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	28119^22268+22268^28119	122253	Hans Havermann	03/2021
5252	32167^6312+6312^32167	122240	Hans Havermann	03/2021
5253	3^256199-2^256199	122238	Mike Oakes	06/2005
5254	27678^26053+26053^27678	122223	Hans Havermann	03/2021
5255	2^405992-78557	122216	Jorge Menendez	03/2018
5256	(8*10^122203+43)/3	122204	Robert Price	06/2018
5257	(58*10^122170+329)/9	122171	Robert Price	05/2019
5258	2^405774+179149	122151	Enzo Doria	06/2016
5259	2^405693+20417	122126	Enzo Doria	07/2023
5260	(218*10^122109+7)/9	122111	Robert Price	06/2022
5261	29189^15246+15246^29189	122103	Hans Havermann	03/2021
5263	34*10^122082-9	122084	Robert Price	06/2020
5262	33442^4473+4473^33442	122084	Hans Havermann	03/2021
5264	5*10^122082+41	122083	Robert Price	03/2019
5265	31849^6808+6808^31849	122078	Hans Havermann	03/2021
5267	2^405514-3311	122072	Yves Minet	12/2014
5268	2^405514-115511	122072	Enzo Doria	07/2015
5266	23*10^122070-7	122072	Robert Price	02/2020
5269	2^405422-113261	122045	Enzo Doria	07/2014
5270	2^405173+71237	121970	Enzo Doria	04/2016
5271	fibonacci(583574)+2	121960	Jon Grantham	08/2023
5272	(154*10^121953+17)/9	121955	Robert Price	06/2022
5273	(34*10^121924+191)/9	121925	Robert Price	08/2021
5274	(2^405016+1)/257	121920	Lelio R Paula	04/2014
5275	28557^18590+18590^28557	121918	Hans Havermann	03/2021
5276	28641^18002+18002^28641	121877	Hans Havermann	03/2021
5277	2^404858+71329	121875	Enzo Doria	04/2016
5278	2^404813-114703	121861	Enzo Doria	04/2015
5279	2^404764+77791	121847	Enzo Doria	05/2016
5280	28830^16841+16841^28830	121847	Hans Havermann	03/2021
5281	(4*10^121825+89)/3	121826	Robert Price	08/2021
5282	317^48694+48694^317	121787	Norbert Schneider	08/2015
5283	2^404536-115259	121778	Enzo Doria	06/2015
5284	2^404501-631	121767	Yves Minet	07/2012
5285	5*10^121764-69	121765	Robert Price	02/2021
5286	28236^20485+20485^28236	121738	Hans Havermann	02/2021
5287	(382*10^121694-31)/9	121696	Robert Price	06/2022
5288	63^67620+2	121672	Lelio R Paula	08/2015
5289	(25*34^79445-28062367)/33	121669	Eric Chen	08/2023
5290	(13*33^80110-121453)/32	121648	Eric Chen	12/2023
5291	(16*10^121633+167)/3	121634	Robert Price	06/2019
5292	29955^11494+11494^29955	121632	Hans Havermann	02/2021
5293	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
5294	31088^8163+8163^31088	121612	Hans Havermann	02/2021
5295	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
5296	(211^52301-1)/210	121560	Anonymous	04/2024
5297	(10^121543-79)/3	121543	Robert Price	01/2018
5298	2^403676+76831	121519	Enzo Doria	05/2016
5299	(7*10^121487+143)/3	121488	Robert Price	03/2018
5300	27965^22086+22086^27965	121484	Hans Havermann	02/2021
5301	(893*10^121470+7)/9	121472	Robert Price	06/2021
5302	(206*10^121462-11)/3	121464	Robert Price	02/2022
5303	26282^27481-27481^26282	121457	Frank Doornink	03/2024
5304	(77*10^121455+67)/9	121456	Robert Price	12/2021
5305	2^403363-113635	121425	Enzo Doria	08/2014
5306	25531^27552-27552^25531	121424	Frank Doornink	02/2024
5307	(17*10^121418-113)/3	121419	Robert Price	06/2021
5308	2^403336-1861469	121417	Enzo Doria	03/2016
5309	27929^22186+22186^27929	121382	Hans Havermann	02/2021
5310	p(24442)#/2-64	121381	Robert Price	04/2017
5311	11^116555-720	121380	Enzo Doria	11/2012
5312	2^403100-461267	121346	Enzo Doria	07/2015
5313	2^403093-112213	121344	Enzo Doria	06/2014
5314	29404^13385+13385^29404	121340	Hans Havermann	02/2021
5315	28106^20745+20745^28106	121332	Hans Havermann	02/2021
5316	(316^48539+1)/317	121330	Eric Chen	10/2017
5317	(23*10^121320-71)/3	121321	Robert Price	07/2020
5318	2^403004+1866361	121317	Enzo Doria	03/2016
5319	2^402953+89	121301	Lelio R Paula	10/2013
5320	2^402944-2788319	121299	Enzo Doria	03/2016
5321	(44*10^121297-719)/9	121298	Robert Price	12/2018
5322	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
5323	2^402828-113183	121264	Enzo Doria	07/2014
5324	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
5325	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
5327	2^402715+1874223	121230	Enzo Doria	06/2016
5326	(35*10^121229-593)/9	121230	Robert Price	07/2018
5328	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
5329	28719^16568+16568^28719	121174	Hans Havermann	02/2021
5330	7*10^121144+9	121145	Robert Price	09/2015
5331	27490^25467+25467^27490	121121	Hans Havermann	02/2021
5332	34575^3182+3182^34575	121106	Hans Havermann	02/2021
5333	5*10^121100-37	121101	Robert Price	11/2021
5334	F(579521)/516247738177	121101	Serge Batalov	07/2024
5335	25592^27467-27467^25592	121078	Frank Doornink	02/2024
5336	29954^10935+10935^29954	120979	Hans Havermann	02/2021
5337	33585^3992+3992^33585	120946	Hans Havermann	02/2021
5338	40296^1003+1003^40296	120941	Hans Havermann	02/2021
5339	2^401725-113251	120932	Enzo Doria	07/2014
5340	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
5341	2^401652+73711	120910	Enzo Doria	04/2016
5342	(2^401632+3)/79	120902	Lelio R Paula	04/2014
5343	40450^973+973^40450	120870	Hans Havermann	01/2021
5344	(8*10^120851-11)/3	120852	Robert Price	07/2023
5345	10^120841+88417	120842	Patrick De Geest	04/2020
5346	10^120841-123456789	120841	Robert Price	02/2020
5347	10^120841-176853	120841	Patrick De Geest	04/2020
5348	2^401406-2791331	120836	Enzo Doria	03/2016
5349	(28^83497+1)/29	120832	Robert Price	07/2013
5350	(22*10^120828+161)/3	120829	Robert Price	05/2019
5351	2^401369+1867367	120825	Enzo Doria	03/2016
5352	(5*10^120821+43)/3	120822	Robert Price	12/2021
5353	26990^27263-27263^26990	120808	Frank Doornink	03/2024
5354	(10^120782+29)/3	120782	Serge Batalov	12/2014
5355	2^401215-1657	120778	Yves Minet	07/2014
5356	2^401159+53	120761	Lelio R Paula	10/2013
5357	27782^22179+22179^27782	120739	Hans Havermann	01/2021
5358	32974^4585+4585^32974	120730	Hans Havermann	02/2021
5359	2^401031-113047	120723	Enzo Doria	07/2014
5360	30598^8813+8813^30598	120713	Hans Havermann	02/2021
5361	(71*10^120703-287)/9	120704	Robert Price	09/2019
5362	25671^27370-27370^25671	120687	Frank Doornink	02/2024
5363	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
5364	34793^2940+2940^34793	120675	Hans Havermann	02/2021
5365	26028^27329-27329^26028	120670	Frank Doornink	03/2024
5366	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
5367	(166*10^120654+11)/3	120656	Robert Price	03/2021
5368	34066^3481+3481^34066	120652	Hans Havermann	02/2021
5369	8*10^120637-27	120638	Robert Price	10/2021
5370	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
5371	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
5372	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
5373	9*10^120617-61	120618	Robert Price	06/2021
5374	(29*10^120590-71)/3	120591	Robert Price	07/2021
5375	2^400571-15	120584	Lelio R Paula	10/2013
5376	(10^120574+359)/9	120574	Serge Batalov	12/2014
5377	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
5378	27431^24810+24810^27431	120550	Hans Havermann	02/2021
5379	2^400424-216413	120540	Enzo Doria	04/2013
5380	29090^13911+13911^29090	120531	Hans Havermann	02/2021
5381	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
5382	27899^20868+20868^27899	120510	Hans Havermann	02/2021
5383	33740^3729+3729^33740	120506	Hans Havermann	02/2021
5384	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
5385	2^400166+1874899	120462	Enzo Doria	06/2016
5386	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
5387	37078^1771+1771^37078	120438	Hans Havermann	02/2021
5388	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
5389	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
5390	2^399999+54173	120412	Norman Luhn	08/2023
5391	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
5392	2^399966+73759	120402	Enzo Doria	04/2016
5393	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
5394	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
5396	2^399918-95	120388	Lelio R Paula	04/2013
5395	2^399918+214009	120388	Enzo Doria	10/2023
5397	(28*10^120381-67)/3	120382	Robert Price	10/2020
5398	(49*10^120380-139)/9	120381	Robert Price	03/2019
5399	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
5400	2^399792-1849259	120350	Enzo Doria	08/2015
5401	9*10^120342-7	120343	Robert Price	09/2015
5402	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
5403	(331*10^120332-7)/9	120334	Robert Price	04/2022
5404	(13*10^120306-37)/3	120307	Robert Price	01/2019
5405	(23*10^120299+37)/3	120300	Robert Price	02/2022
5406	25935^27254-27254^25935	120297	Frank Doornink	03/2024
5407	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
5408	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
5409	2^399526-1861721	120270	Enzo Doria	11/2015
5410	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
5411	32016^5687+5687^32016	120217	Hans Havermann	01/2021
5412	(205*10^120212-1)/3	120214	Robert Price	11/2021
5413	2^399322-2798111	120208	Enzo Doria	04/2016
5414	30438^8867+8867^30438	120163	Hans Havermann	02/2021
5415	3^251841-5*2^251841	120159	Jon Grantham	08/2023
5417	72^64693-71^64693	120157	Robert Price	03/2014
5416	(17*10^120156-161)/9	120157	Robert Price	02/2021
5418	2^399111-28489	120145	Enzo Doria	08/2015
5419	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
5420	30254^9333+9333^30254	120110	Hans Havermann	02/2021
5421	30882^7745+7745^30882	120101	Hans Havermann	02/2021
5423	2^398877+105	120074	Donovan Johnson	01/2006
5422	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
5424	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
5425	U(686581)/4280145953	120067	Serge Batalov	07/2024
5426	2^398710+57	120024	Lelio R Paula	04/2013
5427	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
5428	2^398691-115057	120018	Enzo Doria	06/2015
5429	L(574219)	120005	Renaud Lifchitz	03/2004
5430	2^398571+60413	119982	Yves Minet	03/2011
5431	28623^15538+15538^28623	119971	Hans Havermann	02/2021
5432	p(24179)#/2-64	119949	Robert Price	04/2017
5433	2^398448+1872001	119945	Enzo Doria	05/2016
5434	(10^119946*19-91)/6093	119944	Alfred Reich	10/2023
5435	(19*10^119946-91)/9/677	119944	Alfred Reich	11/2023
5436	(191*10^119941-17)/3	119943	Robert Price	11/2021
5437	634^42803+42803^634	119938	Norbert Schneider	07/2019
5438	31083^7220+7220^31083	119935	Hans Havermann	01/2021
5439	(68*10^119931-11)/3	119933	Robert Price	01/2020
5440	8*10^119930-3	119931	Ray Chandler	04/2011
5441	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
5442	(10^119880+179)/9	119880	Serge Batalov	12/2014
5443	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
5444	(10^119836+77)/3	119836	Robert Price	01/2018
5445	26681^27074-27074^26681	119835	Frank Doornink	03/2024
5446	28179^17870+17870^28179	119821	Hans Havermann	02/2021
5447	2^398029+1872527	119819	Enzo Doria	05/2016
5448	33142^4119+4119^33142	119802	Hans Havermann	01/2021
5449	2^397897-113541	119779	Enzo Doria	08/2014
5450	28636^15171+15171^28636	119728	Hans Havermann	02/2021
5451	(10556^29929-1)/(10556^173-1)	119724	Ryan Propper	11/2023
5452	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
5454	(19*10^119716+101)/3	119717	Robert Price	09/2019
5453	29563^11208+11208^29563	119717	Hans Havermann	02/2021
5455	2^397655-933075	119707	Paul Bourdelais	06/2021
5456	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
5457	28243^17308+17308^28243	119701	Hans Havermann	02/2021
5458	77*10^119688+3	119690	Robert Price	06/2020
5459	586*25^85601+3717	119668	Eric Chen	10/2023
5460	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
5461	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
5462	2^397426+73849	119638	Enzo Doria	04/2016
5463	8*10^119509+29	119510	Robert Price	11/2021
5464	2^396933-112723	119489	Enzo Doria	06/2014
5465	11^114738-150	119488	Enzo Doria	10/2012
5466	(4*10^119474+149)/9	119474	Robert Price	04/2018
5467	26964^26964-13^13	119472	Henri Lifchitz	08/2024
5468	2^396790-21	119446	Lelio R Paula	04/2013
5469	32061^5300+5300^32061	119405	Hans Havermann	01/2021
5470	(2^396633-7)/5	119398	Lelio R Paula	04/2014
5471	27382^22913+22913^27382	119388	Hans Havermann	03/2021
5472	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
5473	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
5474	(47*10^119354+259)/9	119355	Robert Price	03/2022
5476	105^59050+104	119352	Norbert Schneider	11/2016
5475	126^56824-125	119352	Norbert Schneider	12/2018
5477	2^396469+111546435	119350	Paul Bourdelais	10/2021
5478	139^55690-138	119345	Norbert Schneider	04/2019
5479	790^41179+41179^790	119322	Norbert Schneider	04/2019
5480	2^396374+73729	119321	Enzo Doria	04/2016
5481	88*10^119295+3	119297	Robert Price	05/2020
5482	2^396258-459491	119286	Enzo Doria	05/2015
5483	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
5484	2^396128-396128-1	119247	Karsten Bonath	06/2018
5485	(893*10^119228+7)/9	119230	Robert Price	06/2021
5486	(31*10^119229+257)/9	119230	Robert Price	12/2021
5487	(28*10^119206-67)/3	119207	Robert Price	10/2020
5488	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
5489	11^114458+6	119196	Paul Bourdelais	02/2021
5490	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
5491	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
5492	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
5493	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
5494	29548^10725+10725^29548	119091	Hans Havermann	02/2021
5495	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
5496	(30^80599+1)/31	119054	Robert Price	07/2013
5497	(232*10^119047+17)/3	119049	Robert Price	04/2021
5498	(43*10^119024-403)/9	119025	Robert Price	01/2019
5499	(4*10^119021+47)/3	119022	Robert Price	01/2022
5500	fibonacci(569433)+3	119005	Jon Grantham	08/2023

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