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	2^256460-112757	77203	Enzo Doria	06/2014
5252	2^256398+23299	77184	Yves Minet	02/2011
5253	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
5254	(2^256391-9)/56593	77177	Lelio R Paula	10/2012
5255	(2^256308+9)/10585	77153	Lelio R Paula	10/2012
5256	21^58348-2	77149	Lelio R Paula	08/2013
5257	(17*2^256291-1)/4785	77149	Lelio R Paula	02/2014
5258	(5*2^256274-1)/2141	77144	Lelio R Paula	02/2014
5259	19^60321+82	77136	Lelio R Paula	03/2015
5260	5*2^256233-3	77135	Lelio R Paula	06/2014
5261	3*2^256149+7	77110	Lelio R Paula	06/2014
5262	3^161594-106	77100	Lelio R Paula	02/2015
5263	2^256114-185	77098	Lelio R Paula	03/2012
5264	8^85349-85349^8	77078	Norbert Schneider	05/2017
5265	2^256043-2786377	77077	Enzo Doria	03/2016
5266	2^255973+1869947	77056	Enzo Doria	05/2016
5267	12^71393-43	77046	Lelio R Paula	02/2015
5268	15^65490+44	77023	Lelio R Paula	02/2015
5269	(3^161411-7)/940	77010	Lelio R Paula	10/2012
5270	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
5271	(570^27943-1)/569	77005	Serge Batalov	12/2016
5272	2^255750-75	76989	Lelio R Paula	03/2012
5273	3*6^98926-5	76980	Lelio R Paula	10/2014
5274	18^61320-1433	76974	Enzo Doria	03/2013
5275	6^98916-17093	76972	Enzo Doria	02/2013
5276	2^255659-110131	76962	Enzo Doria	04/2014
5277	12^71303+91	76949	Lelio R Paula	02/2015
5278	18^61298+59	76946	Lelio R Paula	02/2015
5279	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
5280	(2^255613-5)/281517	76942	Lelio R Paula	10/2012
5281	18^61290-11	76936	Lelio R Paula	02/2015
5283	63^42752-2	76926	Lelio R Paula	08/2013
5282	(11*2^255545-1)/117	76926	Lelio R Paula	02/2014
5284	2^255517+56387	76919	Yves Minet	02/2011
5285	2^255499-112567	76913	Enzo Doria	06/2014
5286	2^255492+345	76911	Lelio R Paula	06/2013
5287	10^76875+217591	76876	Patrick De Geest	05/2013
5289	10^76875-53	76875	Robert Price	05/2011
5288	11^73819-5880	76875	Enzo Doria	01/2013
5290	2^255313+18915	76857	Lelio R Paula	06/2013
5291	(2^255320-1017)/1446667	76853	Lelio R Paula	10/2012
5292	2^255296+5775	76852	Lelio R Paula	06/2013
5293	14^67052-29	76851	Lelio R Paula	02/2015
5294	(7*10^76818-313)/9	76818	Robert Price	11/2016
5295	10^76801+69	76802	Robert Price	03/2011
5296	10^76801-80943	76801	Patrick De Geest	06/2013
5297	2^255105+57	76795	Lelio R Paula	03/2012
5298	(lucasV(1,2,510187)+2)/(3511)	76789	Mike Oakes	04/2017
5299	(2^255097-7)/20020055	76785	Lelio R Paula	10/2012
5300	2^255055+1869353	76780	Enzo Doria	05/2016
5301	17^62396-90	76776	Lelio R Paula	03/2015
5302	7^90833-60	76763	Lelio R Paula	02/2015
5303	13^68901-56	76752	Lelio R Paula	03/2015
5304	2^254961+1869917	76751	Enzo Doria	05/2016
5305	9*5^109791-8	76742	Lelio R Paula	10/2014
5306	82^40089+40089^82	76723	Serge Batalov	02/2012
5307	2^254861-2790013	76721	Enzo Doria	03/2016
5308	10^76705+13	76706	Robert Price	01/2011
5309	10^76705-94077	76705	Patrick De Geest	06/2013
5310	(5*2^254785-1)/999	76696	Lelio R Paula	02/2014
5311	2^254758-110405	76690	Enzo Doria	05/2014
5312	2^254716-3779	76678	Yves Minet	04/2017
5313	2^254708-110507	76675	Enzo Doria	05/2014
5314	(47*10^76672+133)/9	76673	Robert Price	04/2017
5315	2^254670-112901	76664	Enzo Doria	06/2014
5316	(3^160665+7)/981350	76651	Lelio R Paula	10/2012
5317	2^254598-113183	76642	Enzo Doria	07/2014
5318	19^59932+22	76639	Lelio R Paula	01/2015
5319	2^254569-112213	76633	Enzo Doria	06/2014
5320	2*5^109626+9	76626	Lelio R Paula	10/2014
5321	2^254521+1872527	76619	Enzo Doria	05/2016
5322	(76*10^76615+167)/9	76616	Robert Price	08/2016
5323	25^54799-24^54799	76606	Robert Price	07/2012
5324	(24737*2^254464+1)/9	76605	Lelio R Paula	06/2014
5325	12^70961-85	76580	Lelio R Paula	02/2015
5326	7^90590-38	76558	Lelio R Paula	02/2015
5327	2^254304+5227	76554	Lelio R Paula	06/2013
5328	18^60979-5363	76546	Enzo Doria	03/2013
5329	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
5331	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
5330	(7*10^76536-313)/9	76536	Robert Price	11/2016
5332	2^254239-27	76534	Lelio R Paula	03/2012
5333	2^254238-1841	76534	Yves Minet	03/2013
5334	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
5335	2^254189-112225	76519	Enzo Doria	06/2014
5336	18^60938-1397	76494	Enzo Doria	03/2013
5337	2^254075-2788417	76485	Enzo Doria	03/2016
5338	7*10^76483-23	76484	Robert Price	04/2016
5339	2^254042-112913	76475	Enzo Doria	06/2014
5340	14^66723-37	76474	Lelio R Paula	02/2015
5341	2^254037-110305	76473	Enzo Doria	05/2014
5342	2^253931-111109	76441	Enzo Doria	05/2014
5343	2^253926-1167	76440	Lelio R Paula	05/2013
5344	(49*10^76438-13)/9	76439	Robert Price	07/2015
5345	(21*2^253845-1)/143	76415	Lelio R Paula	02/2014
5346	10^76374+31	76375	Robert Price	03/2011
5347	10^76374-222159	76374	Patrick De Geest	05/2013
5348	2^253561-110533	76330	Enzo Doria	05/2014
5349	gcd(V(917285),5F(183457)(F(183457)+1)+1)	76321	Serge Batalov	04/2015
5350	9*5^109182+2	76316	Lelio R Paula	10/2014
5351	11^73279-3690	76313	Enzo Doria	12/2012
5352	(598*10^76309-31)/9	76311	Robert Price	02/2017
5353	11^73274-24000	76308	Enzo Doria	12/2012
5354	7^90291-6	76305	Theodore Burton	11/2005
5355	(21181*2^253432+1)/21437	76291	Lelio R Paula	06/2014
5356	6^98025+145	76279	Lelio R Paula	01/2015
5357	2^253355+1155	76268	Lelio R Paula	05/2013
5358	2^253292-71219	76249	Enzo Doria	04/2016
5359	7^90221-36	76246	Lelio R Paula	02/2015
5360	18^60727-3473	76229	Enzo Doria	03/2013
5361	(78557*2^253184+1)/3	76221	Lelio R Paula	06/2014
5362	(44791^20480+1)/(44791^4096+1)	76206	Serge Batalov	01/2017
5363	11^73163-2010	76192	Enzo Doria	12/2012
5364	2^253060+54615	76179	Lelio R Paula	05/2013
5365	2^253029+1869761	76170	Enzo Doria	05/2016
5366	2^252955-111007	76148	Enzo Doria	05/2014
5367	2*5^108931+7	76140	Lelio R Paula	10/2014
5368	(86*10^76128+121)/9	76129	Robert Price	03/2017
5369	22154*29^52050+9	76123	Curtis Bright	05/2015
5370	3^159530-112358	76116	Enzo Doria	06/2014
5371	11^73089-48	76115	Lelio R Paula	02/2015
5372	86^39337-85	76098	Norbert Schneider	10/2015
5373	(3^159505-7)/313297316	76095	Lelio R Paula	06/2012
5374	6^97783+77	76090	Lelio R Paula	01/2015
5375	2^252712-105	76074	Lelio R Paula	03/2012
5376	131^35927+2	76068	Lelio R Paula	05/2013
5377	(41*10^76067+373)/9	76068	Robert Price	04/2017
5378	2^252683-139	76066	Lelio R Paula	03/2012
5379	137^35597-136	76061	Norbert Schneider	05/2015
5380	3^159413+106	76060	Lelio R Paula	01/2015
5381	9^79677+38^79677-24^79677-3*2^79677	76032	Mike Oakes	12/2010
5382	(2^252557-9)/71	76026	Lelio R Paula	07/2012
5383	11^72989+80	76011	Lelio R Paula	02/2015
5384	2^252449-459523	75995	Enzo Doria	05/2015
5385	20^58408+73	75991	Lelio R Paula	01/2015
5386	2^252418-1421	75986	Yves Minet	01/2013
5387	(11*2^252396-1)/5	75980	Lelio R Paula	02/2014
5388	2^252365-110689	75970	Enzo Doria	05/2014
5389	11^72949-1020	75969	Enzo Doria	11/2012
5390	(2^252294+47)/6549	75945	Lelio R Paula	07/2012
5391	2^252261-110595	75939	Enzo Doria	05/2014
5392	7^89853+76	75935	Lelio R Paula	01/2015
5393	3^159132+56	75926	Lelio R Paula	01/2015
5394	730^26513+26513^730	75916	Norbert Schneider	11/2016
5395	(27*2^252163-1)/1945	75907	Lelio R Paula	01/2014
5396	5^108596-14846	75906	Enzo Doria	02/2013
5397	5^108560-14846	75881	Enzo Doria	02/2013
5398	2^252051-110359	75875	Enzo Doria	05/2014
5399	2^251971-110509	75851	Enzo Doria	05/2014
5400	(42457^16384+1)/327682	75819	Lelio R Paula	11/2011
5401	99655!6-2	75811	Robert Price	07/2017
5402	14*10^75798+1089	75800	Jens K. Andersen	11/2007
5403	2^251784-455	75795	Yves Minet	03/2012
5404	2^251780-1289	75794	Yves Minet	01/2013
5405	2^251760-215609	75788	Paul Bourdelais	03/2013
5406	99^37973+2	75781	Lelio R Paula	05/2013
5407	(185*10^75777+7)/3	75779	Robert Price	02/2017
5408	5*2^251690+3	75767	Lelio R Paula	06/2014
5409	6^97366+95	75766	Lelio R Paula	01/2015
5410	8*6^97337-7	75744	Lelio R Paula	10/2014
5411	2^251588-111677	75736	Enzo Doria	05/2014
5412	5^108346-13256	75731	Enzo Doria	02/2013
5413	(31^50777+1)/32	75726	Robert Price	07/2013
5414	(10^75707+77)/3	75707	Robert Price	01/2017
5415	2^251466+193	75699	Lelio R Paula	03/2012
5416	(5*2^251464+1)/9423	75695	Lelio R Paula	07/2012
5417	2^251422-109991	75686	Enzo Doria	04/2014
5418	4*5^108245-3	75661	Lelio R Paula	10/2014
5419	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
5420	12^70066+95	75614	Lelio R Paula	02/2015
5421	-E20534/2063	75607	Thomas Ritschel	02/2017
5422	19^59120-50	75600	Lelio R Paula	01/2015
5423	18^60222-4697	75596	Enzo Doria	03/2013
5424	18^60211-4355	75582	Enzo Doria	03/2013
5425	7*2^251014-9	75564	Lelio R Paula	06/2014
5426	6^97101-25	75560	Lelio R Paula	01/2015
5427	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
5428	3^158331-140	75544	Lelio R Paula	01/2015
5429	(37^48157-1)/36	75519	Robert Price	03/2012
5430	10^75516+31467	75517	Patrick De Geest	03/2016
5432	10^75516-10^2256-1	75516	Serge Batalov	01/2011
5431	10^75516-66591	75516	Patrick De Geest	03/2016
5433	2^250851-187	75514	Lelio R Paula	03/2012
5434	(43*10^75498-7)/9	75499	Robert Price	12/2014
5435	(3^158244-5)/247916	75497	Lelio R Paula	06/2012
5436	4*5^107971-3	75470	Lelio R Paula	10/2014
5437	(25*10^75465+71)/3	75466	Robert Price	01/2017
5438	(5*2^250681-1)/999	75461	Lelio R Paula	01/2014
5439	(182*10^75456+1)/3	75458	Robert Price	02/2017
5440	(2^250669-9)/98897729	75451	Lelio R Paula	07/2012
5441	10^75441+13	75442	Robert Price	01/2011
5442	10^75441-9923	75441	Patrick De Geest	05/2013
5443	(27*2^250546-1)/6457	75420	Lelio R Paula	01/2014
5444	5*7^89231-6	75410	Lelio R Paula	10/2014
5446	2^250503-16995	75409	Lelio R Paula	05/2013
5445	11^72411-28	75409	Lelio R Paula	02/2015
5447	3*5^107860-8	75392	Lelio R Paula	10/2014
5449	2^250426+29835	75386	Lelio R Paula	05/2013
5448	8*3^157999-7	75386	Lelio R Paula	05/2014
5450	(88*10^75381-43)/9	75382	Robert Price	11/2015
5451	2^250382-111755	75373	Enzo Doria	05/2014
5452	2^250374-2798051	75371	Eric Chen	03/2016
5453	(22*10^75368-1)/3	75369	Robert Price	12/2014
5454	(19*10^75338+119)/3	75339	Robert Price	02/2017
5455	2^250223-1859167	75325	Enzo Doria	03/2016
5456	(3^157854-7)/66025282	75308	Lelio R Paula	06/2012
5457	3^157831-98	75305	Lelio R Paula	01/2015
5458	(46^45281+11^45281)/57	75290	Serge Batalov	12/2016
5459	92^38335-91	75282	Norbert Schneider	01/2016
5460	2^250020+18915	75264	Lelio R Paula	05/2013
5461	2^250002+8193	75259	Lelio R Paula	05/2013
5462	(11*2^249977-7)/15	75251	Renaud Lifchitz	02/2011
5463	(2^249968+78557)/63	75247	Lelio R Paula	07/2012
5464	(5*10^75244+91)/3	75245	Robert Price	11/2016
5465	(10489!)^2+Prime(10489)	75242	Robert Price	08/2014
5466	14^65644+67	75237	Lelio R Paula	01/2015
5467	(2^249928-5)/11859059	75229	Lelio R Paula	06/2012
5468	129^35638+2	75218	Lelio R Paula	05/2013
5469	2^249853-110475	75214	Enzo Doria	05/2014
5470	2^249762+75409	75186	Enzo Doria	04/2016
5471	565^27318+27318^565	75181	Norbert Schneider	12/2016
5472	(2^249741-7)/685	75177	Lelio R Paula	06/2012
5473	2^249726-112181	75176	Enzo Doria	06/2014
5474	2^249721+11715	75174	Lelio R Paula	05/2013
5475	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
5476	2^249658-47355	75155	Lelio R Paula	05/2013
5477	155^34311+2	75153	Lelio R Paula	05/2013
5478	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
5479	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
5480	2^249522+8415	75114	Lelio R Paula	05/2013
5481	2^249489-110911	75104	Enzo Doria	05/2014
5482	(28*10^75078+131)/3	75079	Robert Price	02/2017
5483	(206*10^75073-17)/9	75075	Robert Price	03/2017
5484	2^249368-110573	75068	Enzo Doria	05/2014
5485	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
5486	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
5487	2^249272+193	75039	Lelio R Paula	03/2012
5488	14^65468+43	75035	Lelio R Paula	01/2015
5489	37^47844+36	75030	Norbert Schneider	05/2014
5490	(52*10^75027-7)/9	75028	Robert Price	12/2014
5491	20^57653+89	75009	Lelio R Paula	01/2015
5492	2^249061-1868353	74975	Enzo Doria	04/2016
5493	7^88713+2*3^88713	74972	Mike Oakes	07/2010
5494	2*6^96313+5	74947	Lelio R Paula	10/2014
5495	(8*10^74944+49)/3	74945	Robert Price	03/2016
5496	300^30247+30247^300	74926	Norbert Schneider	11/2014
5497	2^248866-171	74917	Lelio R Paula	03/2012
5498	6*5^107168-7	74908	Lelio R Paula	10/2014
5499	11^71926+78	74904	Lelio R Paula	02/2015
5500	2^248824+1869391	74904	Enzo Doria	05/2016

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PRP Records

Probable Primes Top 10000

(181746 PRPs in the top)