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	10^148934-512057	148934	Patrick De Geest	02/2021
4252	39000^6571+6571^39000	148888	Hans Havermann	10/2020
4253	2^494586-2791991	148886	Enzo Doria	02/2016
4254	8*10^148860-3	148861	Ray Chandler	04/2011
4255	38262^7769+7769^38262	148854	Hans Havermann	10/2020
4256	10^148816-500001	148816	Robert Price	03/2022
4257	(53*10^148811-287)/9	148812	Robert Price	02/2022
4258	2^494333-286183	148810	Enzo Doria	06/2015
4259	2^494144-264119	148753	Enzo Doria	05/2014
4260	6*10^148734+47	148735	Robert Price	06/2022
4261	28724^33353-33353^28724	148696	Frank Doornink	06/2024
4262	36502^11823+11823^36502	148663	Hans Havermann	11/2020
4263	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
4264	64239^206+206^64239	148641	Hans Havermann	10/2020
4265	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
4266	(23*10^148627-137)/3	148628	Robert Price	08/2021
4267	(151*10^148601-1)/3	148603	Robert Price	03/2020
4268	2^493636+82081	148600	Enzo Doria	09/2016
4269	((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	148593	Serge Batalov	07/2016
4270	27134^33509-33509^27134	148563	Frank Doornink	01/2024
4271	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
4272	(2*10^148460-23)/3	148460	Robert Price	04/2018
4273	(28*10^148445+101)/3	148446	Robert Price	09/2020
4274	2^493065+225	148428	Henri Lifchitz	11/2024
4275	36203^12556+12556^36203	148391	Hans Havermann	10/2020
4276	33912^23749+23749^33912	148387	Hans Havermann	10/2020
4277	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
4278	34294^21117+21117^34294	148309	Hans Havermann	10/2020
4279	(71*10^148306-539)/9	148307	Robert Price	07/2019
4280	30814^33039-33039^30814	148304	Frank Doornink	06/2024
4281	38042^7875+7875^38042	148222	Hans Havermann	10/2020
4282	5^211959-12874	148153	Enzo Doria	05/2014
4283	34142^21831+21831^34142	148145	Hans Havermann	10/2020
4284	10^148112+34059	148113	Patrick De Geest	05/2021
4285	10^148112-70000001	148112	Robert Price	03/2021
4286	10^148112-106593	148112	Patrick De Geest	05/2021
4287	36303^12016+12016^36303	148108	Hans Havermann	10/2020
4288	(77*10^148089-149)/9	148090	Robert Price	03/2022
4289	(16*10^148071+41)/3	148072	Robert Price	03/2019
4290	187^65175-2	148068	Lelio R Paula	11/2017
4291	2^491851+1871453	148062	Enzo Doria	05/2016
4292	(68*10^148060-257)/9	148061	Robert Price	07/2019
4293	(151*10^148020-1)/3	148022	Robert Price	03/2020
4294	39153^6032+6032^39153	148017	Hans Havermann	10/2020
4295	36798^10507+10507^36798	147983	Hans Havermann	12/2020
4296	(26*10^147973-23)/3	147974	Robert Price	12/2019
4297	2^491521-1865323	147963	Enzo Doria	02/2016
4298	(2^491476+7)/71	147948	Lelio R Paula	10/2015
4299	2*10^147928+47	147929	Robert Price	12/2021
4300	2^491391-7807	147924	Lelio R Paula	01/2013
4301	2^491384+236221	147922	Enzo Doria	05/2025
4302	39736^5279+5279^39736	147920	Hans Havermann	11/2020
4303	2^491370-113297	147918	Enzo Doria	07/2014
4304	(3^707753)%F(707753)	147912	Henri Lifchitz	06/2025
4305	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
4306	44368^2155+2155^44368	147899	Hans Havermann	12/2020
4307	(17*10^147890+79)/3	147891	Robert Price	04/2019
4308	94*10^147871-3	147873	Robert Price	05/2020
4309	10^147843+620967	147844	Patrick De Geest	05/2021
4310	10^147843-50000000001	147843	Robert Price	12/2020
4311	10^147843-182891	147843	Patrick De Geest	05/2021
4312	35805^13346+13346^35805	147709	Hans Havermann	11/2020
4313	2^490672+255255	147707	Paul Bourdelais	10/2021
4314	2^490660-17	147704	Lelio R Paula	12/2017
4315	(229*10^147699-1)/3	147701	Robert Price	07/2020
4316	40656^4289+4289^40656	147678	Hans Havermann	11/2020
4317	(85*10^147676-31)/9	147677	Rytis Slatkevicius	12/2024
4318	2^490550+1179439	147671	Enzo Doria	06/2016
4319	27249^33292-33292^27249	147662	Frank Doornink	06/2024
4320	(23*10^147649-59)/9	147650	Robert Price	05/2018
4321	2^490303+2793653	147596	Enzo Doria	03/2016
4322	2^490266+255255	147585	Paul Bourdelais	10/2021
4323	199^64181-2	147543	Lelio R Paula	11/2017
4324	32849^30958+30958^32849	147518	Hans Havermann	11/2020
4325	2^489871-286987	147466	Enzo Doria	07/2015
4326	2^489864-351899	147464	Enzo Doria	07/2015
4327	175^65724-2	147422	Lelio R Paula	11/2017
4328	2^489712+1874851	147419	Enzo Doria	06/2016
4329	34473^18830+18830^34473	147367	Hans Havermann	11/2020
4330	63^81896-2	147359	Lelio R Paula	10/2017
4331	34580^18237+18237^34580	147344	Hans Havermann	11/2020
4332	(11*10^147313-107)/3	147314	Robert Price	09/2018
4333	(397*10^147310+17)/9	147312	Robert Price	03/2022
4334	2^489305-59815	147296	Enzo Doria	10/2015
4335	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
4336	2*10^147264-61	147265	Robert Price	10/2021
4337	2*10^147260+29	147261	Robert Price	02/2021
4338	33556^24457+24457^33556	147258	Hans Havermann	11/2020
4339	12^136450-11	147255	Riley Fisher	12/2024
4340	2^489125+80357	147242	Enzo Doria	06/2016
4341	10^147240-40000001	147240	Robert Price	07/2022
4342	10^147240-371331	147240	Alfred Reich	09/2024
4343	10^147240-464727	147240	Alfred Reich	09/2024
4344	32835^30452+30452^32835	147220	Hans Havermann	12/2020
4345	(19*10^147213-97)/3	147214	Robert Price	10/2021
4346	27123^33190-33190^27123	147143	Frank Doornink	01/2024
4347	(148*10^147139-1)/3	147141	Robert Price	03/2020
4348	34338^19255+19255^34338	147123	Hans Havermann	11/2020
4349	2^488648-112799	147098	Enzo Doria	07/2014
4350	2^488627-350317	147092	Enzo Doria	06/2015
4351	33432^25075+25075^33432	147076	Hans Havermann	12/2020
4352	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
4353	2^488280-2165	146987	Yves Minet	07/2014
4354	2^488278+45	146987	Lelio R Paula	12/2017
4355	(3^834646)/(2^834646)	146974	Henri Lifchitz	06/2025
4356	32568^32568+32561^32561	146973	Henri Lifchitz	08/2024
4357	2^487927-39	146881	Lelio R Paula	12/2017
4358	(7*10^146860-13)/3	146861	Robert Price	07/2018
4359	(26*10^146856-77)/3	146857	Robert Price	11/2019
4360	32948^28611+28611^32948	146834	Hans Havermann	11/2020
4361	42596^2799+2799^42596	146829	Hans Havermann	12/2020
4362	2^487726-1863341	146821	Enzo Doria	12/2015
4363	43838^2229+2229^43838	146775	Hans Havermann	11/2020
4364	35005^15594+15594^35005	146775	Hans Havermann	11/2020
4365	(167*10^146764+7)/3	146766	Robert Price	04/2021
4366	53^85114+85114	146761	Kellen Shenton	05/2022
4367	(59*10^146738+157)/9	146739	Robert Price	12/2021
4368	((10^73362-1)10000/9+6701)10^73362+(10^73362-1)/9	146728	Hans Havermann	09/2019
4369	32963^28234+28234^32963	146711	Hans Havermann	12/2020
4370	(22*10^146661-19)/3	146662	Robert Price	04/2019
4371	33958^20825+20825^33958	146651	Hans Havermann	12/2020
4372	26289^33178-33178^26289	146640	Frank Doornink	03/2024
4373	2^487121-39523	146639	Enzo Doria	09/2015
4374	61063^252+252^61063	146637	Hans Havermann	12/2020
4375	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
4376	34099^19900+19900^34099	146587	Hans Havermann	11/2020
4377	2^486893-79	146570	Yves Minet	09/2017
4378	36818^9567+9567^36818	146565	Hans Havermann	12/2020
4379	2^486840+1879141	146554	Enzo Doria	08/2016
4380	2^486774-87	146534	Lelio R Paula	12/2017
4381	38655^6176+6176^38655	146530	Hans Havermann	11/2020
4382	8*10^146522-81	146523	Robert Price	02/2021
4383	32820^29059+29059^32820	146485	Hans Havermann	12/2020
4384	37261^8530+8530^37261	146472	Hans Havermann	12/2020
4385	66953^154+154^66953	146462	Hans Havermann	12/2020
4386	96^73877-95^73877	146445	Robert Price	10/2015
4387	8*10^146421+81	146422	Robert Price	08/2019
4388	33153^26090+26090^33153	146420	Hans Havermann	11/2020
4389	2^486275+23961	146384	Enzo Doria	10/2023
4390	(12^135607-1)/18437127731	146335	Paul Vanderveen	06/2025
4391	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
4392	179^64935+2	146290	Lelio R Paula	10/2017
4393	32595^30758+30758^32595	146285	Hans Havermann	11/2020
4394	34972^15157+15157^34972	146205	Hans Havermann	12/2020
4395	(16*10^146200+131)/3	146201	Robert Price	03/2022
4396	(19*10^146181-49)/3	146182	Robert Price	05/2019
4397	2^485531-114621	146160	Enzo Doria	05/2015
4398	2^485473-933075	146142	Paul Bourdelais	06/2021
4399	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
4400	(22*10^146130-193)/9	146131	Robert Price	07/2022
4401	2^485389+81887	146117	Enzo Doria	08/2016
4402	32554^30773+30773^32554	146108	Hans Havermann	11/2020
4403	28075^32844-32844^28075	146101	Frank Doornink	06/2024
4404	(10^146063+71)/9	146063	Serge Batalov	07/2015
4405	2*10^146051-63	146052	Robert Price	01/2022
4406	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
4407	(22*10^146029+257)/9	146030	Robert Price	06/2018
4408	7*10^145982-53	145983	Robert Price	06/2020
4409	2^484743+1872923	145923	Enzo Doria	05/2016
4410	33140^25287+25287^33140	145913	Hans Havermann	01/2021
4411	37875^7112+7112^37875	145895	Hans Havermann	01/2021
4412	30542^32529-32529^30542	145890	Frank Doornink	06/2024
4413	32862^27473+27473^32862	145872	Hans Havermann	01/2021
4414	V(1046652)/2093303	145817	Serge Batalov	07/2024
4415	32836^27587+27587^32836	145815	Hans Havermann	01/2021
4416	2^484341+1879157	145802	Enzo Doria	08/2016
4417	2*10^145784-91	145785	Robert Price	04/2020
4418	2^484271-51	145781	Lelio R Paula	11/2017
4419	(188*10^145750-11)/3	145752	Robert Price	02/2022
4420	70^78989-69^78989	145743	Robert Price	01/2014
4421	51^85334+2	145714	Robert Price	07/2015
4422	10^2^72843+72843^2^10	145687	Henri Lifchitz	03/2025
4423	2^483886-1857101	145665	Enzo Doria	10/2015
4424	29312^32607-32607^29312	145657	Frank Doornink	06/2024
4425	33350^23307+23307^33350	145656	Hans Havermann	01/2021
4426	(19*10^145585+131)/3	145586	Robert Price	06/2020
4427	31815^32332-32332^31815	145580	Frank Doornink	01/2024
4428	2^483563-1863457	145567	Enzo Doria	12/2015
4429	4*10^145563-69	145564	Robert Price	01/2022
4430	2^483516-1861409	145553	Enzo Doria	11/2015
4431	2^483384-115019	145514	Enzo Doria	06/2015
4432	(259*10^145501-1)/3	145503	Robert Price	12/2020
4433	(19*10^145499-61)/3	145500	Robert Price	05/2019
4434	2^483302-3221	145489	Lelio R Paula	12/2012
4435	(23*10^145463+61)/3	145464	Robert Price	01/2022
4436	35523^12434+12434^35523	145453	Hans Havermann	01/2021
4437	(29121^32761-1)/(29121^181-1)	145444	Ryan Propper	11/2023
4438	2^483046+1874029	145412	Enzo Doria	06/2016
4439	2^482991-2789317	145395	Enzo Doria	12/2015
4440	2^482978-2789711	145391	Enzo Doria	12/2015
4441	2^482966-2789711	145388	Enzo Doria	12/2015
4442	2^482817-1858843	145343	Enzo Doria	10/2015
4443	235*29^99378+4	145333	Eric Chen	06/2025
4444	2^482751-113635	145323	Enzo Doria	08/2014
4445	2^482705-459763	145309	Enzo Doria	05/2015
4446	(4^241306+11)/3	145281	Robert Price	03/2017
4447	(238*10^145276-1)/3	145278	Robert Price	04/2020
4448	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
4449	53^84239-52^84239	145252	Robert Price	01/2013
4450	U(1042497)	145243	Serge Batalov	07/2024
4451	2^482386+212419	145213	Enzo Doria	08/2023
4452	47952^1067+1067^47952	145207	Hans Havermann	01/2021
4453	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
4454	2^482087+72623	145123	Enzo Doria	04/2016
4455	2^482016-286565	145102	Enzo Doria	07/2015
4456	(19*10^145093+101)/3	145094	Robert Price	09/2019
4457	2^481956+121	145084	Stefano Morozzi	04/2021
4458	27535^32676-32676^27535	145078	Frank Doornink	06/2024
4459	2^481840+15	145049	Robert Price	09/2015
4460	(23*10^145040+7)/3	145041	Robert Price	05/2023
4461	2^481801-481801	145037	Henri Lifchitz	03/2005
4462	2^481775+1869083	145029	Enzo Doria	05/2016
4463	29^99167+2	145022	Ray Chandler	08/2011
4464	2^481663+1875653	144996	Enzo Doria	07/2016
4465	8*10^144977+27	144978	Robert Price	09/2021
4466	29840^32393-32393^29840	144953	Frank Doornink	06/2024
4467	36486^9379+9379^36486	144929	Hans Havermann	12/2020
4468	31580^32209-32209^31580	144922	Frank Doornink	01/2024
4469	35111^13378+13378^35111	144882	Hans Havermann	01/2021
4470	2^481149-459073	144841	Enzo Doria	05/2015
4471	2^481113+181419	144830	Boyan Hu	04/2024
4472	34619^15246+15246^34619	144817	Hans Havermann	01/2021
4473	2^481045-113215	144809	Enzo Doria	07/2014
4474	(64*10^144797+287)/9	144798	Robert Price	04/2019
4475	27320^32629-32629^27320	144758	Frank Doornink	06/2024
4476	2^480859-113695	144753	Enzo Doria	09/2014
4477	(106*10^144744+17)/3	144746	Robert Price	04/2021
4478	7*10^144742-27	144743	Robert Price	11/2022
4479	2^480766-2787191	144725	Enzo Doria	11/2015
4480	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
4481	28915^32438-32438^28915	144710	Frank Doornink	06/2024
4482	2^480678+1874239	144699	Enzo Doria	06/2016
4483	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
4484	L(692147)	144651	Henri Lifchitz	10/2008
4485	(76*10^144648+77)/9	144649	Robert Price	10/2019
4486	32672^26721+26721^32672	144635	Hans Havermann	01/2021
4487	31478^32153-32153^31478	144625	Frank Doornink	01/2024
4488	2^480417+35	144620	Robert Price	11/2015
4489	2^480296-59879	144584	Enzo Doria	10/2015
4490	33157^22878+22878^33157	144546	Hans Havermann	12/2020
4491	27520^32541-32541^27520	144471	Frank Doornink	06/2024
4492	45494^1497+1497^45494	144454	Hans Havermann	12/2020
4493	2^479844+3	144448	Donovan Johnson	06/2006
4494	33442^20803+20803^33442	144407	Hans Havermann	01/2021
4495	(441*33^95095-3833)/32	144405	Eric Chen	12/2023
4496	31892^32061-32061^31892	144393	Norbert Schneider	01/2023
4497	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
4498	(56*10^144380+169)/9	144381	Robert Price	03/2022
4499	44917^1638+1638^44917	144378	Hans Havermann	12/2020
4500	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015

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Probable Primes Top 10000

(301901 PRPs in the top)