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 ?
5251	18^60979-5363	76546	Enzo Doria	03/2013
5252	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
5254	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
5253	(7*10^76536-313)/9	76536	Robert Price	11/2016
5256	2^254239-27	76534	Lelio R Paula	03/2012
5255	2^254238-1841	76534	Yves Minet	03/2013
5257	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
5258	2^254189-112225	76519	Enzo Doria	06/2014
5259	18^60938-1397	76494	Enzo Doria	03/2013
5260	2^254075-2788417	76485	Enzo Doria	03/2016
5261	7*10^76483-23	76484	Robert Price	04/2016
5262	2^254042-112913	76475	Enzo Doria	06/2014
5263	14^66723-37	76474	Lelio R Paula	02/2015
5264	2^254037-110305	76473	Enzo Doria	05/2014
5265	2^253931-111109	76441	Enzo Doria	05/2014
5266	2^253926-1167	76440	Lelio R Paula	05/2013
5267	(49*10^76438-13)/9	76439	Robert Price	07/2015
5268	(21*2^253845-1)/143	76415	Lelio R Paula	02/2014
5269	10^76374+31	76375	Robert Price	03/2011
5270	10^76374-222159	76374	Patrick De Geest	05/2013
5271	2^253561-110533	76330	Enzo Doria	05/2014
5272	gcd(V(917285),5F(183457)(F(183457)+1)+1)	76321	Serge Batalov	04/2015
5273	9*5^109182+2	76316	Lelio R Paula	10/2014
5274	11^73279-3690	76313	Enzo Doria	12/2012
5275	(598*10^76309-31)/9	76311	Robert Price	02/2017
5276	11^73274-24000	76308	Enzo Doria	12/2012
5277	7^90291-6	76305	Theodore Burton	11/2005
5278	(21181*2^253432+1)/21437	76291	Lelio R Paula	06/2014
5279	6^98025+145	76279	Lelio R Paula	01/2015
5280	2^253355+1155	76268	Lelio R Paula	05/2013
5281	2^253292-71219	76249	Enzo Doria	04/2016
5282	7^90221-36	76246	Lelio R Paula	02/2015
5283	18^60727-3473	76229	Enzo Doria	03/2013
5284	(78557*2^253184+1)/3	76221	Lelio R Paula	06/2014
5285	(44791^20480+1)/(44791^4096+1)	76206	Serge Batalov	01/2017
5286	11^73163-2010	76192	Enzo Doria	12/2012
5287	2^253060+54615	76179	Lelio R Paula	05/2013
5288	2^253029+1869761	76170	Enzo Doria	05/2016
5289	2^252955-111007	76148	Enzo Doria	05/2014
5290	2*5^108931+7	76140	Lelio R Paula	10/2014
5291	(86*10^76128+121)/9	76129	Robert Price	03/2017
5292	22154*29^52050+9	76123	Curtis Bright	05/2015
5293	3^159530-112358	76116	Enzo Doria	06/2014
5294	11^73089-48	76115	Lelio R Paula	02/2015
5295	86^39337-85	76098	Norbert Schneider	10/2015
5296	(3^159505-7)/313297316	76095	Lelio R Paula	06/2012
5297	6^97783+77	76090	Lelio R Paula	01/2015
5298	2^252712-105	76074	Lelio R Paula	03/2012
5299	131^35927+2	76068	Lelio R Paula	05/2013
5300	(41*10^76067+373)/9	76068	Robert Price	04/2017
5301	2^252683-139	76066	Lelio R Paula	03/2012
5302	137^35597-136	76061	Norbert Schneider	05/2015
5303	3^159413+106	76060	Lelio R Paula	01/2015
5304	9^79677+38^79677-24^79677-3*2^79677	76032	Mike Oakes	12/2010
5305	(2^252557-9)/71	76026	Lelio R Paula	07/2012
5306	11^72989+80	76011	Lelio R Paula	02/2015
5307	2^252449-459523	75995	Enzo Doria	05/2015
5308	20^58408+73	75991	Lelio R Paula	01/2015
5309	2^252418-1421	75986	Yves Minet	01/2013
5310	(11*2^252396-1)/5	75980	Lelio R Paula	02/2014
5311	2^252365-110689	75970	Enzo Doria	05/2014
5312	11^72949-1020	75969	Enzo Doria	11/2012
5313	(2^252294+47)/6549	75945	Lelio R Paula	07/2012
5314	2^252261-110595	75939	Enzo Doria	05/2014
5315	7^89853+76	75935	Lelio R Paula	01/2015
5316	3^159132+56	75926	Lelio R Paula	01/2015
5317	730^26513+26513^730	75916	Norbert Schneider	11/2016
5318	(27*2^252163-1)/1945	75907	Lelio R Paula	01/2014
5319	5^108596-14846	75906	Enzo Doria	02/2013
5320	5^108560-14846	75881	Enzo Doria	02/2013
5321	2^252051-110359	75875	Enzo Doria	05/2014
5322	2^251971-110509	75851	Enzo Doria	05/2014
5323	(42457^16384+1)/327682	75819	Lelio R Paula	11/2011
5324	99655!6-2	75811	Robert Price	07/2017
5325	14*10^75798+1089	75800	Jens K. Andersen	11/2007
5326	2^251784-455	75795	Yves Minet	03/2012
5327	2^251780-1289	75794	Yves Minet	01/2013
5328	2^251760-215609	75788	Paul Bourdelais	03/2013
5329	99^37973+2	75781	Lelio R Paula	05/2013
5330	(185*10^75777+7)/3	75779	Robert Price	02/2017
5331	5*2^251690+3	75767	Lelio R Paula	06/2014
5332	6^97366+95	75766	Lelio R Paula	01/2015
5333	8*6^97337-7	75744	Lelio R Paula	10/2014
5334	2^251588-111677	75736	Enzo Doria	05/2014
5335	5^108346-13256	75731	Enzo Doria	02/2013
5336	(31^50777+1)/32	75726	Robert Price	07/2013
5337	(10^75707+77)/3	75707	Robert Price	01/2017
5338	2^251466+193	75699	Lelio R Paula	03/2012
5339	(5*2^251464+1)/9423	75695	Lelio R Paula	07/2012
5340	2^251422-109991	75686	Enzo Doria	04/2014
5341	4*5^108245-3	75661	Lelio R Paula	10/2014
5342	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
5343	12^70066+95	75614	Lelio R Paula	02/2015
5344	-E20534/2063	75607	Thomas Ritschel	02/2017
5345	19^59120-50	75600	Lelio R Paula	01/2015
5346	18^60222-4697	75596	Enzo Doria	03/2013
5347	18^60211-4355	75582	Enzo Doria	03/2013
5348	7*2^251014-9	75564	Lelio R Paula	06/2014
5349	6^97101-25	75560	Lelio R Paula	01/2015
5350	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
5351	3^158331-140	75544	Lelio R Paula	01/2015
5352	(37^48157-1)/36	75519	Robert Price	03/2012
5353	10^75516+31467	75517	Patrick De Geest	03/2016
5355	10^75516-10^2256-1	75516	Serge Batalov	01/2011
5354	10^75516-66591	75516	Patrick De Geest	03/2016
5356	2^250851-187	75514	Lelio R Paula	03/2012
5357	(43*10^75498-7)/9	75499	Robert Price	12/2014
5358	(3^158244-5)/247916	75497	Lelio R Paula	06/2012
5359	4*5^107971-3	75470	Lelio R Paula	10/2014
5360	(25*10^75465+71)/3	75466	Robert Price	01/2017
5361	(5*2^250681-1)/999	75461	Lelio R Paula	01/2014
5362	(182*10^75456+1)/3	75458	Robert Price	02/2017
5363	(2^250669-9)/98897729	75451	Lelio R Paula	07/2012
5364	10^75441+13	75442	Robert Price	01/2011
5365	10^75441-9923	75441	Patrick De Geest	05/2013
5366	(27*2^250546-1)/6457	75420	Lelio R Paula	01/2014
5367	5*7^89231-6	75410	Lelio R Paula	10/2014
5369	2^250503-16995	75409	Lelio R Paula	05/2013
5368	11^72411-28	75409	Lelio R Paula	02/2015
5370	3*5^107860-8	75392	Lelio R Paula	10/2014
5372	2^250426+29835	75386	Lelio R Paula	05/2013
5371	8*3^157999-7	75386	Lelio R Paula	05/2014
5373	(88*10^75381-43)/9	75382	Robert Price	11/2015
5374	2^250382-111755	75373	Enzo Doria	05/2014
5375	2^250374-2798051	75371	Eric Chen	03/2016
5376	(22*10^75368-1)/3	75369	Robert Price	12/2014
5377	(19*10^75338+119)/3	75339	Robert Price	02/2017
5378	2^250223-1859167	75325	Enzo Doria	03/2016
5379	(3^157854-7)/66025282	75308	Lelio R Paula	06/2012
5380	3^157831-98	75305	Lelio R Paula	01/2015
5381	(46^45281+11^45281)/57	75290	Serge Batalov	12/2016
5382	92^38335-91	75282	Norbert Schneider	01/2016
5383	2^250020+18915	75264	Lelio R Paula	05/2013
5384	2^250002+8193	75259	Lelio R Paula	05/2013
5385	(11*2^249977-7)/15	75251	Renaud Lifchitz	02/2011
5386	(2^249968+78557)/63	75247	Lelio R Paula	07/2012
5387	(5*10^75244+91)/3	75245	Robert Price	11/2016
5388	(10489!)^2+Prime(10489)	75242	Robert Price	08/2014
5389	14^65644+67	75237	Lelio R Paula	01/2015
5390	(2^249928-5)/11859059	75229	Lelio R Paula	06/2012
5391	129^35638+2	75218	Lelio R Paula	05/2013
5392	2^249853-110475	75214	Enzo Doria	05/2014
5393	2^249762+75409	75186	Enzo Doria	04/2016
5394	565^27318+27318^565	75181	Norbert Schneider	12/2016
5395	(2^249741-7)/685	75177	Lelio R Paula	06/2012
5396	2^249726-112181	75176	Enzo Doria	06/2014
5397	2^249721+11715	75174	Lelio R Paula	05/2013
5398	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
5399	2^249658-47355	75155	Lelio R Paula	05/2013
5400	155^34311+2	75153	Lelio R Paula	05/2013
5401	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
5402	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
5403	2^249522+8415	75114	Lelio R Paula	05/2013
5404	2^249489-110911	75104	Enzo Doria	05/2014
5405	(28*10^75078+131)/3	75079	Robert Price	02/2017
5406	(206*10^75073-17)/9	75075	Robert Price	03/2017
5407	2^249368-110573	75068	Enzo Doria	05/2014
5408	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
5409	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
5410	2^249272+193	75039	Lelio R Paula	03/2012
5411	14^65468+43	75035	Lelio R Paula	01/2015
5412	37^47844+36	75030	Norbert Schneider	05/2014
5413	(52*10^75027-7)/9	75028	Robert Price	12/2014
5414	20^57653+89	75009	Lelio R Paula	01/2015
5415	2^249061-1868353	74975	Enzo Doria	04/2016
5416	7^88713+2*3^88713	74972	Mike Oakes	07/2010
5417	2*6^96313+5	74947	Lelio R Paula	10/2014
5418	(8*10^74944+49)/3	74945	Robert Price	03/2016
5419	300^30247+30247^300	74926	Norbert Schneider	11/2014
5420	2^248866-171	74917	Lelio R Paula	03/2012
5421	6*5^107168-7	74908	Lelio R Paula	10/2014
5422	11^71926+78	74904	Lelio R Paula	02/2015
5423	2^248824+1869391	74904	Enzo Doria	05/2016
5424	2^248816+1111	74902	Lelio R Paula	01/2011
5425	V(388219)	74890	Serge Batalov	03/2015
5426	2*F(358297)-1	74880	Henri Lifchitz	12/2009
5427	(22*10^74874-31)/9	74875	Robert Price	04/2015
5428	11^71892-76800000	74868	Enzo Doria	01/2013
5429	9*5^107107-4	74866	Lelio R Paula	10/2014
5430	2^248678-710111	74860	Paul Bourdelais	03/2013
5431	13^67194+12	74851	Lelio R Paula	01/2015
5432	(7*2^248634+1)/71	74846	Lelio R Paula	08/2012
5433	11^71867-3090	74842	Enzo Doria	12/2012
5434	2^248609+262145	74839	Lelio R Paula	05/2013
5435	3^156852+50	74838	Lelio R Paula	01/2015
5436	18^59607-11	74824	Lelio R Paula	01/2015
5437	2^248556-110507	74823	Enzo Doria	05/2014
5438	7^88531-36	74818	Lelio R Paula	01/2015
5439	p(15738)#/2+1024	74814	Robert Price	07/2017
5440	4*3^156740-5	74785	Lelio R Paula	05/2014
5441	(32*10^74773-41)/9	74774	Robert Price	05/2015
5442	(29*2^248384-1)/13	74772	Lelio R Paula	01/2014
5443	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
5444	2^248357-12797413	74763	Enzo Doria	03/2016
5445	42^46057+41	74762	Lelio R Paula	07/2012
5446	11^71784-3000	74756	Enzo Doria	12/2012
5447	19^58458+18	74754	Lelio R Paula	01/2015
5448	12^69265-35	74750	Lelio R Paula	02/2015
5449	11^71771-48000	74742	Enzo Doria	12/2012
5450	(7*10^74741+197)/3	74742	Robert Price	07/2017
5451	(2^248282-5)/50129	74736	Lelio R Paula	06/2012
5452	2^248252-110105	74732	Enzo Doria	04/2014
5453	(7*10^74729+71)/3	74730	Robert Price	03/2016
5454	3^156614-50	74724	Lelio R Paula	01/2015
5455	(7*2^248213+1)/135	74719	Lelio R Paula	07/2012
5456	(2^248173+78557)/767	74705	Lelio R Paula	07/2012
5457	125^35622+124	74697	Norbert Schneider	02/2015
5458	(19*2^248099-1)/29	74686	Lelio R Paula	01/2014
5459	(86*10^74676-41)/9	74677	Robert Price	11/2015
5460	10^74670+31	74671	Robert Price	01/2011
5461	10^74670-122463	74670	Patrick De Geest	05/2013
5462	2^248036-69	74667	Lelio R Paula	03/2012
5463	11^71698-6000	74666	Enzo Doria	12/2012
5464	58(10^(324887)-1)/111-1	74661	Robert Price	10/2014
5465	14^65139-45	74658	Lelio R Paula	01/2015
5466	6^95921-133	74642	Lelio R Paula	01/2015
5467	11^71675+78	74642	Lelio R Paula	02/2015
5468	18^59449-91	74625	Lelio R Paula	01/2015
5469	6^95864-16043	74597	Enzo Doria	02/2013
5470	5*7^88261+6	74590	Lelio R Paula	10/2014
5471	9*5^106710+4	74589	Lelio R Paula	10/2014
5472	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
5473	(265*10^74579+17)/3	74581	Robert Price	05/2016
5474	(2^247759-1017)/3318311717	74574	Lelio R Paula	07/2012
5475	5^106682-24	74568	Lelio R Paula	08/2014
5476	474^27863+27863^474	74556	Norbert Schneider	01/2017
5477	(35365^16384+1)/2	74524	Lelio R Paula	11/2011
5478	3^156161+2660	74508	Lelio R Paula	01/2015
5479	2^247474-58695	74498	Lelio R Paula	05/2013
5480	11^71519-90	74480	Enzo Doria	07/2012
5481	(19*2^247419-1)/23202983	74475	Lelio R Paula	01/2014
5483	(2^247394-7)/3	74473	Lelio R Paula	06/2012
5482	18^59328+17	74473	Lelio R Paula	01/2015
5484	2^247379-181	74469	Lelio R Paula	03/2012
5485	(15*2^247370-1)/479	74465	Lelio R Paula	01/2014
5486	2^247344+2047	74458	Lelio R Paula	05/2013
5487	2^247311-1017	74449	Lelio R Paula	05/2013
5488	2^247280+7	74439	Lelio R Paula	03/2012
5489	(68*10^74434+13)/9	74435	Ray Chandler	11/2010
5490	3^156004-62	74433	Lelio R Paula	01/2015
5491	36095!2-64	74416	Robert Price	06/2015
5492	2^247165-3	74405	M. Frind & P. Underwood	07/2002
5493	2^247150+32769	74400	Lelio R Paula	05/2013
5494	12^68911+73	74368	Lelio R Paula	01/2015
5495	2^246999+74903	74355	Enzo Doria	04/2016
5496	2^246989-110643	74352	Enzo Doria	05/2014
5497	(10^74350+11)/3	74350	Robert Price	11/2014
5498	10^74350-400000001	74350	Robert Price	07/2017
5499	10^74335+13659	74336	Patrick De Geest	05/2013
5500	10^74335-53	74335	Robert Price	05/2011

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Probable Primes Top 10000

(177649 PRPs in the top)