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	(844*10^151396-7)/9	151398	Robert Price	05/2021
4252	(26*10^151391-503)/9	151392	Robert Price	07/2018
4253	2^502769+1877567	151349	Enzo Doria	08/2016
4254	2^502576-4019	151291	Yves Minet	10/2011
4255	5*10^151257+41	151258	Robert Price	03/2019
4256	2^502290-2792501	151205	Enzo Doria	02/2016
4257	17015^35734+35734^17015	151185	Norbert Schneider	12/2025
4258	2^502181+1868417	151172	Enzo Doria	04/2016
4259	2^502055+22583	151134	Enzo Doria	09/2023
4260	(3*23^110967+41)/22	151106	Anonymous	12/2023
4261	6*10^151063-77	151064	Robert Price	09/2021
4262	2^501781-1850503	151052	Enzo Doria	08/2015
4263	(2^82589933-1)%(10^151020)	151020	Anonymous	05/2025
4264	(5*10^151007+37)/3	151008	Robert Price	03/2018
4265	3^316494+5*2^316494	151007	Jon Grantham	08/2023
4266	2^501627-991	151005	Yves Minet	02/2014
4267	2^501577-115333	150990	Enzo Doria	07/2015
4268	25239^34298-34298^25239	150983	Frank Doornink	12/2023
4269	(19*10^150977-7)/3	150978	Robert Price	12/2023
4270	8*10^150975+3	150976	Robert Price	08/2015
4271	2^501512-113669	150971	Enzo Doria	09/2014
4272	34180^26101+26101^34180	150962	Norman Luhn	04/2024
4273	U(1083477)/2166953	150949	Serge Batalov	07/2024
4274	(83*10^150908+493)/9	150909	Robert Price	12/2021
4275	36267^14482+14482^36267	150901	Norman Luhn	04/2024
4276	2*10^150818+83	150819	Robert Price	12/2021
4277	48753^1240+1240^48753	150814	Norman Luhn	04/2024
4278	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
4279	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
4280	2^500899-500899	150786	Henri Lifchitz	04/2005
4281	2^500832+1876801	150766	Enzo Doria	07/2016
4282	(23*10^150763-59)/9	150764	Robert Price	05/2018
4283	46002^1891+1891^46002	150735	Norman Luhn	04/2024
4284	32001^33458-33458^32001	150734	Frank Doornink	01/2024
4285	2^500699+1884953	150726	Enzo Doria	02/2017
4286	(13*10^150675-37)/3	150676	Robert Price	01/2019
4287	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
4288	35365^18204+18204^35365	150661	Norman Luhn	05/2024
4290	2^500337-71101	150617	Enzo Doria	04/2016
4289	(74*10^150616+133)/9	150617	Robert Price	06/2019
4291	(2*10^150612-17)/3	150612	Serge Batalov	11/2022
4292	4*10^150577+91	150578	Robert Price	08/2018
4293	5649^40132+40132^5649	150575	Norbert Schneider	04/2024
4294	2^500160+80071	150564	Enzo Doria	06/2016
4295	(2^500120+5)/9	150551	Lelio R Paula	12/2017
4297	(43*10^150515-421)/9	150516	Robert Price	01/2019
4296	4695^40994+40994^4695	150516	Norbert Schneider	11/2023
4298	2^499999+15981	150515	Norman Luhn	08/2023
4299	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
4300	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
4301	26614^34005-34005^26614	150476	Frank Doornink	03/2024
4302	2^499861-29503	150474	Enzo Doria	08/2015
4303	Phi(64793,-7#)	150462	Henri Lifchitz	12/2025
4304	2^499653-113533	150411	Enzo Doria	08/2014
4305	(14*10^150391-191)/3	150392	Robert Price	10/2020
4306	29033^33696+33696^29033	150382	Norbert Schneider	10/2023
4307	2^499534-221	150375	Yves Minet	06/2012
4308	30110^33567+33567^30110	150337	Norbert Schneider	10/2023
4309	26212^34023-34023^26212	150331	Frank Doornink	03/2024
4310	(28*10^150294+41)/3	150295	Robert Price	07/2021
4311	2^499225+49727	150282	Enzo Doria	09/2016
4312	(695*10^150274+7)/9	150276	Robert Price	12/2021
4313	2^499054-29261	150231	Enzo Doria	07/2015
4314	18580^35187+35187^18580	150215	Norbert Schneider	10/2023
4315	(844*10^150196-7)/9	150198	Robert Price	05/2021
4316	2^498907-933075	150186	Paul Bourdelais	06/2021
4317	(2^498898-7)/9	150183	Lelio R Paula	10/2015
4318	3*10^150182+17	150183	Robert Price	07/2018
4319	5*10^150175+63	150176	Robert Price	09/2020
4320	29273^33618-33618^29273	150154	Frank Doornink	06/2024
4321	32363^33292+33292^32363	150149	Norbert Schneider	07/2022
4322	32^99753-99753^32	150144	Henri Lifchitz	08/2024
4323	(77*10^150128+67)/9	150129	Robert Price	12/2021
4324	(710^(275062+1)-9*10^75062-7)/9	150125	Robert Price	12/2023
4325	2^498623+1866983	150101	Enzo Doria	03/2016
4326	33194^33194-213^213	150073	Serge Batalov	04/2024
4327	27868^33759-33759^27868	150063	Frank Doornink	06/2024
4328	(25*10^150050-403)/9	150051	Robert Price	12/2020
4329	numbpart(18140942830)	150033	Serge Batalov	04/2017
4330	10^150029+4381	150030	Patrick De Geest	05/2016
4331	10^150029-41	150029	Serge Batalov	12/2014
4332	33185^33185+618^618	150028	Serge Batalov	04/2024
4333	9*34^97952+529	150013	Eric Chen	08/2023
4334	10^150000+1158603	150001	Patrick De Geest	09/2018
4335	10^150000-245703	150000	Patrick De Geest	09/2018
4336	(38*10^149999+691)/9	150000	Robert Price	10/2018
4337	2043563126843649194^8192+2043563126843649185^8192	150000	Youcef Lemsafer	01/2023
4338	(2043563126843649232^8192+2043563126843649201^8192)/147457	149994	Youcef Lemsafer	01/2023
4339	2^498238-53	149985	Lelio R Paula	12/2017
4340	45728^1905+1905^45728	149984	Hans Havermann	10/2020
4341	(211^65024+1)/(211^512+1)	149945	Martin Hopf	12/2023
4342	5*10^149907+23	149908	Robert Price	03/2019
4343	32^99585-829	149891	Eric Chen	11/2023
4344	39347^6442+6442^39347	149874	Hans Havermann	09/2020
4345	2^497850+81049	149868	Enzo Doria	07/2016
4346	V(1075416)	149830	Serge Batalov	07/2024
4347	37228^10575+10575^37228	149816	Hans Havermann	10/2020
4348	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
4349	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
4350	(2*10^149803-143)/3	149803	Robert Price	03/2018
4351	33845^26604+26604^33845	149763	Hans Havermann	09/2020
4352	2^497434-2784191	149743	Enzo Doria	10/2015
4353	(865*10^149737-1)/9	149739	Robert Price	04/2020
4354	10^149695-7000001	149695	Robert Price	06/2021
4355	38237^8214+8214^38237	149681	Hans Havermann	09/2020
4356	Phi(745791,2)/1491583	149664	Anonymous	03/2025
4357	(497167*2^497167-1)/70975	149664	Anonymous	04/2025
4358	(23*10^149655+19)/3	149656	Robert Price	07/2019
4359	2^497068-113579	149633	Enzo Doria	08/2014
4360	2^497037+73727	149624	Enzo Doria	04/2016
4361	11*10^149618+3	149620	Robert Price	07/2021
4362	34942^19067+19067^34942	149562	Hans Havermann	09/2020
4363	33696^27449+27449^33696	149561	Hans Havermann	09/2020
4364	2^496773+77747	149544	Enzo Doria	05/2016
4365	29937^33400-33400^29937	149506	Frank Doornink	06/2024
4366	(7*10^149483-493)/9	149483	Robert Price	04/2021
4367	(206*10^149459+7)/3	149461	Robert Price	07/2020
4368	34589^20940+20940^34589	149459	Hans Havermann	09/2020
4369	2^496477-113485	149455	Enzo Doria	08/2014
4370	(496423*2^496423-1)/223573	149439	Anonymous	04/2025
4371	3*2^496411-5	149436	Jon Grantham	07/2023
4372	((10^74703-1)10000/9+7481)10^74703+(10^74703-1)/9	149410	Hans Havermann	09/2019
4373	2^496270-49451	149393	Enzo Doria	10/2015
4374	2^496238-1865081	149383	Enzo Doria	01/2016
4375	33831^26030+26030^33831	149380	Hans Havermann	09/2020
4376	34131^23780+23780^34131	149365	Hans Havermann	09/2020
4377	(5*10^149335-53)/3	149336	Robert Price	09/2020
4378	26043^33818-33818^26043	149330	Frank Doornink	03/2024
4379	2^495968-1853699	149302	Enzo Doria	09/2015
4380	2^495935-4117	149292	Yves Minet	02/2018
4381	5*2^495930+3	149291	Jon Grantham	07/2023
4382	35816^14709+14709^35816	149267	Hans Havermann	09/2020
4383	(10^149264+7)/191/2683/80557	149254	Alfred Reich	07/2021
4384	10^149240-40000001	149240	Robert Price	07/2022
4385	10^149240-10809	149240	Alfred Reich	08/2024
4386	2^495712-396765	149225	Enzo Doria	07/2013
4387	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
4388	2^495420+1880701	149137	Enzo Doria	10/2016
4389	25646^33823-33823^25646	149127	Frank Doornink	02/2024
4390	2^495337-1847293	149112	Enzo Doria	07/2015
4391	(2^495193-7)/5	149068	Lelio R Paula	10/2015
4392	2^495163+111546435	149059	Paul Bourdelais	10/2021
4393	33282^30097+30097^33282	149055	Hans Havermann	09/2020
4394	37384^9705+9705^37384	149050	Hans Havermann	09/2020
4395	34808^19143+19143^34808	149049	Hans Havermann	09/2020
4396	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
4397	30657^33212-33212^30657	149007	Frank Doornink	06/2024
4398	47^89113-46^89113	149006	Robert Price	10/2012
4399	V(891190)	148997	Serge Batalov	07/2024
4400	2^494916+87855	148985	Lelio R Paula	01/2016
4401	6*10^148982+73	148983	Robert Price	04/2019
4402	3^312155-4	148936	Anonymous	02/2023
4403	10^148934+1530019	148935	Patrick De Geest	02/2021
4404	10^148934-1000000001	148934	Robert Price	11/2020
4405	10^148934-512057	148934	Patrick De Geest	02/2021
4406	39000^6571+6571^39000	148888	Hans Havermann	10/2020
4407	2^494586-2791991	148886	Enzo Doria	02/2016
4408	Phi(117375,3^5)	148862	Henri Lifchitz	12/2025
4409	8*10^148860-3	148861	Ray Chandler	04/2011
4410	38262^7769+7769^38262	148854	Hans Havermann	10/2020
4411	10^148816-500001	148816	Robert Price	03/2022
4412	(53*10^148811-287)/9	148812	Robert Price	02/2022
4413	2^494333-286183	148810	Enzo Doria	06/2015
4414	2^494144-264119	148753	Enzo Doria	05/2014
4415	6*10^148734+47	148735	Robert Price	06/2022
4416	28724^33353-33353^28724	148696	Frank Doornink	06/2024
4417	36502^11823+11823^36502	148663	Hans Havermann	11/2020
4418	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
4419	64239^206+206^64239	148641	Hans Havermann	10/2020
4420	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
4421	(23*10^148627-137)/3	148628	Robert Price	08/2021
4422	(151*10^148601-1)/3	148603	Robert Price	03/2020
4423	2^493636+82081	148600	Enzo Doria	09/2016
4424	((((((((((((((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
4425	27134^33509-33509^27134	148563	Frank Doornink	01/2024
4426	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
4427	(2*10^148460-23)/3	148460	Robert Price	04/2018
4428	(28*10^148445+101)/3	148446	Robert Price	09/2020
4429	2^493065+225	148428	Henri Lifchitz	11/2024
4430	36203^12556+12556^36203	148391	Hans Havermann	10/2020
4431	33912^23749+23749^33912	148387	Hans Havermann	10/2020
4432	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
4433	34294^21117+21117^34294	148309	Hans Havermann	10/2020
4434	(71*10^148306-539)/9	148307	Robert Price	07/2019
4435	30814^33039-33039^30814	148304	Frank Doornink	06/2024
4436	38042^7875+7875^38042	148222	Hans Havermann	10/2020
4437	5^211959-12874	148153	Enzo Doria	05/2014
4438	34142^21831+21831^34142	148145	Hans Havermann	10/2020
4439	10^148112+34059	148113	Patrick De Geest	05/2021
4440	10^148112-70000001	148112	Robert Price	03/2021
4441	10^148112-106593	148112	Patrick De Geest	05/2021
4442	36303^12016+12016^36303	148108	Hans Havermann	10/2020
4443	(77*10^148089-149)/9	148090	Robert Price	03/2022
4444	(16*10^148071+41)/3	148072	Robert Price	03/2019
4445	187^65175-2	148068	Lelio R Paula	11/2017
4446	2^491851+1871453	148062	Enzo Doria	05/2016
4447	(68*10^148060-257)/9	148061	Robert Price	07/2019
4448	Phi(162903,-5#)	148043	Henri Lifchitz	12/2025
4449	(151*10^148020-1)/3	148022	Robert Price	03/2020
4450	39153^6032+6032^39153	148017	Hans Havermann	10/2020
4451	36798^10507+10507^36798	147983	Hans Havermann	12/2020
4452	(26*10^147973-23)/3	147974	Robert Price	12/2019
4453	Phi(65997,11#)	147973	Henri Lifchitz	12/2025
4454	2^491521-1865323	147963	Enzo Doria	02/2016
4455	(2^491476+7)/71	147948	Lelio R Paula	10/2015
4456	2*10^147928+47	147929	Robert Price	12/2021
4457	2^491391-7807	147924	Lelio R Paula	01/2013
4458	2^491384+236221	147922	Enzo Doria	05/2025
4459	39736^5279+5279^39736	147920	Hans Havermann	11/2020
4460	2^491370-113297	147918	Enzo Doria	07/2014
4461	(3^707753)%F(707753)	147912	Henri Lifchitz	06/2025
4462	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
4463	44368^2155+2155^44368	147899	Hans Havermann	12/2020
4464	(17*10^147890+79)/3	147891	Robert Price	04/2019
4465	94*10^147871-3	147873	Robert Price	05/2020
4466	10^147843+620967	147844	Patrick De Geest	05/2021
4467	10^147843-50000000001	147843	Robert Price	12/2020
4468	10^147843-182891	147843	Patrick De Geest	05/2021
4469	35805^13346+13346^35805	147709	Hans Havermann	11/2020
4470	2^490672+255255	147707	Paul Bourdelais	10/2021
4471	2^490660-17	147704	Lelio R Paula	12/2017
4472	(229*10^147699-1)/3	147701	Robert Price	07/2020
4473	40656^4289+4289^40656	147678	Hans Havermann	11/2020
4474	(85*10^147676-31)/9	147677	Rytis Slatkevicius	12/2024
4475	2^490550+1179439	147671	Enzo Doria	06/2016
4476	27249^33292-33292^27249	147662	Frank Doornink	06/2024
4477	(23*10^147649-59)/9	147650	Robert Price	05/2018
4478	2^490303+2793653	147596	Enzo Doria	03/2016
4479	2^490266+255255	147585	Paul Bourdelais	10/2021
4480	199^64181-2	147543	Lelio R Paula	11/2017
4481	32849^30958+30958^32849	147518	Hans Havermann	11/2020
4482	2^489871-286987	147466	Enzo Doria	07/2015
4483	2^489864-351899	147464	Enzo Doria	07/2015
4484	175^65724-2	147422	Lelio R Paula	11/2017
4485	2^489712+1874851	147419	Enzo Doria	06/2016
4486	34473^18830+18830^34473	147367	Hans Havermann	11/2020
4487	63^81896-2	147359	Lelio R Paula	10/2017
4488	34580^18237+18237^34580	147344	Hans Havermann	11/2020
4489	(11*10^147313-107)/3	147314	Robert Price	09/2018
4490	(397*10^147310+17)/9	147312	Robert Price	03/2022
4491	2^489305-59815	147296	Enzo Doria	10/2015
4492	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
4493	2*10^147264-61	147265	Robert Price	10/2021
4494	2*10^147260+29	147261	Robert Price	02/2021
4495	33556^24457+24457^33556	147258	Hans Havermann	11/2020
4496	12^136450-11	147255	Riley Fisher	12/2024
4497	2^489125+80357	147242	Enzo Doria	06/2016
4498	10^147240-40000001	147240	Robert Price	07/2022
4499	10^147240-371331	147240	Alfred Reich	09/2024
4500	10^147240-464727	147240	Alfred Reich	09/2024

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Probable Primes Top 10000

(302548 PRPs in the top)