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	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5252	31251^20158+20158^31251	134519	Hans Havermann	11/2020
5253	2^446782-39701	134495	Enzo Doria	09/2015
5254	31817^16858+16858^31817	134485	Hans Havermann	12/2020
5255	32448^13937+13937^32448	134471	Hans Havermann	12/2020
5256	5^192321+3^192321-1	134427	Jon Grantham	08/2023
5257	2^446494-16485	134409	Enzo Doria	04/2013
5258	30042^29785+29785^30042	134408	Hans Havermann	12/2020
5259	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
5260	2^446441+65	134393	Lelio R Paula	08/2017
5261	(10^134385+719)/9	134385	Serge Batalov	12/2014
5262	30043^29688+29688^30043	134370	Hans Havermann	12/2020
5263	(2*10^134364+529)/9	134364	Robert Price	01/2018
5264	34657^7512+7512^34657	134323	Hans Havermann	11/2020
5265	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
5266	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
5267	42035^1564+1564^42035	134270	Hans Havermann	12/2020
5269	(2^446022-7)/339	134264	Lelio R Paula	07/2015
5268	30621^24248+24248^30621	134264	Hans Havermann	12/2020
5270	30341^26562+26562^30341	134237	Hans Havermann	11/2020
5271	(189^58967-1)/188	134234	Anonymous	06/2024
5272	10^134209+99867	134210	Patrick De Geest	05/2021
5273	10^134209-80000001	134209	Robert Price	04/2021
5274	10^134209-323283	134209	Patrick De Geest	05/2021
5275	29976^29953+29953^29976	134186	Hans Havermann	12/2020
5276	35038^6755+6755^35038	134183	Hans Havermann	12/2020
5277	63^74568+2	134174	Lelio R Paula	06/2017
5278	2^445671-22071	134161	Enzo Doria	07/2013
5279	532^49205+49205^532	134129	Norbert Schneider	02/2019
5280	36453^4780+4780^36453	134127	Hans Havermann	04/2021
5281	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
5282	2^445515-113859	134114	Enzo Doria	10/2014
5284	(22*10^134111-37)/3	134112	Robert Price	04/2019
5283	31083^20636+20636^31083	134112	Hans Havermann	04/2021
5285	3*2^445478+5	134103	Jon Grantham	07/2023
5286	31622^17379+17379^31622	134079	Hans Havermann	04/2021
5287	5*2^445380-3	134074	Jon Grantham	07/2023
5288	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
5289	(277*10^134059-7)/9	134061	Robert Price	02/2022
5290	2^445328-216917	134058	Enzo Doria	05/2014
5291	2^445202+1874899	134020	Enzo Doria	06/2016
5292	5^191739-3^191739-1	134020	Jon Grantham	08/2023
5293	(35*10^134003-89)/9	134004	Robert Price	02/2022
5294	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
5295	(35*10^133979-593)/9	133980	Robert Price	07/2018
5296	2*10^133955+51	133956	Robert Price	05/2018
5297	(49*10^133952+437)/9	133953	Robert Price	09/2021
5298	2^444964-113639	133948	Enzo Doria	08/2014
5299	31811^16240+16240^31811	133943	Hans Havermann	04/2021
5300	10^133902+167841	133903	Patrick De Geest	05/2021
5302	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
5301	10^133902-100001	133902	Robert Price	07/2020
5303	2^444784-113859	133894	Enzo Doria	10/2014
5304	(132^63127-1)/131	133864	Anonymous	06/2024
5305	32303^13914+13914^32303	133846	Hans Havermann	04/2021
5306	(29^91493-3^91493)/26	133798	Robert Price	06/2025
5307	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
5308	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
5309	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
5310	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
5311	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
5312	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
5313	30739^22458+22458^30739	133757	Hans Havermann	04/2021
5314	34942^6721+6721^34942	133739	Hans Havermann	04/2021
5315	(3^280229-1)/1120918	133698	Aurel Gibier	03/2025
5316	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
5317	34792^6935+6935^34792	133638	Hans Havermann	04/2021
5318	(266*10^133603+1)/3	133605	Robert Price	04/2020
5319	32261^13842+13842^32261	133600	Hans Havermann	04/2021
5320	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
5321	(134*10^133573-11)/3	133575	Robert Price	01/2022
5322	26726^30173-30173^26726	133574	Frank Doornink	03/2024
5323	2^443721+39527	133574	Enzo Doria	11/2024
5324	62^74521-61^74521	133571	Robert Price	05/2013
5325	(182*10^133543+1)/3	133545	Robert Price	02/2020
5326	(103*10^133535+11)/3	133537	Robert Price	01/2021
5327	32589^12520+12520^32589	133537	Hans Havermann	03/2021
5328	L(638839)/274700771	133502	Serge Batalov	07/2024
5329	34516^7373+7373^34516	133496	Hans Havermann	04/2021
5330	8*10^133487-37	133488	Robert Price	03/2022
5331	30135^26882+26882^30135	133482	Hans Havermann	04/2021
5332	2^443198-1867301	133416	Enzo Doria	03/2016
5333	27^93192+26	133392	Anonymous	09/2024
5334	(19*10^133390+101)/3	133391	Robert Price	09/2019
5335	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
5336	(17508!^2+1)/(1453817*25094393)	133366	Michael Porter	09/2025
5337	36117^4910+4910^36117	133311	Hans Havermann	04/2021
5338	2^442799+1874633	133296	Enzo Doria	06/2016
5339	L(637751)	133283	Henri Lifchitz	09/2008
5340	109^65410-2	133269	Lelio R Paula	10/2017
5341	2^442688-113489	133263	Enzo Doria	08/2014
5342	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
5343	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
5344	2^442437-1849993	133187	Enzo Doria	08/2015
5345	2^442430-2791721	133185	Enzo Doria	03/2016
5346	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
5347	29959^27870+27870^29959	133172	Hans Havermann	03/2021
5348	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
5349	2^442368+213691	133167	Enzo Doria	09/2023
5350	34240^7737+7737^34240	133145	Hans Havermann	03/2021
5351	452^50145+50145^452	133142	Norbert Schneider	09/2020
5352	(355^52201-1)/354	133122	Tom Wu	08/2024
5353	(3^278981-1)/14507014	133101	Paul Vanderveen	05/2025
5354	30659^21796+21796^30659	133011	Hans Havermann	04/2021
5355	33276^9935+9935^33276	133010	Hans Havermann	04/2021
5356	30111^26122+26122^30111	133001	Hans Havermann	04/2021
5357	30790^20869+20869^30790	132998	Hans Havermann	04/2021
5359	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
5358	8*10^132994-27	132995	Robert Price	10/2021
5360	(109*10^132992+11)/3	132994	Robert Price	06/2022
5361	2^441781-2787883	132990	Enzo Doria	03/2016
5362	fibonacci(636232)+4	132965	Jon Grantham	08/2023
5363	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
5364	2^441618+37	132941	Lelio R Paula	08/2017
5365	34857^6514+6514^34857	132940	Hans Havermann	04/2021
5366	34065^7988+7988^34065	132937	Hans Havermann	04/2021
5367	35571^5452+5452^35571	132914	Hans Havermann	04/2021
5368	2^441521-113575	132912	Enzo Doria	08/2014
5369	7*10^132884-99	132885	Robert Price	06/2019
5370	26987^29988-29988^26987	132882	Frank Doornink	03/2024
5371	(103*10^132879+17)/3	132881	Robert Price	08/2020
5372	2^441396-65	132874	Lelio R Paula	08/2017
5373	33350^9633+9633^33350	132859	Hans Havermann	04/2021
5374	2^441330+1871959	132854	Enzo Doria	05/2016
5375	25772^30111-30111^25772	132825	Frank Doornink	02/2024
5376	2^441063+383	132774	Lelio R Paula	06/2012
5377	(10^132753+7)/17/19	132751	Alfred Reich	06/2021
5378	(22*10^132746+53)/3	132747	Robert Price	07/2019
5379	(77*10^132744-149)/9	132745	Robert Price	03/2022
5380	(22*10^132732+119)/3	132733	Robert Price	04/2021
5381	2^440846+1870909	132708	Enzo Doria	05/2016
5382	(948^44579-1)/947	132701	Jinyuan Wang	04/2023
5383	2^440656-113489	132651	Enzo Doria	08/2014
5384	numbpart(14180123587)	132646	Serge Batalov	04/2017
5385	32950^10591+10591^32950	132622	Hans Havermann	04/2021
5386	33302^9597+9597^33302	132614	Hans Havermann	04/2021
5387	(19*10^132550+191)/3	132551	Robert Price	05/2019
5388	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
5389	(38^83891+1)/39	132529	Robert Price	09/2013
5390	2*10^132493-43	132494	Robert Price	04/2018
5391	31352^16809+16809^31352	132480	Hans Havermann	04/2021
5392	(418*10^132441+23)/9	132443	Robert Price	02/2020
5393	2^439931-21	132433	Lelio R Paula	08/2017
5394	47^79201-46^79201	132432	Robert Price	10/2012
5395	2^439897-113653	132423	Enzo Doria	08/2014
5396	35505^5362+5362^35505	132410	Hans Havermann	03/2021
5397	30079^25222+25222^30079	132402	Hans Havermann	04/2021
5398	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
5399	(695*10^132356+7)/9	132358	Robert Price	12/2021
5400	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
5401	2^439576-113247	132326	Enzo Doria	07/2014
5402	(7^156589-1)/65346468774	132323	Paul Vanderveen	05/2025
5403	30059^25230+25230^30059	132318	Hans Havermann	04/2021
5404	2^439497-29143	132302	Enzo Doria	07/2015
5405	2^439409-114193	132276	Enzo Doria	12/2014
5406	(39^83137+2^83137)/41	132275	Robert Price	12/2024
5407	(44*10^132233-233)/9	132234	Robert Price	01/2019
5408	25507^30000-30000^25507	132200	Frank Doornink	02/2024
5409	9*10^132148-7	132149	Robert Price	09/2015
5410	V(790390)	132144	Serge Batalov	07/2024
5411	(47*10^132125-119)/9	132126	Robert Price	05/2019
5412	2^438900+214051	132123	Enzo Doria	10/2023
5413	2^438845+1870217	132106	Enzo Doria	05/2016
5414	2^438789+87855	132089	Lelio R Paula	01/2016
5415	2^438774-2786411	132085	Enzo Doria	03/2016
5416	2^438755-1848205	132079	Enzo Doria	07/2015
5417	30502^21381+21381^30502	132075	Hans Havermann	04/2021
5418	2^438739-112087	132074	Enzo Doria	06/2014
5419	(588859*29^90289-19)/28	132043	Eric Chen	06/2025
5420	(2^438438+100280245065)	131983	Paul Bourdelais	05/2022
5421	35872^4777+4777^35872	131979	Hans Havermann	04/2021
5422	31198^16945+16945^31198	131938	Hans Havermann	03/2021
5423	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
5424	L(631181)	131910	Henri Lifchitz	09/2008
5425	(47*10^131886-119)/9	131887	Robert Price	05/2019
5426	5*2^438096-3	131881	Jon Grantham	07/2023
5427	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
5428	2^438079-1863877	131875	Enzo Doria	03/2016
5429	(16*10^131872-37)/3	131873	Robert Price	05/2021
5430	(2^438067+5)/329	131869	Lelio R Paula	06/2015
5431	2^437908-113855	131824	Enzo Doria	09/2014
5432	2^437884-286349	131817	Enzo Doria	07/2015
5433	15^112072+14	131807	Alfred Reich	10/2023
5434	5^188558+4	131797	Tyler NeSmith	05/2021
5435	(11*10^131784-17)/3	131785	Robert Price	06/2018
5436	(166^59357-1)/165	131777	Anonymous	06/2024
5437	4*10^131719-93	131720	Robert Price	07/2020
5438	31629^14606+14606^31629	131720	Hans Havermann	04/2021
5439	3^276062-112292	131716	Enzo Doria	07/2014
5440	2^437539+2025	131713	Henri Lifchitz	01/2025
5441	11*31^88313+322688	131708	Eric Chen	05/2024
5442	(7*10^131682+89)/3	131683	Robert Price	08/2020
5443	29512^28969+28969^29512	131681	Hans Havermann	03/2021
5444	2^437343+75953	131654	Enzo Doria	04/2016
5445	35^85243-34^85243	131621	Robert Price	05/2012
5446	(28*10^131586+59)/3	131587	Robert Price	05/2021
5447	(59*10^131575+391)/9	131576	Robert Price	03/2021
5448	Phi(51051,-17#)	131513	Henri Lifchitz	12/2025
5449	39984^1945+1945^39984	131505	Hans Havermann	03/2021
5450	25842^29801-29801^25842	131492	Frank Doornink	03/2024
5451	28592^29505-29505^28592	131482	Frank Doornink	05/2024
5452	25647^29818-29818^25647	131469	Frank Doornink	02/2024
5453	(203*10^131457+1)/3	131459	Robert Price	03/2020
5454	7*10^131421-41	131422	Robert Price	08/2021
5455	87309^32+32^87309	131414	Hans Havermann	03/2021
5456	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
5457	2^436521+224885	131406	Enzo Doria	07/2024
5458	(650*10^131391+43)/9	131393	Tyler Busby	01/2023
5459	2^436451+1884713	131385	Enzo Doria	03/2017
5460	2^436365+35	131359	Robert Price	11/2015
5462	2^436300+1866871	131340	Enzo Doria	03/2016
5461	(7*10^131339+179)/3	131340	Robert Price	09/2018
5463	14^114592-3	131338	Paul Bourdelais	12/2020
5464	36197^4236+4236^36197	131285	Hans Havermann	04/2021
5465	(37*10^131270+341)/9	131271	Robert Price	08/2018
5466	29863^24790+24790^29863	131227	Hans Havermann	03/2021
5467	(5*10^131223-29)/3	131224	Robert Price	03/2018
5468	29524^27825+27825^29524	131218	Hans Havermann	03/2021
5469	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
5470	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
5471	30639^19136+19136^30639	131192	Hans Havermann	04/2021
5472	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
5473	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
5474	2^435773+1875557	131181	Enzo Doria	06/2016
5476	(16*10^131180+167)/3	131181	Robert Price	06/2019
5475	(26*10^131180-77)/3	131181	Robert Price	11/2019
5477	(25*10^131144-7)/9	131145	Robert Price	05/2018
5478	29299^29358-29358^29299	131138	Norbert Schneider	03/2022
5479	2^435612-2789939	131133	Enzo Doria	12/2015
5480	33976^7231+7231^33976	131121	Hans Havermann	03/2021
5481	33715^7746+7746^33715	131121	Hans Havermann	03/2021
5482	66^72047-65^72047	131093	Robert Price	09/2013
5483	(5*10^131090+37)/3	131091	Robert Price	03/2018
5484	2^435468+75631	131089	Enzo Doria	04/2016
5485	37^83588-2	131083	Lelio R Paula	08/2015
5486	(4^217720+11)/3	131081	Robert Price	02/2017
5487	30407^20448+20448^30407	131074	Hans Havermann	04/2021
5488	(22*10^131070+179)/3	131071	Robert Price	02/2022
5489	28831^29388-29388^28831	131067	Frank Doornink	05/2024
5490	29487^27836+27836^29487	131059	Hans Havermann	04/2021
5491	29962^23615+23615^29962	131030	Hans Havermann	03/2021
5492	2^435202-113193	131009	Enzo Doria	07/2014
5493	41705^1384+1384^41705	131002	Hans Havermann	04/2021
5494	9*10^130998-19	130999	Robert Price	07/2019
5495	36243^4108+4108^36243	130969	Hans Havermann	04/2021
5496	(445^49433+1)/446	130914	Jinyuan Wang	05/2024
5497	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
5498	2^434835-111937	130899	Enzo Doria	05/2014
5499	(62*10^130895-629)/9	130896	Robert Price	07/2021
5500	2^434807+225	130890	Henri Lifchitz	11/2024

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PRP Records

Probable Primes Top 10000

(302275 PRPs in the top)