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 ?
4501	63^74568+2	134174	Lelio R Paula	06/2017
4502	2^445671-22071	134161	Enzo Doria	07/2013
4503	532^49205+49205^532	134129	Norbert Schneider	02/2019
4504	36453^4780+4780^36453	134127	Hans Havermann	04/2021
4505	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
4506	2^445515-113859	134114	Enzo Doria	10/2014
4508	(22*10^134111-37)/3	134112	Robert Price	04/2019
4507	31083^20636+20636^31083	134112	Hans Havermann	04/2021
4509	3*2^445478+5	134103	Jon Grantham	07/2023
4510	31622^17379+17379^31622	134079	Hans Havermann	04/2021
4511	5*2^445380-3	134074	Jon Grantham	07/2023
4512	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
4513	(277*10^134059-7)/9	134061	Robert Price	02/2022
4514	2^445328-216917	134058	Enzo Doria	05/2014
4515	2^445202+1874899	134020	Enzo Doria	06/2016
4516	5^191739-3^191739-1	134020	Jon Grantham	08/2023
4517	(35*10^134003-89)/9	134004	Robert Price	02/2022
4518	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
4519	(35*10^133979-593)/9	133980	Robert Price	07/2018
4520	2*10^133955+51	133956	Robert Price	05/2018
4521	(49*10^133952+437)/9	133953	Robert Price	09/2021
4522	2^444964-113639	133948	Enzo Doria	08/2014
4523	31811^16240+16240^31811	133943	Hans Havermann	04/2021
4524	10^133902+167841	133903	Patrick De Geest	05/2021
4526	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
4525	10^133902-100001	133902	Robert Price	07/2020
4527	2^444784-113859	133894	Enzo Doria	10/2014
4528	(132^63127-1)/131	133864	Anonymous	06/2024
4529	32303^13914+13914^32303	133846	Hans Havermann	04/2021
4530	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
4531	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
4532	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
4533	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
4534	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
4535	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
4536	30739^22458+22458^30739	133757	Hans Havermann	04/2021
4537	34942^6721+6721^34942	133739	Hans Havermann	04/2021
4538	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
4539	34792^6935+6935^34792	133638	Hans Havermann	04/2021
4540	(266*10^133603+1)/3	133605	Robert Price	04/2020
4541	32261^13842+13842^32261	133600	Hans Havermann	04/2021
4542	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
4543	(134*10^133573-11)/3	133575	Robert Price	01/2022
4544	26726^30173-30173^26726	133574	Frank Doornink	03/2024
4545	2^443721+39527	133574	Enzo Doria	11/2024
4546	62^74521-61^74521	133571	Robert Price	05/2013
4547	(182*10^133543+1)/3	133545	Robert Price	02/2020
4548	(103*10^133535+11)/3	133537	Robert Price	01/2021
4549	32589^12520+12520^32589	133537	Hans Havermann	03/2021
4550	L(638839)/274700771	133502	Serge Batalov	07/2024
4551	34516^7373+7373^34516	133496	Hans Havermann	04/2021
4552	8*10^133487-37	133488	Robert Price	03/2022
4553	30135^26882+26882^30135	133482	Hans Havermann	04/2021
4554	2^443198-1867301	133416	Enzo Doria	03/2016
4555	27^93192+26	133392	Anonymous	09/2024
4556	(19*10^133390+101)/3	133391	Robert Price	09/2019
4557	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
4558	36117^4910+4910^36117	133311	Hans Havermann	04/2021
4559	2^442799+1874633	133296	Enzo Doria	06/2016
4560	L(637751)	133283	Henri Lifchitz	09/2008
4561	109^65410-2	133269	Lelio R Paula	10/2017
4562	2^442688-113489	133263	Enzo Doria	08/2014
4563	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
4564	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
4565	2^442437-1849993	133187	Enzo Doria	08/2015
4566	2^442430-2791721	133185	Enzo Doria	03/2016
4567	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
4568	29959^27870+27870^29959	133172	Hans Havermann	03/2021
4569	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
4570	2^442368+213691	133167	Enzo Doria	09/2023
4571	34240^7737+7737^34240	133145	Hans Havermann	03/2021
4572	452^50145+50145^452	133142	Norbert Schneider	09/2020
4573	(355^52201-1)/354	133122	Tom Wu	08/2024
4574	30659^21796+21796^30659	133011	Hans Havermann	04/2021
4575	33276^9935+9935^33276	133010	Hans Havermann	04/2021
4576	30111^26122+26122^30111	133001	Hans Havermann	04/2021
4577	30790^20869+20869^30790	132998	Hans Havermann	04/2021
4579	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
4578	8*10^132994-27	132995	Robert Price	10/2021
4580	(109*10^132992+11)/3	132994	Robert Price	06/2022
4581	2^441781-2787883	132990	Enzo Doria	03/2016
4582	fibonacci(636232)+4	132965	Jon Grantham	08/2023
4583	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
4584	2^441618+37	132941	Lelio R Paula	08/2017
4585	34857^6514+6514^34857	132940	Hans Havermann	04/2021
4586	34065^7988+7988^34065	132937	Hans Havermann	04/2021
4587	35571^5452+5452^35571	132914	Hans Havermann	04/2021
4588	2^441521-113575	132912	Enzo Doria	08/2014
4589	7*10^132884-99	132885	Robert Price	06/2019
4590	26987^29988-29988^26987	132882	Frank Doornink	03/2024
4591	(103*10^132879+17)/3	132881	Robert Price	08/2020
4592	2^441396-65	132874	Lelio R Paula	08/2017
4593	33350^9633+9633^33350	132859	Hans Havermann	04/2021
4594	2^441330+1871959	132854	Enzo Doria	05/2016
4595	25772^30111-30111^25772	132825	Frank Doornink	02/2024
4596	2^441063+383	132774	Lelio R Paula	06/2012
4597	(10^132753+7)/17/19	132751	Alfred Reich	06/2021
4598	(22*10^132746+53)/3	132747	Robert Price	07/2019
4599	(77*10^132744-149)/9	132745	Robert Price	03/2022
4600	(22*10^132732+119)/3	132733	Robert Price	04/2021
4601	2^440846+1870909	132708	Enzo Doria	05/2016
4602	(948^44579-1)/947	132701	Jinyuan Wang	04/2023
4603	2^440656-113489	132651	Enzo Doria	08/2014
4604	numbpart(14180123587)	132646	Serge Batalov	04/2017
4605	32950^10591+10591^32950	132622	Hans Havermann	04/2021
4606	33302^9597+9597^33302	132614	Hans Havermann	04/2021
4607	(19*10^132550+191)/3	132551	Robert Price	05/2019
4608	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
4609	(38^83891+1)/39	132529	Robert Price	09/2013
4610	2*10^132493-43	132494	Robert Price	04/2018
4611	31352^16809+16809^31352	132480	Hans Havermann	04/2021
4612	(418*10^132441+23)/9	132443	Robert Price	02/2020
4613	2^439931-21	132433	Lelio R Paula	08/2017
4614	47^79201-46^79201	132432	Robert Price	10/2012
4615	2^439897-113653	132423	Enzo Doria	08/2014
4616	35505^5362+5362^35505	132410	Hans Havermann	03/2021
4617	30079^25222+25222^30079	132402	Hans Havermann	04/2021
4618	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
4619	(695*10^132356+7)/9	132358	Robert Price	12/2021
4620	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
4621	2^439576-113247	132326	Enzo Doria	07/2014
4622	30059^25230+25230^30059	132318	Hans Havermann	04/2021
4623	2^439497-29143	132302	Enzo Doria	07/2015
4624	2^439409-114193	132276	Enzo Doria	12/2014
4625	(44*10^132233-233)/9	132234	Robert Price	01/2019
4626	25507^30000-30000^25507	132200	Frank Doornink	02/2024
4627	9*10^132148-7	132149	Robert Price	09/2015
4628	V(790390)	132144	Serge Batalov	07/2024
4629	(47*10^132125-119)/9	132126	Robert Price	05/2019
4630	2^438900+214051	132123	Enzo Doria	10/2023
4631	2^438845+1870217	132106	Enzo Doria	05/2016
4632	2^438789+87855	132089	Lelio R Paula	01/2016
4633	2^438774-2786411	132085	Enzo Doria	03/2016
4634	2^438755-1848205	132079	Enzo Doria	07/2015
4635	30502^21381+21381^30502	132075	Hans Havermann	04/2021
4636	2^438739-112087	132074	Enzo Doria	06/2014
4637	(2^438438+100280245065)	131983	Paul Bourdelais	05/2022
4638	35872^4777+4777^35872	131979	Hans Havermann	04/2021
4639	31198^16945+16945^31198	131938	Hans Havermann	03/2021
4640	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
4641	L(631181)	131910	Henri Lifchitz	09/2008
4642	(47*10^131886-119)/9	131887	Robert Price	05/2019
4643	5*2^438096-3	131881	Jon Grantham	07/2023
4644	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
4645	2^438079-1863877	131875	Enzo Doria	03/2016
4646	(16*10^131872-37)/3	131873	Robert Price	05/2021
4647	(2^438067+5)/329	131869	Lelio R Paula	06/2015
4648	2^437908-113855	131824	Enzo Doria	09/2014
4649	2^437884-286349	131817	Enzo Doria	07/2015
4650	15^112072+14	131807	Alfred Reich	10/2023
4651	5^188558+4	131797	Tyler NeSmith	05/2021
4652	(11*10^131784-17)/3	131785	Robert Price	06/2018
4653	(166^59357-1)/165	131777	Anonymous	06/2024
4655	4*10^131719-93	131720	Robert Price	07/2020
4654	31629^14606+14606^31629	131720	Hans Havermann	04/2021
4656	3^276062-112292	131716	Enzo Doria	07/2014
4657	11*31^88313+322688	131708	Eric Chen	05/2024
4658	(7*10^131682+89)/3	131683	Robert Price	08/2020
4659	29512^28969+28969^29512	131681	Hans Havermann	03/2021
4660	2^437343+75953	131654	Enzo Doria	04/2016
4661	35^85243-34^85243	131621	Robert Price	05/2012
4662	(28*10^131586+59)/3	131587	Robert Price	05/2021
4663	(59*10^131575+391)/9	131576	Robert Price	03/2021
4664	39984^1945+1945^39984	131505	Hans Havermann	03/2021
4665	25842^29801-29801^25842	131492	Frank Doornink	03/2024
4666	28592^29505-29505^28592	131482	Frank Doornink	05/2024
4667	25647^29818-29818^25647	131469	Frank Doornink	02/2024
4668	(203*10^131457+1)/3	131459	Robert Price	03/2020
4669	7*10^131421-41	131422	Robert Price	08/2021
4670	87309^32+32^87309	131414	Hans Havermann	03/2021
4671	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
4672	2^436521+224885	131406	Enzo Doria	07/2024
4673	(650*10^131391+43)/9	131393	Tyler Busby	01/2023
4674	2^436451+1884713	131385	Enzo Doria	03/2017
4675	2^436365+35	131359	Robert Price	11/2015
4677	2^436300+1866871	131340	Enzo Doria	03/2016
4676	(7*10^131339+179)/3	131340	Robert Price	09/2018
4678	14^114592-3	131338	Paul Bourdelais	12/2020
4679	36197^4236+4236^36197	131285	Hans Havermann	04/2021
4680	(37*10^131270+341)/9	131271	Robert Price	08/2018
4681	29863^24790+24790^29863	131227	Hans Havermann	03/2021
4682	(5*10^131223-29)/3	131224	Robert Price	03/2018
4683	29524^27825+27825^29524	131218	Hans Havermann	03/2021
4684	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
4685	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
4686	30639^19136+19136^30639	131192	Hans Havermann	04/2021
4687	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
4688	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
4689	2^435773+1875557	131181	Enzo Doria	06/2016
4690	(16*10^131180+167)/3	131181	Robert Price	06/2019
4691	(26*10^131180-77)/3	131181	Robert Price	11/2019
4692	(25*10^131144-7)/9	131145	Robert Price	05/2018
4693	29299^29358-29358^29299	131138	Norbert Schneider	03/2022
4694	2^435612-2789939	131133	Enzo Doria	12/2015
4695	33976^7231+7231^33976	131121	Hans Havermann	03/2021
4696	33715^7746+7746^33715	131121	Hans Havermann	03/2021
4697	66^72047-65^72047	131093	Robert Price	09/2013
4698	(5*10^131090+37)/3	131091	Robert Price	03/2018
4699	2^435468+75631	131089	Enzo Doria	04/2016
4700	37^83588-2	131083	Lelio R Paula	08/2015
4701	(4^217720+11)/3	131081	Robert Price	02/2017
4702	30407^20448+20448^30407	131074	Hans Havermann	04/2021
4703	(22*10^131070+179)/3	131071	Robert Price	02/2022
4704	28831^29388-29388^28831	131067	Frank Doornink	05/2024
4705	29487^27836+27836^29487	131059	Hans Havermann	04/2021
4706	29962^23615+23615^29962	131030	Hans Havermann	03/2021
4707	2^435202-113193	131009	Enzo Doria	07/2014
4708	41705^1384+1384^41705	131002	Hans Havermann	04/2021
4709	9*10^130998-19	130999	Robert Price	07/2019
4710	36243^4108+4108^36243	130969	Hans Havermann	04/2021
4711	(445^49433+1)/446	130914	Jinyuan Wang	05/2024
4712	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
4713	2^434835-111937	130899	Enzo Doria	05/2014
4714	(62*10^130895-629)/9	130896	Robert Price	07/2021
4715	2^434807+225	130890	Henri Lifchitz	11/2024
4716	2^434685+72257	130854	Enzo Doria	04/2016
4717	(7*10^130825+113)/3	130826	Robert Price	02/2018
4718	2^434539-29317	130810	Enzo Doria	07/2015
4719	(74*10^130791+637)/9	130792	Robert Price	01/2022
4720	2^434469-114259	130789	Enzo Doria	01/2015
4721	(5*10^130763+103)/9	130763	Robert Price	04/2022
4722	2^434246+33	130722	Robert Price	11/2015
4723	30156^21599+21599^30156	130710	Hans Havermann	04/2021
4724	(17*10^130695-161)/9	130696	Robert Price	02/2021
4725	30513^19148+19148^30513	130661	Hans Havermann	03/2021
4726	29736^24761+24761^29736	130654	Hans Havermann	04/2021
4727	9*10^130638+41	130639	Robert Price	08/2020
4728	2^433911-91	130621	Lelio R Paula	06/2017
4729	30786^17449+17449^30786	130588	Hans Havermann	03/2021
4730	2^433744-114419	130570	Enzo Doria	02/2015
4732	2^433708+1869451	130560	Enzo Doria	05/2016
4731	2^433710+93	130560	Lelio R Paula	06/2017
4733	7*10^130535-27	130536	Robert Price	11/2022
4734	(9629^32768+1)/120501441265666	130520	Kellen Shenton	05/2021
4735	804*34^85220+713	130516	Eric Chen	08/2023
4736	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
4737	3^273521+10	130503	Tyler NeSmith	01/2021
4738	41659^1356+1356^41659	130487	Hans Havermann	03/2021
4739	4*10^130480+9	130481	Robert Price	05/2015
4740	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
4741	3*2^433422+5	130474	Jon Grantham	07/2023
4742	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
4743	(31*10^130414-49)/9	130415	Robert Price	11/2021
4744	26462^29485-29485^26462	130402	Frank Doornink	03/2024
4745	33481^7848+7848^33481	130401	Hans Havermann	03/2021
4746	(17*10^130393+7)/3	130394	Robert Price	06/2023
4747	(22*10^130392+203)/9	130393	Robert Price	10/2021
4748	29773^23950+23950^29773	130386	Hans Havermann	04/2021
4749	2^433023-113497	130353	Enzo Doria	08/2014
4750	31175^15178+15178^31175	130350	Hans Havermann	04/2021

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PRP Records

Probable Primes Top 10000

(300560 PRPs in the top)