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	2*10^145784-91	145785	Robert Price	04/2020
4252	2^484271-51	145781	Lelio R Paula	11/2017
4253	(188*10^145750-11)/3	145752	Robert Price	02/2022
4254	70^78989-69^78989	145743	Robert Price	01/2014
4255	51^85334+2	145714	Robert Price	07/2015
4256	10^2^72843+72843^2^10	145687	Henri Lifchitz	03/2025
4257	2^483886-1857101	145665	Enzo Doria	10/2015
4258	29312^32607-32607^29312	145657	Frank Doornink	06/2024
4259	33350^23307+23307^33350	145656	Hans Havermann	01/2021
4260	(19*10^145585+131)/3	145586	Robert Price	06/2020
4261	31815^32332-32332^31815	145580	Frank Doornink	01/2024
4262	2^483563-1863457	145567	Enzo Doria	12/2015
4263	4*10^145563-69	145564	Robert Price	01/2022
4264	2^483516-1861409	145553	Enzo Doria	11/2015
4265	2^483384-115019	145514	Enzo Doria	06/2015
4266	(259*10^145501-1)/3	145503	Robert Price	12/2020
4267	(19*10^145499-61)/3	145500	Robert Price	05/2019
4268	2^483302-3221	145489	Lelio R Paula	12/2012
4269	(23*10^145463+61)/3	145464	Robert Price	01/2022
4270	35523^12434+12434^35523	145453	Hans Havermann	01/2021
4271	(29121^32761-1)/(29121^181-1)	145444	Ryan Propper	11/2023
4272	2^483046+1874029	145412	Enzo Doria	06/2016
4273	2^482991-2789317	145395	Enzo Doria	12/2015
4274	2^482978-2789711	145391	Enzo Doria	12/2015
4275	2^482966-2789711	145388	Enzo Doria	12/2015
4276	2^482817-1858843	145343	Enzo Doria	10/2015
4277	235*29^99378+4	145333	Eric Chen	06/2025
4278	2^482751-113635	145323	Enzo Doria	08/2014
4279	2^482705-459763	145309	Enzo Doria	05/2015
4280	(4^241306+11)/3	145281	Robert Price	03/2017
4281	(238*10^145276-1)/3	145278	Robert Price	04/2020
4282	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
4283	53^84239-52^84239	145252	Robert Price	01/2013
4284	U(1042497)	145243	Serge Batalov	07/2024
4285	2^482386+212419	145213	Enzo Doria	08/2023
4286	47952^1067+1067^47952	145207	Hans Havermann	01/2021
4287	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
4288	2^482087+72623	145123	Enzo Doria	04/2016
4289	2^482016-286565	145102	Enzo Doria	07/2015
4290	(19*10^145093+101)/3	145094	Robert Price	09/2019
4291	2^481956+121	145084	Stefano Morozzi	04/2021
4292	27535^32676-32676^27535	145078	Frank Doornink	06/2024
4293	2^481840+15	145049	Robert Price	09/2015
4294	(23*10^145040+7)/3	145041	Robert Price	05/2023
4295	2^481801-481801	145037	Henri Lifchitz	03/2005
4296	2^481775+1869083	145029	Enzo Doria	05/2016
4297	29^99167+2	145022	Ray Chandler	08/2011
4298	2^481663+1875653	144996	Enzo Doria	07/2016
4299	8*10^144977+27	144978	Robert Price	09/2021
4300	29840^32393-32393^29840	144953	Frank Doornink	06/2024
4301	36486^9379+9379^36486	144929	Hans Havermann	12/2020
4302	31580^32209-32209^31580	144922	Frank Doornink	01/2024
4303	35111^13378+13378^35111	144882	Hans Havermann	01/2021
4304	2^481149-459073	144841	Enzo Doria	05/2015
4305	2^481113+181419	144830	Boyan Hu	04/2024
4306	34619^15246+15246^34619	144817	Hans Havermann	01/2021
4307	2^481045-113215	144809	Enzo Doria	07/2014
4308	(64*10^144797+287)/9	144798	Robert Price	04/2019
4309	27320^32629-32629^27320	144758	Frank Doornink	06/2024
4310	2^480859-113695	144753	Enzo Doria	09/2014
4311	(106*10^144744+17)/3	144746	Robert Price	04/2021
4312	7*10^144742-27	144743	Robert Price	11/2022
4313	2^480766-2787191	144725	Enzo Doria	11/2015
4314	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
4315	28915^32438-32438^28915	144710	Frank Doornink	06/2024
4316	2^480678+1874239	144699	Enzo Doria	06/2016
4317	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
4318	L(692147)	144651	Henri Lifchitz	10/2008
4319	(76*10^144648+77)/9	144649	Robert Price	10/2019
4320	32672^26721+26721^32672	144635	Hans Havermann	01/2021
4321	31478^32153-32153^31478	144625	Frank Doornink	01/2024
4322	2^480417+35	144620	Robert Price	11/2015
4323	2^480296-59879	144584	Enzo Doria	10/2015
4324	33157^22878+22878^33157	144546	Hans Havermann	12/2020
4325	27520^32541-32541^27520	144471	Frank Doornink	06/2024
4326	45494^1497+1497^45494	144454	Hans Havermann	12/2020
4327	2^479844+3	144448	Donovan Johnson	06/2006
4328	33442^20803+20803^33442	144407	Hans Havermann	01/2021
4329	(441*33^95095-3833)/32	144405	Eric Chen	12/2023
4330	31892^32061-32061^31892	144393	Norbert Schneider	01/2023
4331	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
4332	(56*10^144380+169)/9	144381	Robert Price	03/2022
4333	44917^1638+1638^44917	144378	Hans Havermann	12/2020
4334	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
4335	(11^138641-1)/6631590024336120710	144361	Paul Vanderveen	05/2025
4336	(56*10^144336+583)/9	144337	Robert Price	08/2021
4337	5*2^479430-3	144324	Jon Grantham	07/2023
4338	2^479348-2792219	144299	Enzo Doria	02/2016
4339	31134^32111-32111^31134	144283	Frank Doornink	01/2024
4340	3^302389-6242	144277	Enzo Doria	05/2014
4341	31665^32056-32056^31665	144271	Frank Doornink	01/2024
4342	33778^18641+18641^33778	144248	Hans Havermann	01/2021
4343	29083^32312-32312^29083	144230	Frank Doornink	06/2024
4344	2*10^144220-3	144221	Robert Price	07/2015
4345	25313^32750-32750^25313	144210	Frank Doornink	01/2024
4346	2^478904-109109	144165	Enzo Doria	04/2014
4347	43698^1987+1987^43698	144125	Hans Havermann	12/2020
4348	79^75948+75948	144121	Kellen Shenton	06/2023
4349	26941^32522-32522^26941	144086	Frank Doornink	06/2024
4350	36128^9723+9723^36128	144072	Hans Havermann	01/2021
4351	32817^24518+24518^32817	144050	Hans Havermann	12/2020
4352	(772*10^144036-7)/9	144038	Robert Price	06/2022
4353	34295^15828+15828^34295	144020	Hans Havermann	01/2021
4354	2^478337-115333	143994	Enzo Doria	07/2015
4355	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
4356	88^74047-87^74047	143984	Robert Price	05/2015
4357	33242^21441+21441^33242	143980	Hans Havermann	01/2021
4358	(19*10^143963+467)/9	143964	Robert Price	02/2018
4359	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
4360	33490^19859+19859^33490	143939	Hans Havermann	01/2021
4361	(853*10^143931-7)/9	143933	Robert Price	07/2021
4362	2^478088+27	143919	Robert Price	11/2015
4363	(8*10^143898-137)/3	143899	Robert Price	03/2022
4364	7*10^143857-93	143858	Robert Price	08/2020
4365	3*10^143844+61	143845	Robert Price	09/2020
4366	41358^3005+3005^41358	143837	Hans Havermann	01/2021
4367	2^477475-22071	143735	Enzo Doria	07/2013
4368	2^477417-22123	143717	Enzo Doria	07/2013
4369	2^477359-3577	143700	Yves Minet	03/2017
4370	39435^4402+4402^39435	143688	Hans Havermann	01/2021
4371	(14*10^143662-71)/3	143663	Robert Price	12/2018
4372	6^184614+5	143658	Paul Bourdelais	01/2021
4373	46371^1252+1252^46371	143640	Hans Havermann	12/2020
4374	34975^12748+12748^34975	143588	Hans Havermann	01/2021
4375	2^476936-396765	143573	Enzo Doria	07/2013
4376	2^476888-2791229	143558	Enzo Doria	01/2016
4377	2^476868-1859939	143552	Enzo Doria	11/2015
4378	40807^3294+3294^40807	143548	Hans Havermann	12/2020
4379	755^49878+49878^755	143547	Norbert Schneider	04/2019
4380	(19^112247-4^112247)/15	143536	Robert Price	03/2021
4381	35561^10872+10872^35561	143536	Hans Havermann	06/2021
4382	37637^6492+6492^37637	143487	Hans Havermann	05/2021
4383	61567^214+214^61567	143477	Hans Havermann	05/2021
4384	25933^32504-32504^25933	143468	Frank Doornink	03/2024
4385	2^476558-113627	143459	Enzo Doria	08/2014
4386	2^476478-45	143435	Lelio R Paula	11/2017
4387	36380^8757+8757^36380	143423	Hans Havermann	06/2021
4388	32510^25707+25707^32510	143371	Hans Havermann	05/2021
4389	8*10^143361+17	143362	Robert Price	07/2021
4390	(2^475854+9)/73	143245	Lelio R Paula	08/2015
4391	2^475813-113239	143234	Enzo Doria	07/2014
4392	(19*10^143212+137)/3	143213	Robert Price	03/2022
4393	32218^27849+27849^32218	143203	Hans Havermann	04/2021
4394	580*33^94296+19	143193	Eric Chen	12/2023
4395	2^475624-114059	143178	Enzo Doria	11/2014
4396	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
4397	2^475480-2786129	143134	Enzo Doria	10/2015
4398	33912^16621+16621^33912	143131	Hans Havermann	05/2021
4399	(19*10^143129-43)/3	143130	Robert Price	05/2019
4400	31830^31373+31373^31830	143126	Hans Havermann	05/2021
4401	2^475392+1334025	143108	Henri Lifchitz	01/2025
4402	6*10^143105-53	143106	Robert Price	05/2021
4403	(14*10^143097+73)/3	143098	Robert Price	12/2018
4404	2^475299-111937	143080	Enzo Doria	05/2014
4405	35488^10753+10753^35488	143071	Hans Havermann	04/2021
4406	29695^31986-31986^29695	143064	Frank Doornink	06/2024
4407	2^475160-2797859	143038	Enzo Doria	04/2016
4408	(2^475069+3)/395	143008	Lelio R Paula	08/2015
4409	2^475027-461437	142998	Enzo Doria	07/2015
4410	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
4411	(8*10^142932+43)/3	142933	Robert Price	06/2018
4412	35055^11942+11942^35055	142922	Hans Havermann	05/2021
4413	37650^6239+6239^37650	142887	Hans Havermann	05/2021
4414	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
4415	31205^31784-31784^31205	142845	Frank Doornink	01/2024
4416	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
4417	2^474417-59923	142814	Enzo Doria	10/2015
4418	4*10^142810-21	142811	Robert Price	09/2018
4419	32287^26494+26494^32287	142811	Hans Havermann	06/2021
4420	37162^6965+6965^37162	142811	Hans Havermann	06/2021
4421	(34*10^142805-601)/9	142806	Robert Price	07/2022
4422	37456^6493+6493^37456	142799	Hans Havermann	05/2021
4423	35141^11572+11572^35141	142793	Hans Havermann	05/2021
4424	32231^26908+26908^32231	142780	Hans Havermann	05/2021
4425	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
4426	2^474053+2897	142705	Lelio R Paula	08/2012
4427	(10^142699+359)/9	142699	Serge Batalov	12/2014
4428	26073^32312-32312^26073	142696	Frank Doornink	03/2024
4429	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
4430	2^473740-1856639	142610	Enzo Doria	09/2015
4431	(25*10^142573-403)/9	142574	Robert Price	12/2020
4432	2^473617-114223	142573	Enzo Doria	12/2014
4433	36115^8856+8856^36115	142555	Hans Havermann	05/2021
4434	fibonacci(682007)+4	142531	Jon Grantham	08/2023
4435	2^473257+1873217	142465	Enzo Doria	06/2016
4436	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
4437	32750^22371+22371^32750	142453	Hans Havermann	06/2021
4438	(61*10^142446-1)/3	142448	Robert Price	01/2020
4439	(14*10^142440+61)/3	142441	Robert Price	12/2018
4440	(10^142425+359)/9	142425	Serge Batalov	12/2014
4441	2^473101+773027	142418	Enzo Doria	05/2016
4442	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
4443	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
4444	36915^7162+7162^36915	142309	Hans Havermann	05/2021
4445	2^472634-109511	142278	Enzo Doria	04/2014
4446	31870^28997+28997^31870	142216	Hans Havermann	06/2021
4447	(48^84589+1)/49	142213	Robert Price	01/2014
4448	7*10^142189+87	142190	Robert Price	07/2019
4449	2^472258+7	142164	Lelio R Paula	08/2015
4450	40135^3484+3484^40135	142162	Hans Havermann	05/2021
4451	9*33^93598+26	142131	Eric Chen	12/2023
4452	(23*10^142105+91)/3	142106	Robert Price	08/2019
4453	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
4454	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
4455	(16*10^142058+197)/3	142059	Robert Price	04/2019
4456	9*10^142037+91	142038	Robert Price	10/2020
4457	(4*10^142034+17)/3	142035	Tyler Busby	01/2023
4458	2^471792+1880881	142024	Enzo Doria	11/2016
4459	(509*10^142018+31)/9	142020	Robert Price	08/2022
4460	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
4461	(4*10^141926-79)/3	141927	Robert Price	02/2018
4462	2^471464-111546435	141925	Paul Bourdelais	10/2021
4463	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
4464	(14*10^141853+37)/3	141854	Robert Price	12/2018
4465	(12^131449-1)/4199006867	141848	Paul Vanderveen	06/2025
4466	(41*10^141836-59)/9	141837	Robert Price	10/2018
4467	4*5^202913-9	141831	Lelio R Paula	04/2015
4468	2*7^167812-3	141818	Lelio R Paula	12/2014
4469	2^471043+35	141799	Robert Price	11/2015
4470	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
4471	43636^1773+1773^43636	141761	Hans Havermann	05/2021
4472	(2*10^141751-17)/3	141751	Serge Batalov	11/2022
4473	(53*10^141722-611)/9	141723	Robert Price	02/2022
4474	(11*10^141718-131)/3	141719	Robert Price	09/2018
4475	(61*10^141716+47)/9	141717	Robert Price	07/2022
4476	26057^32088-32088^26057	141699	Frank Doornink	03/2024
4477	2^470692+76771	141693	Enzo Doria	05/2016
4478	50160^667+667^50160	141659	Hans Havermann	05/2021
4479	31522^31181+31181^31522	141657	Hans Havermann	05/2021
4480	29487^31690-31690^29487	141643	Frank Doornink	06/2024
4481	33076^19135+19135^33076	141626	Hans Havermann	04/2021
4482	28237^31818-31818^28237	141617	Frank Doornink	06/2024
4483	(91*10^141610+71)/9	141612	Robert Price	01/2022
4484	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
4485	(5*10^141594-23)/9	141594	Serge Batalov	11/2022
4486	31932^27155+27155^31932	141582	Hans Havermann	05/2021
4487	36449^7660+7660^36449	141577	Hans Havermann	05/2021
4488	2^470305-459373	141576	Enzo Doria	05/2015
4489	32195^24936+24936^32195	141556	Hans Havermann	05/2021
4490	2^470183+72623	141540	Enzo Doria	04/2016
4491	2^470173-16465	141537	Enzo Doria	04/2013
4492	37297^6234+6234^37297	141534	Hans Havermann	05/2021
4493	2^4^117533+117533^4^2	141524	Henri Lifchitz	03/2025
4494	(509*10^141479+13)/9	141481	Robert Price	05/2022
4495	44*10^141476+9	141478	Robert Price	10/2020
4496	2^469974-1841	141477	Enzo Doria	05/2014
4497	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
4498	312*33^93158+23	141465	Eric Chen	12/2023
4499	2*10^141448+63	141449	Robert Price	05/2018
4500	2^469824+43	141432	Lelio R Paula	09/2017

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Probable Primes Top 10000

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