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	2^443721+39527	133574	Enzo Doria	11/2024
5252	62^74521-61^74521	133571	Robert Price	05/2013
5253	(182*10^133543+1)/3	133545	Robert Price	02/2020
5254	(103*10^133535+11)/3	133537	Robert Price	01/2021
5255	32589^12520+12520^32589	133537	Hans Havermann	03/2021
5256	L(638839)/274700771	133502	Serge Batalov	07/2024
5257	34516^7373+7373^34516	133496	Hans Havermann	04/2021
5258	8*10^133487-37	133488	Robert Price	03/2022
5259	30135^26882+26882^30135	133482	Hans Havermann	04/2021
5260	2^443198-1867301	133416	Enzo Doria	03/2016
5261	27^93192+26	133392	Anonymous	09/2024
5262	(19*10^133390+101)/3	133391	Robert Price	09/2019
5263	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
5264	(17508!^2+1)/(1453817*25094393)	133366	Michael Porter	09/2025
5265	36117^4910+4910^36117	133311	Hans Havermann	04/2021
5266	2^442799+1874633	133296	Enzo Doria	06/2016
5267	L(637751)	133283	Henri Lifchitz	09/2008
5268	109^65410-2	133269	Lelio R Paula	10/2017
5269	2^442688-113489	133263	Enzo Doria	08/2014
5270	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
5271	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
5272	2^442437-1849993	133187	Enzo Doria	08/2015
5273	2^442430-2791721	133185	Enzo Doria	03/2016
5274	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
5275	29959^27870+27870^29959	133172	Hans Havermann	03/2021
5276	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
5277	2^442368+213691	133167	Enzo Doria	09/2023
5278	34240^7737+7737^34240	133145	Hans Havermann	03/2021
5279	452^50145+50145^452	133142	Norbert Schneider	09/2020
5280	(355^52201-1)/354	133122	Tom Wu	08/2024
5281	(3^278981-1)/14507014	133101	Paul Vanderveen	05/2025
5282	30659^21796+21796^30659	133011	Hans Havermann	04/2021
5283	33276^9935+9935^33276	133010	Hans Havermann	04/2021
5284	30111^26122+26122^30111	133001	Hans Havermann	04/2021
5285	30790^20869+20869^30790	132998	Hans Havermann	04/2021
5287	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
5286	8*10^132994-27	132995	Robert Price	10/2021
5288	(109*10^132992+11)/3	132994	Robert Price	06/2022
5289	2^441781-2787883	132990	Enzo Doria	03/2016
5290	fibonacci(636232)+4	132965	Jon Grantham	08/2023
5291	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
5292	2^441618+37	132941	Lelio R Paula	08/2017
5293	34857^6514+6514^34857	132940	Hans Havermann	04/2021
5294	34065^7988+7988^34065	132937	Hans Havermann	04/2021
5295	35571^5452+5452^35571	132914	Hans Havermann	04/2021
5296	2^441521-113575	132912	Enzo Doria	08/2014
5297	7*10^132884-99	132885	Robert Price	06/2019
5298	26987^29988-29988^26987	132882	Frank Doornink	03/2024
5299	(103*10^132879+17)/3	132881	Robert Price	08/2020
5300	2^441396-65	132874	Lelio R Paula	08/2017
5301	33350^9633+9633^33350	132859	Hans Havermann	04/2021
5302	2^441330+1871959	132854	Enzo Doria	05/2016
5303	25772^30111-30111^25772	132825	Frank Doornink	02/2024
5304	2^441063+383	132774	Lelio R Paula	06/2012
5305	(10^132753+7)/17/19	132751	Alfred Reich	06/2021
5306	(22*10^132746+53)/3	132747	Robert Price	07/2019
5307	(77*10^132744-149)/9	132745	Robert Price	03/2022
5308	(22*10^132732+119)/3	132733	Robert Price	04/2021
5309	2^440846+1870909	132708	Enzo Doria	05/2016
5310	(948^44579-1)/947	132701	Jinyuan Wang	04/2023
5311	2^440656-113489	132651	Enzo Doria	08/2014
5312	numbpart(14180123587)	132646	Serge Batalov	04/2017
5313	32950^10591+10591^32950	132622	Hans Havermann	04/2021
5314	33302^9597+9597^33302	132614	Hans Havermann	04/2021
5315	(19*10^132550+191)/3	132551	Robert Price	05/2019
5316	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
5317	(38^83891+1)/39	132529	Robert Price	09/2013
5318	2*10^132493-43	132494	Robert Price	04/2018
5319	31352^16809+16809^31352	132480	Hans Havermann	04/2021
5320	(418*10^132441+23)/9	132443	Robert Price	02/2020
5321	2^439931-21	132433	Lelio R Paula	08/2017
5322	47^79201-46^79201	132432	Robert Price	10/2012
5323	2^439897-113653	132423	Enzo Doria	08/2014
5324	35505^5362+5362^35505	132410	Hans Havermann	03/2021
5325	30079^25222+25222^30079	132402	Hans Havermann	04/2021
5326	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
5327	(695*10^132356+7)/9	132358	Robert Price	12/2021
5328	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
5329	2^439576-113247	132326	Enzo Doria	07/2014
5330	(7^156589-1)/65346468774	132323	Paul Vanderveen	05/2025
5331	30059^25230+25230^30059	132318	Hans Havermann	04/2021
5332	2^439497-29143	132302	Enzo Doria	07/2015
5333	2^439409-114193	132276	Enzo Doria	12/2014
5334	(39^83137+2^83137)/41	132275	Robert Price	12/2024
5335	(44*10^132233-233)/9	132234	Robert Price	01/2019
5336	25507^30000-30000^25507	132200	Frank Doornink	02/2024
5337	9*10^132148-7	132149	Robert Price	09/2015
5338	V(790390)	132144	Serge Batalov	07/2024
5339	(47*10^132125-119)/9	132126	Robert Price	05/2019
5340	2^438900+214051	132123	Enzo Doria	10/2023
5341	2^438845+1870217	132106	Enzo Doria	05/2016
5342	2^438789+87855	132089	Lelio R Paula	01/2016
5343	2^438774-2786411	132085	Enzo Doria	03/2016
5344	2^438755-1848205	132079	Enzo Doria	07/2015
5345	30502^21381+21381^30502	132075	Hans Havermann	04/2021
5346	2^438739-112087	132074	Enzo Doria	06/2014
5347	(588859*29^90289-19)/28	132043	Eric Chen	06/2025
5348	(2^438438+100280245065)	131983	Paul Bourdelais	05/2022
5349	35872^4777+4777^35872	131979	Hans Havermann	04/2021
5350	31198^16945+16945^31198	131938	Hans Havermann	03/2021
5351	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
5352	L(631181)	131910	Henri Lifchitz	09/2008
5353	(47*10^131886-119)/9	131887	Robert Price	05/2019
5354	5*2^438096-3	131881	Jon Grantham	07/2023
5355	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
5356	2^438079-1863877	131875	Enzo Doria	03/2016
5357	(16*10^131872-37)/3	131873	Robert Price	05/2021
5358	(2^438067+5)/329	131869	Lelio R Paula	06/2015
5359	2^437908-113855	131824	Enzo Doria	09/2014
5360	2^437884-286349	131817	Enzo Doria	07/2015
5361	15^112072+14	131807	Alfred Reich	10/2023
5362	5^188558+4	131797	Tyler NeSmith	05/2021
5363	(11*10^131784-17)/3	131785	Robert Price	06/2018
5364	(166^59357-1)/165	131777	Anonymous	06/2024
5365	4*10^131719-93	131720	Robert Price	07/2020
5366	31629^14606+14606^31629	131720	Hans Havermann	04/2021
5367	3^276062-112292	131716	Enzo Doria	07/2014
5368	2^437539+2025	131713	Henri Lifchitz	01/2025
5369	11*31^88313+322688	131708	Eric Chen	05/2024
5370	(7*10^131682+89)/3	131683	Robert Price	08/2020
5371	29512^28969+28969^29512	131681	Hans Havermann	03/2021
5372	2^437343+75953	131654	Enzo Doria	04/2016
5373	35^85243-34^85243	131621	Robert Price	05/2012
5374	(28*10^131586+59)/3	131587	Robert Price	05/2021
5375	(59*10^131575+391)/9	131576	Robert Price	03/2021
5376	39984^1945+1945^39984	131505	Hans Havermann	03/2021
5377	25842^29801-29801^25842	131492	Frank Doornink	03/2024
5378	28592^29505-29505^28592	131482	Frank Doornink	05/2024
5379	25647^29818-29818^25647	131469	Frank Doornink	02/2024
5380	(203*10^131457+1)/3	131459	Robert Price	03/2020
5381	7*10^131421-41	131422	Robert Price	08/2021
5382	87309^32+32^87309	131414	Hans Havermann	03/2021
5383	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
5384	2^436521+224885	131406	Enzo Doria	07/2024
5385	(650*10^131391+43)/9	131393	Tyler Busby	01/2023
5386	2^436451+1884713	131385	Enzo Doria	03/2017
5387	2^436365+35	131359	Robert Price	11/2015
5389	2^436300+1866871	131340	Enzo Doria	03/2016
5388	(7*10^131339+179)/3	131340	Robert Price	09/2018
5390	14^114592-3	131338	Paul Bourdelais	12/2020
5391	36197^4236+4236^36197	131285	Hans Havermann	04/2021
5392	(37*10^131270+341)/9	131271	Robert Price	08/2018
5393	29863^24790+24790^29863	131227	Hans Havermann	03/2021
5394	(5*10^131223-29)/3	131224	Robert Price	03/2018
5395	29524^27825+27825^29524	131218	Hans Havermann	03/2021
5396	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
5397	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
5398	30639^19136+19136^30639	131192	Hans Havermann	04/2021
5399	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
5400	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
5401	2^435773+1875557	131181	Enzo Doria	06/2016
5403	(16*10^131180+167)/3	131181	Robert Price	06/2019
5402	(26*10^131180-77)/3	131181	Robert Price	11/2019
5404	(25*10^131144-7)/9	131145	Robert Price	05/2018
5405	29299^29358-29358^29299	131138	Norbert Schneider	03/2022
5406	2^435612-2789939	131133	Enzo Doria	12/2015
5407	33976^7231+7231^33976	131121	Hans Havermann	03/2021
5408	33715^7746+7746^33715	131121	Hans Havermann	03/2021
5409	66^72047-65^72047	131093	Robert Price	09/2013
5410	(5*10^131090+37)/3	131091	Robert Price	03/2018
5411	2^435468+75631	131089	Enzo Doria	04/2016
5412	37^83588-2	131083	Lelio R Paula	08/2015
5413	(4^217720+11)/3	131081	Robert Price	02/2017
5414	30407^20448+20448^30407	131074	Hans Havermann	04/2021
5415	(22*10^131070+179)/3	131071	Robert Price	02/2022
5416	28831^29388-29388^28831	131067	Frank Doornink	05/2024
5417	29487^27836+27836^29487	131059	Hans Havermann	04/2021
5418	29962^23615+23615^29962	131030	Hans Havermann	03/2021
5419	2^435202-113193	131009	Enzo Doria	07/2014
5420	41705^1384+1384^41705	131002	Hans Havermann	04/2021
5421	9*10^130998-19	130999	Robert Price	07/2019
5422	36243^4108+4108^36243	130969	Hans Havermann	04/2021
5423	(445^49433+1)/446	130914	Jinyuan Wang	05/2024
5424	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
5425	2^434835-111937	130899	Enzo Doria	05/2014
5426	(62*10^130895-629)/9	130896	Robert Price	07/2021
5427	2^434807+225	130890	Henri Lifchitz	11/2024
5428	2^434685+72257	130854	Enzo Doria	04/2016
5429	(7*10^130825+113)/3	130826	Robert Price	02/2018
5430	2^434539-29317	130810	Enzo Doria	07/2015
5431	(74*10^130791+637)/9	130792	Robert Price	01/2022
5432	2^434469-114259	130789	Enzo Doria	01/2015
5433	(5*10^130763+103)/9	130763	Robert Price	04/2022
5434	2^434246+33	130722	Robert Price	11/2015
5435	30156^21599+21599^30156	130710	Hans Havermann	04/2021
5436	(41^81041-3^81041)/38	130701	Robert Price	09/2025
5437	(17*10^130695-161)/9	130696	Robert Price	02/2021
5438	30513^19148+19148^30513	130661	Hans Havermann	03/2021
5439	29736^24761+24761^29736	130654	Hans Havermann	04/2021
5440	9*10^130638+41	130639	Robert Price	08/2020
5441	2^433911-91	130621	Lelio R Paula	06/2017
5442	30786^17449+17449^30786	130588	Hans Havermann	03/2021
5443	2^433744-114419	130570	Enzo Doria	02/2015
5445	2^433708+1869451	130560	Enzo Doria	05/2016
5444	2^433710+93	130560	Lelio R Paula	06/2017
5446	7*10^130535-27	130536	Robert Price	11/2022
5447	(17^130533)%(10^130533)	130533	Henri Lifchitz	05/2025
5448	(9629^32768+1)/120501441265666	130520	Kellen Shenton	05/2021
5449	804*34^85220+713	130516	Eric Chen	08/2023
5450	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
5451	3^273521+10	130503	Tyler NeSmith	01/2021
5452	41659^1356+1356^41659	130487	Hans Havermann	03/2021
5453	4*10^130480+9	130481	Robert Price	05/2015
5454	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
5455	3*2^433422+5	130474	Jon Grantham	07/2023
5456	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
5457	(31*10^130414-49)/9	130415	Robert Price	11/2021
5458	26462^29485-29485^26462	130402	Frank Doornink	03/2024
5459	33481^7848+7848^33481	130401	Hans Havermann	03/2021
5460	(17*10^130393+7)/3	130394	Robert Price	06/2023
5461	(22*10^130392+203)/9	130393	Robert Price	10/2021
5462	29773^23950+23950^29773	130386	Hans Havermann	04/2021
5463	2^433023-113497	130353	Enzo Doria	08/2014
5464	31175^15178+15178^31175	130350	Hans Havermann	04/2021
5465	2^433002+1179379	130347	Enzo Doria	06/2016
5466	2^432974+19	130339	Robert Price	08/2015
5467	31903^12168+12168^31903	130331	Hans Havermann	04/2021
5468	2^432917+22217	130322	Enzo Doria	09/2023
5469	29387^27112+27112^29387	130278	Hans Havermann	04/2021
5470	2^432768+213181	130277	Enzo Doria	09/2023
5471	29577^25370+25370^29577	130267	Hans Havermann	04/2021
5472	31738^12685+12685^31738	130231	Hans Havermann	03/2021
5473	44235^878+878^44235	130206	Hans Havermann	04/2021
5474	32160^11171+11171^32160	130187	Hans Havermann	04/2021
5475	29489^25956+25956^29489	130172	Hans Havermann	04/2021
5476	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
5477	33005^8766+8766^33005	130133	Hans Havermann	04/2021
5478	(35*10^130132-611)/9	130133	Robert Price	02/2022
5479	(444^49408+1)/(444^256+1)	130125	Martin Hopf	12/2023
5480	2^432217+41	130111	Lelio R Paula	06/2017
5481	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
5482	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
5483	97^65480-2	130094	Lelio R Paula	05/2017
5484	36007^4102+4102^36007	130094	Hans Havermann	04/2021
5485	4*10^130088-89	130089	Robert Price	11/2018
5486	2^432117-113215	130081	Enzo Doria	07/2014
5487	(4*10^130080+41)/9	130080	Serge Batalov	11/2022
5488	9583*29^88890+736	129997	Eric Chen	06/2025
5489	2^431804+72511	129986	Enzo Doria	04/2016
5490	27902^29237-29237^27902	129978	Frank Doornink	03/2024
5491	33^85579+32	129953	Alfred Reich	10/2025
5492	(2313^38809-1)/(2313^197-1)	129898	Ryan Propper	11/2023
5493	(13*10^129896+137)/3	129897	Robert Price	06/2021
5494	(13*10^129890+71)/3	129891	Robert Price	06/2021
5495	29048^29101-29101^29048	129882	Norbert Schneider	03/2022
5496	37832^2709+2709^37832	129871	Hans Havermann	04/2021
5497	31055^15184+15184^31055	129853	Hans Havermann	04/2021
5499	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
5498	Phi(1632846L,3)	129844	Anonymous	03/2025
5500	31385^13702+13702^31385	129833	Hans Havermann	04/2021

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PRP Records

Probable Primes Top 10000

(301978 PRPs in the top)