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 ?
5501	31376^19437+19437^31376	134561	Hans Havermann	12/2020
5502	2^446990-22041	134558	Enzo Doria	07/2013
5503	123^64370+122	134528	Karsten Bonath	04/2018
5504	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5505	31251^20158+20158^31251	134519	Hans Havermann	11/2020
5506	2^446782-39701	134495	Enzo Doria	09/2015
5507	31817^16858+16858^31817	134485	Hans Havermann	12/2020
5508	32448^13937+13937^32448	134471	Hans Havermann	12/2020
5509	5^192321+3^192321-1	134427	Jon Grantham	08/2023
5510	2^446494-16485	134409	Enzo Doria	04/2013
5511	30042^29785+29785^30042	134408	Hans Havermann	12/2020
5512	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
5513	2^446441+65	134393	Lelio R Paula	08/2017
5514	(10^134385+719)/9	134385	Serge Batalov	12/2014
5515	30043^29688+29688^30043	134370	Hans Havermann	12/2020
5516	(2*10^134364+529)/9	134364	Robert Price	01/2018
5517	34657^7512+7512^34657	134323	Hans Havermann	11/2020
5518	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
5519	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
5520	42035^1564+1564^42035	134270	Hans Havermann	12/2020
5522	(2^446022-7)/339	134264	Lelio R Paula	07/2015
5521	30621^24248+24248^30621	134264	Hans Havermann	12/2020
5523	30341^26562+26562^30341	134237	Hans Havermann	11/2020
5524	(189^58967-1)/188	134234	Anonymous	06/2024
5525	10^134209+99867	134210	Patrick De Geest	05/2021
5526	10^134209-80000001	134209	Robert Price	04/2021
5527	10^134209-323283	134209	Patrick De Geest	05/2021
5528	29976^29953+29953^29976	134186	Hans Havermann	12/2020
5529	35038^6755+6755^35038	134183	Hans Havermann	12/2020
5530	63^74568+2	134174	Lelio R Paula	06/2017
5531	2^445671-22071	134161	Enzo Doria	07/2013
5532	532^49205+49205^532	134129	Norbert Schneider	02/2019
5533	36453^4780+4780^36453	134127	Hans Havermann	04/2021
5534	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
5535	2^445515-113859	134114	Enzo Doria	10/2014
5537	(22*10^134111-37)/3	134112	Robert Price	04/2019
5536	31083^20636+20636^31083	134112	Hans Havermann	04/2021
5538	3*2^445478+5	134103	Jon Grantham	07/2023
5539	31622^17379+17379^31622	134079	Hans Havermann	04/2021
5540	5*2^445380-3	134074	Jon Grantham	07/2023
5541	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
5542	(277*10^134059-7)/9	134061	Robert Price	02/2022
5543	2^445328-216917	134058	Enzo Doria	05/2014
5544	2^445202+1874899	134020	Enzo Doria	06/2016
5545	5^191739-3^191739-1	134020	Jon Grantham	08/2023
5546	(35*10^134003-89)/9	134004	Robert Price	02/2022
5547	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
5548	(35*10^133979-593)/9	133980	Robert Price	07/2018
5549	2*10^133955+51	133956	Robert Price	05/2018
5550	(49*10^133952+437)/9	133953	Robert Price	09/2021
5551	2^444964-113639	133948	Enzo Doria	08/2014
5552	31811^16240+16240^31811	133943	Hans Havermann	04/2021
5553	10^133902+167841	133903	Patrick De Geest	05/2021
5555	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
5554	10^133902-100001	133902	Robert Price	07/2020
5556	2^444784-113859	133894	Enzo Doria	10/2014
5557	(132^63127-1)/131	133864	Anonymous	06/2024
5558	32303^13914+13914^32303	133846	Hans Havermann	04/2021
5559	(29^91493-3^91493)/26	133798	Robert Price	06/2025
5560	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
5561	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
5562	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
5563	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
5564	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
5565	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
5566	30739^22458+22458^30739	133757	Hans Havermann	04/2021
5567	34942^6721+6721^34942	133739	Hans Havermann	04/2021
5568	(3^280229-1)/1120918	133698	Aurel Gibier	03/2025
5569	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
5570	34792^6935+6935^34792	133638	Hans Havermann	04/2021
5571	(266*10^133603+1)/3	133605	Robert Price	04/2020
5572	32261^13842+13842^32261	133600	Hans Havermann	04/2021
5573	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
5574	(134*10^133573-11)/3	133575	Robert Price	01/2022
5575	26726^30173-30173^26726	133574	Frank Doornink	03/2024
5576	2^443721+39527	133574	Enzo Doria	11/2024
5577	62^74521-61^74521	133571	Robert Price	05/2013
5578	(182*10^133543+1)/3	133545	Robert Price	02/2020
5579	(103*10^133535+11)/3	133537	Robert Price	01/2021
5580	32589^12520+12520^32589	133537	Hans Havermann	03/2021
5581	2^443590-431651	133534	Maxim Gerspach	08/2026
5582	L(638839)/274700771	133502	Serge Batalov	07/2024
5583	34516^7373+7373^34516	133496	Hans Havermann	04/2021
5584	8*10^133487-37	133488	Robert Price	03/2022
5585	30135^26882+26882^30135	133482	Hans Havermann	04/2021
5586	2^443198-1867301	133416	Enzo Doria	03/2016
5587	27^93192+26	133392	Anonymous	09/2024
5588	(19*10^133390+101)/3	133391	Robert Price	09/2019
5589	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
5590	(17508!^2+1)/(1453817*25094393)	133366	Michael Porter	09/2025
5591	36117^4910+4910^36117	133311	Hans Havermann	04/2021
5592	2^442799+1874633	133296	Enzo Doria	06/2016
5593	L(637751)	133283	Henri Lifchitz	09/2008
5594	109^65410-2	133269	Lelio R Paula	10/2017
5595	2^442688-113489	133263	Enzo Doria	08/2014
5596	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
5597	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
5598	2^442437-1849993	133187	Enzo Doria	08/2015
5599	2^442430-2791721	133185	Enzo Doria	03/2016
5600	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
5601	29959^27870+27870^29959	133172	Hans Havermann	03/2021
5602	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
5603	2^442368+213691	133167	Enzo Doria	09/2023
5604	34240^7737+7737^34240	133145	Hans Havermann	03/2021
5605	452^50145+50145^452	133142	Norbert Schneider	09/2020
5606	(355^52201-1)/354	133122	Tom Wu	08/2024
5607	(3^278981-1)/14507014	133101	Paul Vanderveen	05/2025
5608	30659^21796+21796^30659	133011	Hans Havermann	04/2021
5609	33276^9935+9935^33276	133010	Hans Havermann	04/2021
5610	30111^26122+26122^30111	133001	Hans Havermann	04/2021
5611	30790^20869+20869^30790	132998	Hans Havermann	04/2021
5613	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
5612	8*10^132994-27	132995	Robert Price	10/2021
5614	(109*10^132992+11)/3	132994	Robert Price	06/2022
5615	2^441781-2787883	132990	Enzo Doria	03/2016
5616	fibonacci(636232)+4	132965	Jon Grantham	08/2023
5617	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
5618	2^441618+37	132941	Lelio R Paula	08/2017
5619	34857^6514+6514^34857	132940	Hans Havermann	04/2021
5620	34065^7988+7988^34065	132937	Hans Havermann	04/2021
5621	35571^5452+5452^35571	132914	Hans Havermann	04/2021
5622	2^441521-113575	132912	Enzo Doria	08/2014
5623	7*10^132884-99	132885	Robert Price	06/2019
5624	26987^29988-29988^26987	132882	Frank Doornink	03/2024
5625	(103*10^132879+17)/3	132881	Robert Price	08/2020
5626	2^441396-65	132874	Lelio R Paula	08/2017
5627	33350^9633+9633^33350	132859	Hans Havermann	04/2021
5628	2^441330+1871959	132854	Enzo Doria	05/2016
5629	25772^30111-30111^25772	132825	Frank Doornink	02/2024
5630	2^441063+383	132774	Lelio R Paula	06/2012
5631	(10^132753+7)/17/19	132751	Alfred Reich	06/2021
5632	(22*10^132746+53)/3	132747	Robert Price	07/2019
5633	(77*10^132744-149)/9	132745	Robert Price	03/2022
5634	(22*10^132732+119)/3	132733	Robert Price	04/2021
5635	2^440846+1870909	132708	Enzo Doria	05/2016
5636	(948^44579-1)/947	132701	Jinyuan Wang	04/2023
5637	2^440656-113489	132651	Enzo Doria	08/2014
5638	numbpart(14180123587)	132646	Serge Batalov	04/2017
5639	32950^10591+10591^32950	132622	Hans Havermann	04/2021
5640	33302^9597+9597^33302	132614	Hans Havermann	04/2021
5641	(19*10^132550+191)/3	132551	Robert Price	05/2019
5642	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
5643	(38^83891+1)/39	132529	Robert Price	09/2013
5644	2*10^132493-43	132494	Robert Price	04/2018
5645	31352^16809+16809^31352	132480	Hans Havermann	04/2021
5646	(418*10^132441+23)/9	132443	Robert Price	02/2020
5647	2^439931-21	132433	Lelio R Paula	08/2017
5648	47^79201-46^79201	132432	Robert Price	10/2012
5649	2^439897-113653	132423	Enzo Doria	08/2014
5650	35505^5362+5362^35505	132410	Hans Havermann	03/2021
5651	30079^25222+25222^30079	132402	Hans Havermann	04/2021
5652	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
5653	(695*10^132356+7)/9	132358	Robert Price	12/2021
5654	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
5655	2^439576-113247	132326	Enzo Doria	07/2014
5656	(7^156589-1)/65346468774	132323	Paul Vanderveen	05/2025
5657	30059^25230+25230^30059	132318	Hans Havermann	04/2021
5658	2^439497-29143	132302	Enzo Doria	07/2015
5659	2^439409-114193	132276	Enzo Doria	12/2014
5660	(39^83137+2^83137)/41	132275	Robert Price	12/2024
5661	(44*10^132233-233)/9	132234	Robert Price	01/2019
5662	25507^30000-30000^25507	132200	Frank Doornink	02/2024
5663	9*10^132148-7	132149	Robert Price	09/2015
5664	V(790390)	132144	Serge Batalov	07/2024
5665	(47*10^132125-119)/9	132126	Robert Price	05/2019
5666	2^438900+214051	132123	Enzo Doria	10/2023
5667	2^438845+1870217	132106	Enzo Doria	05/2016
5668	Phi(293229,-5)	132106	Henri Lifchitz	02/2026
5669	2^438789+87855	132089	Lelio R Paula	01/2016
5670	2^438774-2786411	132085	Enzo Doria	03/2016
5671	2^438755-1848205	132079	Enzo Doria	07/2015
5672	30502^21381+21381^30502	132075	Hans Havermann	04/2021
5673	2^438739-112087	132074	Enzo Doria	06/2014
5674	(588859*29^90289-19)/28	132043	Eric Chen	06/2025
5675	(2^438438+100280245065)	131983	Paul Bourdelais	05/2022
5676	35872^4777+4777^35872	131979	Hans Havermann	04/2021
5677	31198^16945+16945^31198	131938	Hans Havermann	03/2021
5678	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
5679	L(631181)	131910	Henri Lifchitz	09/2008
5680	(47*10^131886-119)/9	131887	Robert Price	05/2019
5681	5*2^438096-3	131881	Jon Grantham	07/2023
5682	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
5683	2^438079-1863877	131875	Enzo Doria	03/2016
5684	(16*10^131872-37)/3	131873	Robert Price	05/2021
5685	(2^438067+5)/329	131869	Lelio R Paula	06/2015
5686	2^437908-113855	131824	Enzo Doria	09/2014
5687	2^437884-286349	131817	Enzo Doria	07/2015
5688	15^112072+14	131807	Alfred Reich	10/2023
5689	5^188558+4	131797	Tyler NeSmith	05/2021
5690	(11*10^131784-17)/3	131785	Robert Price	06/2018
5691	(166^59357-1)/165	131777	Anonymous	06/2024
5692	4*10^131719-93	131720	Robert Price	07/2020
5693	31629^14606+14606^31629	131720	Hans Havermann	04/2021
5694	3^276062-112292	131716	Enzo Doria	07/2014
5695	2^437539+2025	131713	Henri Lifchitz	01/2025
5696	11*31^88313+322688	131708	Eric Chen	05/2024
5697	(7*10^131682+89)/3	131683	Robert Price	08/2020
5698	29512^28969+28969^29512	131681	Hans Havermann	03/2021
5699	2^437343+75953	131654	Enzo Doria	04/2016
5700	35^85243-34^85243	131621	Robert Price	05/2012
5701	(28*10^131586+59)/3	131587	Robert Price	05/2021
5702	(59*10^131575+391)/9	131576	Robert Price	03/2021
5703	Phi(51051,-17#)	131513	Henri Lifchitz	12/2025
5704	39984^1945+1945^39984	131505	Hans Havermann	03/2021
5705	25842^29801-29801^25842	131492	Frank Doornink	03/2024
5706	28592^29505-29505^28592	131482	Frank Doornink	05/2024
5707	25647^29818-29818^25647	131469	Frank Doornink	02/2024
5708	(203*10^131457+1)/3	131459	Robert Price	03/2020
5709	7*10^131421-41	131422	Robert Price	08/2021
5710	87309^32+32^87309	131414	Hans Havermann	03/2021
5711	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
5712	2^436521+224885	131406	Enzo Doria	07/2024
5713	(650*10^131391+43)/9	131393	Tyler Busby	01/2023
5714	2^436451+1884713	131385	Enzo Doria	03/2017
5715	2^436365+35	131359	Robert Price	11/2015
5717	2^436300+1866871	131340	Enzo Doria	03/2016
5716	(7*10^131339+179)/3	131340	Robert Price	09/2018
5718	14^114592-3	131338	Paul Bourdelais	12/2020
5719	36197^4236+4236^36197	131285	Hans Havermann	04/2021
5720	(37*10^131270+341)/9	131271	Robert Price	08/2018
5721	29863^24790+24790^29863	131227	Hans Havermann	03/2021
5722	(5*10^131223-29)/3	131224	Robert Price	03/2018
5723	29524^27825+27825^29524	131218	Hans Havermann	03/2021
5724	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
5725	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
5726	30639^19136+19136^30639	131192	Hans Havermann	04/2021
5727	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
5728	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
5729	2^435773+1875557	131181	Enzo Doria	06/2016
5731	(16*10^131180+167)/3	131181	Robert Price	06/2019
5730	(26*10^131180-77)/3	131181	Robert Price	11/2019
5732	(25*10^131144-7)/9	131145	Robert Price	05/2018
5733	29299^29358-29358^29299	131138	Norbert Schneider	03/2022
5734	2^435612-2789939	131133	Enzo Doria	12/2015
5735	33976^7231+7231^33976	131121	Hans Havermann	03/2021
5736	33715^7746+7746^33715	131121	Hans Havermann	03/2021
5737	66^72047-65^72047	131093	Robert Price	09/2013
5738	(5*10^131090+37)/3	131091	Robert Price	03/2018
5739	2^435468+75631	131089	Enzo Doria	04/2016
5740	37^83588-2	131083	Lelio R Paula	08/2015
5741	(4^217720+11)/3	131081	Robert Price	02/2017
5742	30407^20448+20448^30407	131074	Hans Havermann	04/2021
5743	(22*10^131070+179)/3	131071	Robert Price	02/2022
5744	28831^29388-29388^28831	131067	Frank Doornink	05/2024
5745	29487^27836+27836^29487	131059	Hans Havermann	04/2021
5746	29962^23615+23615^29962	131030	Hans Havermann	03/2021
5747	2^435202-113193	131009	Enzo Doria	07/2014
5748	41705^1384+1384^41705	131002	Hans Havermann	04/2021
5749	9*10^130998-19	130999	Robert Price	07/2019
5750	36243^4108+4108^36243	130969	Hans Havermann	04/2021

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PRP Records

Probable Primes Top 10000

(303335 PRPs in the top)