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 (> 50000)	Who ?	When ?
5251	FAB2(300001,29405)	90310	Robert Price	05/2019
5252	(2^299965+2774)/2	90299	Stefano Morozzi	01/2020
5253	2^299949-1005	90294	Lelio R Paula	11/2013
5254	(2^299947+2054)/2	90293	Stefano Morozzi	01/2020
5255	10^90279+62457	90280	Patrick De Geest	07/2019
5256	10^90279-1551	90279	Patrick De Geest	09/2018
5257	(2^299892+1986)/2	90277	Stefano Morozzi	01/2020
5258	(2^299893+3866)/2	90277	Stefano Morozzi	01/2020
5259	2^299868-109613	90270	Enzo Doria	04/2014
5260	10^90259+359299	90260	Patrick De Geest	07/2019
5261	10^90259-9443	90259	Patrick De Geest	09/2018
5262	(2^299831+3786)/2	90258	Stefano Morozzi	01/2020
5263	10^90252+102873	90253	Patrick De Geest	07/2019
5264	10^90252-8103	90252	Patrick De Geest	09/2018
5266	5*2^299799-3	90250	Lelio R Paula	08/2014
5265	(2^299803+3326)/2	90250	Stefano Morozzi	01/2020
5267	13^81008-2	90239	Lelio R Paula	09/2013
5268	80697!4-256	90234	Robert Price	11/2019
5270	64^49957-63^49957	90232	Robert Price	07/2013
5269	(2^299745+2994)/2	90232	Stefano Morozzi	01/2020
5271	10^90227+56281	90228	Patrick De Geest	06/2016
5274	2^299725+315	90227	Lelio R Paula	11/2013
5272	10^90227-1000000001	90227	Robert Price	05/2016
5273	10^90227-68763	90227	Patrick De Geest	06/2016
5275	5^129082+48	90225	Lelio R Paula	03/2016
5276	2^299699+195	90219	Lelio R Paula	10/2012
5277	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
5278	10^90209+8971	90210	Patrick De Geest	09/2018
5279	10^90209-724797	90209	Patrick De Geest	07/2019
5280	10^90208+189531	90209	Patrick De Geest	07/2019
5281	10^90208-2247	90208	Patrick De Geest	09/2018
5282	116^43693-115	90203	Norbert Schneider	08/2018
5283	10^90202+3553	90203	Patrick De Geest	09/2018
5284	3^189053+280	90202	Lelio R Paula	04/2016
5285	10^90202-67793	90202	Patrick De Geest	07/2019
5286	2^299639-187	90201	Lelio R Paula	10/2012
5287	10^90199+254031	90200	Patrick De Geest	07/2019
5288	10^90199-2891	90199	Patrick De Geest	09/2018
5289	2^299631+183	90198	Lelio R Paula	10/2012
5290	10^90196+187539	90197	Patrick De Geest	07/2019
5291	10^90196-9683	90196	Patrick De Geest	09/2018
5292	10^90193+104973	90194	Patrick De Geest	07/2019
5293	10^90193-9809	90193	Patrick De Geest	09/2018
5294	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
5295	2^299567+113	90179	Lelio R Paula	10/2012
5296	2^299550+189	90174	Lelio R Paula	10/2012
5297	10^90170+376063	90171	Patrick De Geest	07/2019
5298	10^90170-6749	90170	Patrick De Geest	09/2018
5299	(2^299535+3)/29	90168	Lelio R Paula	01/2013
5300	(2^299521+13)/15	90164	Stefano Morozzi	03/2020
5301	10^90160+271947	90161	Patrick De Geest	07/2019
5302	10^90160-5613	90160	Patrick De Geest	09/2018
5303	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
5305	3^188938+8680	90147	Lelio R Paula	04/2016
5304	10^90146+160209	90147	Patrick De Geest	07/2019
5306	10^90146-2027	90146	Patrick De Geest	09/2018
5307	6^115840-55	90142	Lelio R Paula	05/2016
5308	(5*10^90142-473)/9	90142	Robert Price	12/2017
5309	8*7^106659+5	90139	Lelio R Paula	10/2014
5312	2^299406-16653	90131	Enzo Doria	05/2013
5310	(317057^16384+1)/2	90131	Richard Fischer	10/2019
5311	(2^299409+834)/2	90131	Stefano Morozzi	01/2020
5313	10^90128+288673	90129	Patrick De Geest	07/2019
5315	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
5314	10^90128-8387	90128	Patrick De Geest	09/2018
5316	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
5317	6^115819-53	90125	Lelio R Paula	05/2016
5318	10^90123+6313	90124	Patrick De Geest	09/2018
5320	6^115816-16853	90123	Enzo Doria	02/2013
5319	10^90123-22617	90123	Patrick De Geest	07/2019
5321	6^115813-23	90121	Lelio R Paula	05/2016
5322	(22*10^90110+161)/3	90111	Robert Price	02/2017
5324	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
5323	10^90105+915759	90106	Patrick De Geest	07/2019
5326	10^90105-767	90105	Patrick De Geest	09/2018
5325	10^90104+48189	90105	Patrick De Geest	07/2019
5327	10^90104-7703	90104	Patrick De Geest	09/2018
5328	10^90103+9159	90104	Patrick De Geest	09/2018
5329	10^90103-208457	90103	Patrick De Geest	07/2019
5330	10^90102+73011	90103	Patrick De Geest	07/2019
5331	10^90102-602433	90102	Patrick De Geest	07/2019
5332	10^90101+1225537	90102	Patrick De Geest	07/2019
5333	10^90101-3207	90101	Patrick De Geest	09/2018
5334	(29*10^90096-17)/3	90097	Erik Branger	09/2014
5335	10^90089+143181	90090	Patrick De Geest	07/2019
5336	10^90089-3573	90089	Patrick De Geest	09/2018
5337	2^299247+1870529	90083	Enzo Doria	05/2016
5338	10^90079+1609	90080	Patrick De Geest	09/2018
5339	10^90079-230043	90079	Patrick De Geest	07/2019
5340	2^299229-2797783	90077	Enzo Doria	04/2016
5341	2^299220-16317	90075	Enzo Doria	04/2013
5342	11^86491-1350	90072	Enzo Doria	12/2012
5343	10^90071+52333	90072	Patrick De Geest	07/2019
5344	10^90071-1233	90071	Patrick De Geest	09/2018
5345	(314401^16384+1)/2	90071	Richard Fischer	10/2019
5346	10^90069+158527	90070	Patrick De Geest	07/2019
5347	10^90069-7841	90069	Patrick De Geest	09/2018
5348	(31*10^90064-1)/3	90066	Robert Price	03/2017
5349	10^90060+149431	90061	Patrick De Geest	07/2019
5350	10^90060-839	90060	Patrick De Geest	09/2018
5351	10^90052+2361	90053	Patrick De Geest	09/2018
5352	10^90052-90929	90052	Patrick De Geest	07/2019
5353	10^90047+619	90048	Patrick De Geest	09/2018
5354	10^90047-151071	90047	Patrick De Geest	07/2019
5355	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
5356	2^299112+73951	90042	Enzo Doria	04/2016
5357	8^99702+7^(99702-1)	90040	Robert Price	02/2016
5358	10^90038+157803	90039	Patrick De Geest	07/2019
5359	10^90038-9687	90038	Patrick De Geest	09/2018
5360	5*10^90033+3	90034	Dmitry Domanov	11/2010
5361	10^90030+225813	90031	Patrick De Geest	07/2019
5362	10^90030-1461	90030	Patrick De Geest	09/2018
5363	243^37738+37738^243	90029	Norbert Schneider	01/2015
5364	10^90025+70569	90026	Patrick De Geest	07/2019
5365	10^90025-8703	90025	Patrick De Geest	09/2018
5366	2^299048-113297	90023	Enzo Doria	07/2014
5367	10^90015+849	90016	Patrick De Geest	09/2018
5368	10^90015-228387	90015	Patrick De Geest	07/2019
5369	10^90010+6811	90011	Patrick De Geest	09/2018
5370	10^90010-183597	90010	Patrick De Geest	11/2018
5371	10^90009+58321	90010	Patrick De Geest	11/2018
5372	10^90008+847	90009	Patrick De Geest	09/2018
5373	10^90009-356013	90009	Patrick De Geest	11/2018
5375	3^188648+92	90008	Lelio R Paula	12/2015
5374	10^90008-706049	90008	Patrick De Geest	11/2018
5376	5*2^298991+7	90006	Lelio R Paula	08/2014
5377	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
5378	10^90000+8869	90001	Patrick De Geest	12/2009
5380	10^89999+82939	90000	Dirk Augustin	04/2007
5379	10^90000-140343	90000	Patrick De Geest	12/2009
5381	10^89999-194891	89999	Patrick De Geest	11/2009
5382	(2^298918+1798)/2	89983	Stefano Morozzi	01/2020
5383	19^70365-78	89980	Lelio R Paula	12/2015
5384	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
5385	2^298852-64875	89964	Lelio R Paula	11/2013
5386	(2^298825+1010)/2	89955	Stefano Morozzi	01/2020
5387	18^71659+37	89952	Lelio R Paula	12/2015
5388	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
5389	(2^298769+1202)/2	89939	Stefano Morozzi	01/2020
5390	17^73067+20	89906	Lelio R Paula	11/2015
5391	2^298637-99	89899	Lelio R Paula	10/2012
5392	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
5393	(2^298558+3654)/2	89875	Stefano Morozzi	01/2020
5394	9*10^89858+19	89859	Robert Price	05/2016
5395	2^298501+1870067	89858	Enzo Doria	05/2016
5396	11^86280-98	89852	Lelio R Paula	11/2015
5397	2^298473-110059	89850	Enzo Doria	04/2014
5398	19^70263-32	89850	Lelio R Paula	12/2015
5399	(299*10^89836-17)/3	89838	Robert Price	01/2017
5400	3^188286+14	89836	Robert Price	09/2013
5401	(2^298408+450)/2	89830	Stefano Morozzi	01/2020
5402	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
5403	2^298367+58905	89818	Lelio R Paula	11/2013
5404	(2^298333+3126)/2	89807	Stefano Morozzi	01/2020
5405	2^298319-109657	89803	Enzo Doria	04/2014
5406	8*10^89800+81	89801	Robert Price	05/2017
5407	(2^298249+714)/2	89782	Stefano Morozzi	01/2020
5409	18^71505-91	89759	Lelio R Paula	12/2015
5408	(2^298171+1586)/2	89759	Stefano Morozzi	01/2020
5410	(2^298161+3530)/2	89756	Stefano Morozzi	01/2020
5411	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
5412	2^298079-109531	89731	Enzo Doria	04/2014
5413	117^43380+116	89718	Norbert Schneider	08/2018
5414	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
5415	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
5416	2^298003-66945	89708	Lelio R Paula	11/2013
5417	(23*10^89705-83)/3	89706	Robert Price	09/2017
5418	17^72900-54	89700	Lelio R Paula	11/2015
5419	(2^297968+2482)/2	89698	Stefano Morozzi	01/2020
5420	3*2^297956+5	89695	Lelio R Paula	08/2014
5421	(2^297952+3558)/2	89693	Stefano Morozzi	01/2020
5422	20^68938-11	89691	Lelio R Paula	01/2016
5423	89*10^89687-7	89689	Robert Price	03/2017
5424	(297847^16384+1)/2	89686	Richard Fischer	08/2019
5425	2^297923+77783	89684	Enzo Doria	05/2016
5426	(2^297893+1694)/2	89675	Stefano Morozzi	01/2020
5427	11^86107-24576000	89672	Enzo Doria	02/2013
5428	2^297878-111911	89671	Enzo Doria	05/2014
5429	(2^297830+3670)/2	89656	Stefano Morozzi	01/2020
5430	7^106084+40	89652	Lelio R Paula	10/2015
5431	(2^297815+618)/2	89651	Stefano Morozzi	01/2020
5433	(86*10^89640-311)/9	89641	Robert Price	10/2017
5432	(2^297781+2094)/2	89641	Stefano Morozzi	01/2020
5434	(2^297741+3326)/2	89629	Stefano Morozzi	01/2020
5435	(2^297724+3606)/2	89624	Stefano Morozzi	01/2020
5436	3*10^89608-59	89609	Robert Price	10/2017
5437	(2^297650+3250)/2	89602	Stefano Morozzi	01/2020
5438	3^187780-11038	89594	Enzo Doria	05/2014
5439	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
5440	5^128141-36	89567	Lelio R Paula	10/2015
5441	4*7^105951+9	89540	Lelio R Paula	10/2014
5442	(7*10^89539-439)/9	89539	Robert Price	09/2017
5443	(2^297401+2954)/2	89527	Stefano Morozzi	01/2020
5444	(2^297403+1670)/2	89527	Stefano Morozzi	01/2020
5445	2^297397+177257	89526	Enzo Doria	05/2016
5447	2^297346-16241	89511	Enzo Doria	04/2013
5446	(5*10^89510+79)/3	89511	Robert Price	11/2017
5448	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
5449	2^297328-869688105	89505	Lelio R Paula	07/2016
5450	2^297325-459043	89504	Enzo Doria	05/2015
5451	2^297310-112391	89500	Enzo Doria	06/2014
5452	2^297296-112157	89496	Enzo Doria	06/2014
5453	57^50966-2	89490	Lelio R Paula	08/2013
5454	(266*10^89482+1)/3	89484	Robert Price	02/2016
5455	(14*10^89480-101)/3	89481	Robert Price	04/2017
5456	2618^26175+26175^2618	89466	Norbert Schneider	01/2020
5457	(2^297150+3922)/2	89451	Stefano Morozzi	01/2020
5458	(2^297141+1842)/2	89449	Stefano Morozzi	01/2020
5459	(2^297140+1458)/2	89448	Stefano Morozzi	01/2020
5460	(2^297129+726)/2	89445	Stefano Morozzi	01/2020
5461	2^297122+99	89443	Lelio R Paula	10/2012
5462	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
5463	(2^297037+3522)/2	89417	Stefano Morozzi	01/2020
5464	(25*10^89413+161)/3	89414	Robert Price	01/2017
5465	2^296990+1870699	89403	Enzo Doria	05/2016
5466	2^296972-1017	89398	Lelio R Paula	11/2013
5467	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
5468	(85*10^89375-31)/9	89376	Robert Price	11/2015
5469	9*2^296870+7	89368	Lelio R Paula	08/2014
5470	100^44683-99^44683	89366	Robert Price	07/2013
5471	2^296810+76519	89349	Enzo Doria	05/2016
5472	8^98928+7^(98928+1)	89341	Robert Price	06/2016
5473	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
5474	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
5475	2^296736-432149	89327	Paul Bourdelais	05/2013
5476	2^296737-112519	89327	Enzo Doria	06/2014
5477	2^296718-3645	89322	Lelio R Paula	11/2013
5478	(2^296702+2338)/2	89316	Stefano Morozzi	01/2020
5479	2^296681-16221	89310	Enzo Doria	04/2013
5480	2^296669-16513	89307	Enzo Doria	04/2013
5481	(2^296626+1282)/2	89294	Stefano Morozzi	01/2020
5482	2^296619-16357	89292	Enzo Doria	04/2013
5483	2^296614-110051	89290	Enzo Doria	04/2014
5484	(2^296601+1730)/2	89286	Stefano Morozzi	01/2020
5485	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
5486	(2*10^89279+457)/9	89279	Robert Price	01/2017
5487	(2^296568+1222)/2	89276	Stefano Morozzi	01/2020
5488	15^75907-28	89274	Lelio R Paula	11/2015
5489	2^296547-37	89270	Yves Minet	01/2012
5490	2^296485+191	89251	Lelio R Paula	10/2012
5491	2^296467-75	89246	Lelio R Paula	10/2012
5492	(2^296462+1674)/2	89244	Stefano Morozzi	01/2020
5493	2^296416-109535	89231	Enzo Doria	04/2014
5494	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
5495	66^49037-65	89225	Norbert Schneider	11/2014
5496	2^296377-16245	89219	Enzo Doria	04/2013
5497	2^296372-64875	89217	Lelio R Paula	11/2013
5498	5*6^114648-7	89215	Lelio R Paula	10/2014
5499	(2^296361+1262)/2	89214	Stefano Morozzi	01/2020
5500	3*10^89206+13	89207	Robert Price	08/2017

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Probable Primes Top 10000

(259919 PRPs in the top)