+70	70810	Lelio R Paula	11/2014
6348	(19*10^70794+17)/9	70795	Robert Price	03/2015
6349	2^235108-232709	70775	Paul Bourdelais	03/2013
6350	(2^235099-2^117550+1)/5	70772		11/2006
6351	19^55325-6	70748	Lelio R Paula	08/2014
6352	257^29356+29356^257	70746	Norbert Schneider	10/2014
6353	22*10^70729+3	70731	Robert Price	10/2017
6354	2^234956+11715	70729	Lelio R Paula	05/2012
6355	(7*10^70727-43)/9	70727	Robert Price	10/2014
6356	2^234890-30341	70709	Enzo Doria	11/2012
6357	17^57461+14	70703	Lelio R Paula	01/2015
6358	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
6359	2*10^70688+51	70689	Robert Price	10/2017
6360	123^33822-122	70685	Norbert Schneider	01/2015
6361	7*10^70680-99	70681	Robert Price	11/2017
6362	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
6363	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
6364	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
6366	2^234655-67	70639	Lelio R Paula	02/2012
6365	(79*10^70638-61)/9	70639	Robert Price	10/2015
6367	2^234652-173	70638	Lelio R Paula	02/2012
6368	2^234618-3645	70628	Lelio R Paula	05/2012
6369	(2^234610-5)/19	70624	Lelio R Paula	05/2012
6370	4*5^101038+9	70624	Lelio R Paula	10/2014
6371	2^234603+71963	70623	Enzo Doria	04/2016
6372	2^234600-113129	70622	Enzo Doria	07/2014
6373	2^234586+9	70618	Lelio R Paula	02/2012
6374	3^148008+26	70618	Robert Price	11/2013
6375	(7*10^70616-151)/9	70616	Robert Price	09/2017
6376	65^38947+32	70608	Lelio R Paula	01/2016
6377	(2^234488-3)/11	70587	Lelio R Paula	05/2012
6378	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
6379	Phi(159495,10)	70560	Maksym Voznyy	09/2015
6380	2^234383-4035	70557	Lelio R Paula	05/2012
6381	2^234315-111241	70536	Enzo Doria	05/2014
6382	14^61526+97	70517	Lelio R Paula	01/2015
6383	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
6384	51^41281-50^41281	70491	Robert Price	02/2013
6385	2^234141-112123	70484	Enzo Doria	06/2014
6386	2^234139+12285	70483	Lelio R Paula	04/2012
6387	2^234133-3163	70482	Yves Minet	04/2009
6388	2^234115+83	70476	Lelio R Paula	02/2012
6389	2^234114-1595	70476	Lelio R Paula	05/2012
6390	24^51061-23^51061	70475	Robert Price	07/2012
6391	19471^16428-2	70467	Faysal YAtim	09/2005
6392	7^83381+12	70466	Robert Price	01/2014
6393	2^234067-111427	70462	Enzo Doria	05/2014
6394	(266*10^70457+1)/3	70459	Robert Price	02/2016
6395	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
6396	2^234026+12909	70449	Lelio R Paula	04/2012
6397	2^233965-19	70431	Lelio R Paula	02/2012
6398	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
6399	2^233908-17109	70414	Enzo Doria	05/2013
6400	695^24772+24772^695	70402	Norbert Schneider	09/2016
6401	3*5^100719-2	70401	Lelio R Paula	10/2014
6402	2^233829-111355	70390	Enzo Doria	05/2014
6403	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
6404	7*3^147519+8	70386	Lelio R Paula	04/2014
6405	141^32749-2	70385	Lelio R Paula	10/2017
6406	5*7^83265+2	70368	Lelio R Paula	10/2014
6407	(23*10^70363+97)/3	70364	Robert Price	02/2017
6408	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
6409	5^100652-13916	70353	Enzo Doria	02/2013
6410	45^42555-2	70353	Lelio R Paula	08/2013
6411	2^233661-61	70339	Lelio R Paula	02/2012
6412	2^233523-112249	70298	Enzo Doria	06/2014
6413	5*3^147324-8	70293	Lelio R Paula	04/2014
6414	2^233488-13065	70287	Enzo Doria	11/2012
6415	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
6416	(22*10^70259+161)/3	70260	Robert Price	02/2017
6417	2^233388+465	70257	Lelio R Paula	11/2012
6418	14^61299+59	70257	Lelio R Paula	01/2015
6419	2^233383+94065	70256	Lelio R Paula	04/2012
6420	49471!3-6561	70253	Robert Price	11/2015
6421	7^83121+6^(83121-1)	70246	Robert Price	03/2016
6422	(197*10^70241-11)/3	70243	Robert Price	10/2017
6423	23*10^70240-7	70242	Robert Price	03/2016
6424	(71*10^70227-53)/9	70228	Robert Price	10/2015
6425	(2^233247-9)/17	70214	Lelio R Paula	05/2012
6426	(11^67421-2^67421)/9	70211	Robert Price	01/2013
6427	(23*10^70209-41)/9	70210	Robert Price	03/2015
6428	(29*10^70194-11)/9	70195	Robert Price	04/2015
6429	3^147109+196	70189	Lelio R Paula	05/2014
6430	(34*10^70191-7)/9/3/40583/573047	70181	Makoto Morimoto	05/2016
6431	9^73538+8^(73538+1)	70174	Robert Price	06/2016
6432	2*5^100391+7	70171	Lelio R Paula	10/2014
6433	99^35156-2	70159	Lelio R Paula	08/2013
6434	(68*10^70148+7)/3	70150	Robert Price	03/2016
6435	11^67360-6030	70149	Enzo Doria	01/2013
6436	(35*10^70130-377)/9	70131	Robert Price	12/2017
6437	49391!3+3^49391	70128	Robert Price	09/2015
6438	(229*10^70122-1)/3	70124	Robert Price	12/2016
6439	7^82975-92	70123	Lelio R Paula	07/2014
6440	65^38670+58	70106	Lelio R Paula	01/2016
6441	105^34684+34684^105	70103	Serge Batalov	05/2014
6442	134^32955-133	70099	Norbert Schneider	03/2015
6444	2^232836-227903	70091	Enzo Doria	12/2012
6443	2^232837-1859173	70091	Enzo Doria	03/2016
6445	3*2^232820+5	70087	Lelio R Paula	04/2014
6447	2^232799+90195	70080	Lelio R Paula	02/2013
6446	2^232799-112237	70080	Enzo Doria	06/2014
6448	2^232759+262145	70068	Lelio R Paula	04/2012
6449	3*2^232750+7	70066	Lelio R Paula	04/2014
6450	12^64918-11	70059	Lelio R Paula	01/2015
6451	7^82899-12	70058	Lelio R Paula	09/2013
6452	(22*10^70051-13)/9	70052	Robert Price	03/2015
6453	(2^232685-7)/2514625	70039	Lelio R Paula	04/2012
6454	18^55786-5363	70027	Enzo Doria	03/2013
6455	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
6456	2^232602+169	70021	Lelio R Paula	02/2012
6457	(137^32768+29^32768)/2	70016	Jeppe Stig Nielsen	04/2018
6458	2^232580+72133	70014	Enzo Doria	04/2016
6459	4*6^89958-7	70002	Lelio R Paula	09/2014
6460	10^70000+80487	70001	Milton L. Brown	05/2006
6461	10^69999+134857	70000	Patrick De Geest	02/2007
6466	10^70000-9273	70000	Patrick De Geest	08/2009
6462	(79*10^69999-7)/9	70000	Robert Price	01/2015
6463	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
6464	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
6465	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
6467	10^69999-88251	69999	Patrick De Geest	08/2009
6468	2^232507+1089	69992	Lelio R Paula	04/2012
6469	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
6470	(529^25693+1)/530	69972	Richard Fischer	12/2017
6471	7^82778+48	69956	Lelio R Paula	09/2013
6472	7*2^232381+3	69955	Lelio R Paula	04/2014
6473	2^232362-110541	69948	Enzo Doria	05/2014
6474	2^232326-112391	69938	Enzo Doria	06/2014
6475	3^146575+236	69935	Lelio R Paula	09/2013
6476	30^47341-29	69929	Norbert Schneider	02/2014
6477	5^100040-68	69925	Lelio R Paula	09/2013
6478	(35*10^69866-593)/9	69867	Robert Price	08/2017
6479	2^232045-17295	69853	Lelio R Paula	04/2012
6480	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
6481	2^231955+74243	69826	Yves Minet	03/2011
6482	2^231946-15873	69823	Enzo Doria	04/2013
6483	18^55618+95	69816	Lelio R Paula	09/2013
6484	6^89712+5^(89712-1)	69810	Robert Price	02/2016
6485	2^231870+135	69800	Lelio R Paula	02/2012
6486	(23*2^231827-1)/4179	69785	Lelio R Paula	01/2014
6487	2^231778+54615	69773	Lelio R Paula	04/2012
6488	(19*2^231780+1)/235	69772	Lelio R Paula	08/2012
6489	14^60866+27	69761	Lelio R Paula	09/2013
6490	13^62619-44	69755	Lelio R Paula	09/2013
6491	(2^231715-509203)/35	69752	Lelio R Paula	05/2012
6492	2^231711-110467	69752	Enzo Doria	05/2014
6493	(19^54547+18^54547)/37	69751	Robert Price	08/2013
6494	(23*2^231697-1)/45	69748	Lelio R Paula	01/2014
6495	2^231696-1861499	69748	Enzo Doria	03/2016
6496	2^231684-147	69744	Lelio R Paula	02/2012
6497	(23*2^231686-1)/1183	69743	Lelio R Paula	01/2014
6498	2^231591-477397	69716	Paul Bourdelais	03/2013
6499	11^66916-420	69686	Enzo Doria	08/2012
6500	5^99680-13706	69674	Enzo Doria	02/2013

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Probable Primes Top 10000

(205869 PRPs in the top)