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 ?
4251	29695^31986-31986^29695	143064	Frank Doornink	06/2024
4252	2^475160-2797859	143038	Enzo Doria	04/2016
4253	(2^475069+3)/395	143008	Lelio R Paula	08/2015
4254	2^475027-461437	142998	Enzo Doria	07/2015
4255	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
4256	(8*10^142932+43)/3	142933	Robert Price	06/2018
4257	35055^11942+11942^35055	142922	Hans Havermann	05/2021
4258	37650^6239+6239^37650	142887	Hans Havermann	05/2021
4259	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
4260	31205^31784-31784^31205	142845	Frank Doornink	01/2024
4261	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
4262	2^474417-59923	142814	Enzo Doria	10/2015
4263	4*10^142810-21	142811	Robert Price	09/2018
4264	32287^26494+26494^32287	142811	Hans Havermann	06/2021
4265	37162^6965+6965^37162	142811	Hans Havermann	06/2021
4266	(34*10^142805-601)/9	142806	Robert Price	07/2022
4267	37456^6493+6493^37456	142799	Hans Havermann	05/2021
4268	35141^11572+11572^35141	142793	Hans Havermann	05/2021
4269	32231^26908+26908^32231	142780	Hans Havermann	05/2021
4270	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
4271	2^474053+2897	142705	Lelio R Paula	08/2012
4272	(10^142699+359)/9	142699	Serge Batalov	12/2014
4273	26073^32312-32312^26073	142696	Frank Doornink	03/2024
4274	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
4275	2^473740-1856639	142610	Enzo Doria	09/2015
4276	(25*10^142573-403)/9	142574	Robert Price	12/2020
4277	2^473617-114223	142573	Enzo Doria	12/2014
4278	36115^8856+8856^36115	142555	Hans Havermann	05/2021
4279	fibonacci(682007)+4	142531	Jon Grantham	08/2023
4280	2^473257+1873217	142465	Enzo Doria	06/2016
4281	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
4282	32750^22371+22371^32750	142453	Hans Havermann	06/2021
4283	(61*10^142446-1)/3	142448	Robert Price	01/2020
4284	(14*10^142440+61)/3	142441	Robert Price	12/2018
4285	(10^142425+359)/9	142425	Serge Batalov	12/2014
4286	2^473101+773027	142418	Enzo Doria	05/2016
4287	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
4288	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
4289	36915^7162+7162^36915	142309	Hans Havermann	05/2021
4290	2^472634-109511	142278	Enzo Doria	04/2014
4291	31870^28997+28997^31870	142216	Hans Havermann	06/2021
4292	(48^84589+1)/49	142213	Robert Price	01/2014
4293	7*10^142189+87	142190	Robert Price	07/2019
4294	2^472258+7	142164	Lelio R Paula	08/2015
4295	40135^3484+3484^40135	142162	Hans Havermann	05/2021
4296	9*33^93598+26	142131	Eric Chen	12/2023
4297	(23*10^142105+91)/3	142106	Robert Price	08/2019
4298	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
4299	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
4300	(16*10^142058+197)/3	142059	Robert Price	04/2019
4301	9*10^142037+91	142038	Robert Price	10/2020
4302	(4*10^142034+17)/3	142035	Tyler Busby	01/2023
4303	2^471792+1880881	142024	Enzo Doria	11/2016
4304	(509*10^142018+31)/9	142020	Robert Price	08/2022
4305	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
4306	(4*10^141926-79)/3	141927	Robert Price	02/2018
4307	2^471464-111546435	141925	Paul Bourdelais	10/2021
4308	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
4309	(14*10^141853+37)/3	141854	Robert Price	12/2018
4310	(41*10^141836-59)/9	141837	Robert Price	10/2018
4311	4*5^202913-9	141831	Lelio R Paula	04/2015
4312	2*7^167812-3	141818	Lelio R Paula	12/2014
4313	2^471043+35	141799	Robert Price	11/2015
4314	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
4315	43636^1773+1773^43636	141761	Hans Havermann	05/2021
4316	(2*10^141751-17)/3	141751	Serge Batalov	11/2022
4317	(53*10^141722-611)/9	141723	Robert Price	02/2022
4318	(11*10^141718-131)/3	141719	Robert Price	09/2018
4319	(61*10^141716+47)/9	141717	Robert Price	07/2022
4320	26057^32088-32088^26057	141699	Frank Doornink	03/2024
4321	2^470692+76771	141693	Enzo Doria	05/2016
4322	50160^667+667^50160	141659	Hans Havermann	05/2021
4323	31522^31181+31181^31522	141657	Hans Havermann	05/2021
4324	29487^31690-31690^29487	141643	Frank Doornink	06/2024
4325	33076^19135+19135^33076	141626	Hans Havermann	04/2021
4326	28237^31818-31818^28237	141617	Frank Doornink	06/2024
4327	(91*10^141610+71)/9	141612	Robert Price	01/2022
4328	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
4329	(5*10^141594-23)/9	141594	Serge Batalov	11/2022
4330	31932^27155+27155^31932	141582	Hans Havermann	05/2021
4331	36449^7660+7660^36449	141577	Hans Havermann	05/2021
4332	2^470305-459373	141576	Enzo Doria	05/2015
4333	32195^24936+24936^32195	141556	Hans Havermann	05/2021
4334	2^470183+72623	141540	Enzo Doria	04/2016
4335	2^470173-16465	141537	Enzo Doria	04/2013
4336	37297^6234+6234^37297	141534	Hans Havermann	05/2021
4337	2^4^117533+117533^4^2	141524	Henri Lifchitz	03/2025
4338	(509*10^141479+13)/9	141481	Robert Price	05/2022
4339	44*10^141476+9	141478	Robert Price	10/2020
4340	2^469974-1841	141477	Enzo Doria	05/2014
4341	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
4342	312*33^93158+23	141465	Eric Chen	12/2023
4343	2*10^141448+63	141449	Robert Price	05/2018
4344	2^469824+43	141432	Lelio R Paula	09/2017
4345	2*10^141407-27	141408	Robert Price	05/2018
4346	(214*10^141385-1)/3	141387	Robert Price	01/2021
4347	2^469630-59711	141373	Enzo Doria	10/2015
4348	35277^10172+10172^35277	141370	Hans Havermann	04/2021
4349	33397^17100+17100^33397	141370	Hans Havermann	04/2021
4350	(25*10^141366-331)/9	141367	Robert Price	08/2018
4351	36986^6639+6639^36986	141365	Hans Havermann	06/2021
4352	34572^12271+12271^34572	141361	Hans Havermann	06/2021
4353	37179^6338+6338^37179	141353	Hans Havermann	05/2021
4354	(2^469564-3)/611	141351	Lelio R Paula	08/2015
4355	197^61601+2	141342	Lelio R Paula	08/2017
4356	33420^16951+16951^33420	141340	Hans Havermann	05/2021
4357	31623^29458+29458^31623	141330	Hans Havermann	05/2021
4358	48112^865+865^48112	141306	Hans Havermann	05/2021
4359	2^469372-112949	141296	Enzo Doria	07/2014
4360	5*10^141294-63	141295	Robert Price	04/2021
4361	3^296115+4	141283	Tyler NeSmith	01/2021
4362	(64*10^141256+161)/9	141257	Robert Price	08/2022
4363	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
4364	143^65536+106^65536	141253	Serge Batalov	03/2018
4365	(11*10^141243-23)/3	141244	Robert Price	09/2021
4367	2^469198+782569	141243	Enzo Doria	10/2016
4366	38129^5062+5062^38129	141243	Hans Havermann	05/2021
4368	2^469076-2786939	141206	Enzo Doria	11/2015
4369	38630^4521+4521^38630	141202	Hans Havermann	05/2021
4370	31755^27836+27836^31755	141139	Hans Havermann	05/2021
4371	35554^9325+9325^35554	141137	Hans Havermann	05/2021
4372	2^468804+1874941	141125	Enzo Doria	06/2016
4373	2^468787+81353	141119	Enzo Doria	08/2016
4374	30204^31493-31493^30204	141091	Frank Doornink	06/2024
4375	2^468595-350407	141062	Enzo Doria	06/2015
4376	2^468564+87855	141052	Lelio R Paula	01/2016
4377	2^468551-21987	141048	Enzo Doria	07/2013
4378	2^468523-7	141040	Lelio R Paula	08/2015
4379	(25*10^141019-13)/3	141020	Robert Price	09/2019
4380	2^468405+87855	141004	Lelio R Paula	01/2016
4381	39338^3831+3831^39338	140961	Hans Havermann	05/2021
4382	31458^30239+30239^31458	140950	Hans Havermann	05/2021
4383	8*10^140932+29	140933	Robert Price	11/2021
4384	33166^17691+17691^33166	140881	Hans Havermann	06/2021
4385	2^467978-113051	140876	Enzo Doria	07/2014
4386	2^467780-344429	140816	Enzo Doria	07/2015
4387	9*10^140802-89	140803	Robert Price	04/2020
4388	2^467605-1855603	140764	Enzo Doria	09/2015
4389	(9^147503-5^147503)/4	140754	Jon Grantham	07/2023
4390	5*10^140744-7	140745	Robert Price	09/2015
4391	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
4392	2^467401-1850023	140702	Enzo Doria	08/2015
4393	(14*10^140693+13)/9	140694	Tyler Busby	02/2023
4394	(266*10^140681-17)/3	140683	Robert Price	07/2020
4395	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
4396	32138^23781+23781^32138	140644	Hans Havermann	05/2021
4397	31654^27735+27735^31654	140640	Hans Havermann	05/2021
4398	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
4399	2^467166-1854941	140631	Enzo Doria	09/2015
4400	(203*10^140615-11)/3	140617	Robert Price	12/2020
4401	(85*10^140609+473)/9	140610	Robert Price	01/2020
4402	39231^3836+3836^39231	140600	Hans Havermann	06/2021
4403	5*3^294676+2^294676	140597	Jon Grantham	08/2023
4404	2^466866-1840571	140541	Enzo Doria	06/2015
4405	2^466829-459523	140530	Enzo Doria	05/2015
4406	2^466692-113213	140489	Enzo Doria	07/2014
4407	23*10^140464-3	140466	Robert Price	10/2021
4408	(2*10^140461-17)/3	140461	Serge Batalov	11/2022
4409	29^96047-30	140459	Anonymous	09/2024
4410	31335^30364+30364^31335	140455	Hans Havermann	05/2021
4411	28511^31524-31524^28511	140440	Frank Doornink	06/2024
4412	32795^19126+19126^32795	140416	Hans Havermann	05/2021
4413	(44*10^140410-503)/9	140411	Robert Price	12/2018
4414	28332^31535-31535^28332	140403	Frank Doornink	06/2024
4415	153^64265-2	140400	Lelio R Paula	11/2017
4416	30323^31322-31322^30323	140379	Frank Doornink	06/2024
4417	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
4418	(29*10^140337-17)/3	140338	Robert Price	09/2019
4419	2^466181-112735	140335	Enzo Doria	07/2014
4420	(16*10^140290-37)/3	140291	Robert Price	05/2021
4421	(5*10^140281-119)/3	140282	Robert Price	03/2018
4422	34568^11415+11415^34568	140259	Hans Havermann	05/2021
4423	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
4424	33632^14781+14781^33632	140236	Hans Havermann	05/2021
4425	31803^25670+25670^31803	140233	Hans Havermann	05/2021
4426	2^465803-114817	140221	Enzo Doria	05/2015
4427	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
4428	2^465503-112735	140131	Enzo Doria	07/2014
4429	(16*10^140091+167)/3	140092	Robert Price	06/2019
4430	(8*10^140087-137)/3	140088	Robert Price	03/2022
4431	6^179964+179964^6-1	140040	Robert Price	04/2014
4432	(89*10^140008-179)/9	140009	Robert Price	12/2019
4433	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
4434	2^465072-344789	140001	Enzo Doria	07/2015
4435	34742^10683+10683^34742	139965	Hans Havermann	05/2021
4436	5*10^139945+81	139946	Robert Price	03/2019
4437	32648^19335+19335^32648	139941	Hans Havermann	05/2021
4438	2^464864-17	139939	Lelio R Paula	09/2017
4439	8*10^139920+51	139921	Robert Price	08/2019
4440	(85*10^139913-1)/3	139915	Robert Price	02/2020
4441	31203^30436+30436^31203	139896	Hans Havermann	04/2021
4442	2^464642+22189	139872	Enzo Doria	09/2023
4443	26138^31663-31663^26138	139865	Frank Doornink	03/2024
4444	(16^116139+619)/5	139845	Anonymous	08/2022
4445	(2^464556+619)/5	139845	Eric Chen	10/2023
4446	4*10^139839-27	139840	Robert Price	08/2021
4447	33582^14573+14573^33582	139821	Hans Havermann	05/2021
4448	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
4450	2*10^139800-21	139801	Robert Price	09/2020
4449	32628^19261+19261^32628	139801	Hans Havermann	04/2021
4451	(13*10^139782+191)/3	139783	Robert Price	11/2018
4452	(64*10^139776+791)/9	139777	Robert Price	01/2022
4453	(695*10^139772+7)/9	139774	Robert Price	12/2021
4454	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
4455	(74*10^139723+133)/9	139724	Robert Price	06/2019
4456	3*10^139722+13	139723	Robert Price	07/2018
4457	31577^26592+26592^31577	139721	Hans Havermann	05/2021
4458	77*10^139692+3	139694	Robert Price	06/2020
4459	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
4460	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
4461	39640^3321+3321^39640	139584	Hans Havermann	05/2021
4462	36663^6410+6410^36663	139571	Hans Havermann	05/2021
4463	2^463633-2788423	139568	Enzo Doria	11/2015
4464	33659^13978+13978^33659	139532	Hans Havermann	05/2021
4465	31811^24318+24318^31811	139521	Hans Havermann	04/2021
4466	34149^12172+12172^34149	139512	Hans Havermann	04/2021
4467	(29*10^139476+313)/9	139477	Robert Price	04/2021
4468	31721^24940+24940^31721	139474	Hans Havermann	05/2021
4469	32833^17698+17698^32833	139473	Hans Havermann	05/2021
4470	2^463271-109501	139459	Enzo Doria	04/2014
4471	(5*10^139457+79)/3	139458	Robert Price	03/2018
4472	2^463237-99	139449	Lelio R Paula	09/2017
4473	(49*10^139442+383)/9	139443	Robert Price	04/2019
4474	31155^29902+29902^31155	139441	Hans Havermann	05/2021
4475	(7*10^139417-547)/9	139417	Robert Price	01/2018
4476	29636^31175-31175^29636	139409	Frank Doornink	05/2024
4477	(10^139398+191)/3	139398	Robert Price	02/2018
4478	23*10^139386-3	139388	Robert Price	10/2021
4479	2^463019+79463	139383	Enzo Doria	06/2016
4480	3^292129-112756	139381	Enzo Doria	07/2014
4481	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
4482	31922^23205+23205^31922	139359	Hans Havermann	05/2021
4483	(19*10^139336+503)/9	139337	Alfred Reich	11/2023
4485	2^462855-1865707	139334	Enzo Doria	02/2016
4484	31237^28876+28876^31237	139334	Hans Havermann	05/2021
4486	(86*10^139315+121)/9	139316	Robert Price	08/2019
4487	2^462786-292043	139313	Enzo Doria	08/2015
4488	38915^3798+3798^38915	139299	Hans Havermann	05/2021
4490	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
4489	(17*10^139289+7)/3	139290	Robert Price	06/2023
4491	34065^12248+12248^34065	139260	Hans Havermann	05/2021
4492	36425^6654+6654^36425	139256	Hans Havermann	05/2021
4493	39252^3527+3527^39252	139243	Hans Havermann	05/2021
4494	(17*10^139239+67)/3	139240	Robert Price	01/2019
4495	31887^23248+23248^31887	139231	Hans Havermann	05/2021
4496	(25*10^139210-97)/9	139211	Robert Price	01/2022
4497	2^462238-935	139148	Yves Minet	02/2014
4498	(29*10^139134-119)/9	139135	Robert Price	12/2021
4499	U(687859)/4127153	139105	Serge Batalov	07/2024
4500	(109*10^139100-7)/3	139102	Robert Price	03/2021

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Probable Primes Top 10000

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