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	(25*10^124076-67)/3	124077	Robert Price	06/2019
4502	F(593689)	124074	Henri Lifchitz	01/2005
4503	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
4504	35364^3215+3215^35364	124028	Hans Havermann	03/2021
4506	(266*10^124022-11)/3	124024	Robert Price	04/2020
4505	29987^13674+13674^29987	124024	Hans Havermann	03/2021
4507	2^411932-111546435	124004	Paul Bourdelais	10/2021
4508	2^411884-113279	123990	Enzo Doria	07/2014
4509	(2^411832+1)/257	123972	Lelio R Paula	05/2014
4510	(2^411833+2)/514	123972	Stefano Morozzi	03/2020
4511	(26*10^123970-89)/9	123971	Robert Price	06/2018
4512	2^411790-1853531	123962	Enzo Doria	08/2015
4513	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
4514	(101*10^123950+7)/9	123952	Robert Price	02/2022
4515	2^411711-113257	123938	Enzo Doria	07/2014
4516	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
4517	36289^2598+2598^36289	123914	Hans Havermann	03/2021
4518	(11*10^123899-179)/3	123900	Robert Price	09/2018
4519	32276^6879+6879^32276	123860	Hans Havermann	02/2021
4520	2^411325-351103	123822	Enzo Doria	06/2015
4521	(646*10^123817+11)/9	123819	Robert Price	10/2021
4522	30738^10643+10643^30738	123784	Hans Havermann	03/2021
4523	31074^9607+9607^31074	123755	Hans Havermann	03/2021
4524	2^411052+1872481	123739	Enzo Doria	05/2016
4525	34365^3986+3986^34365	123733	Hans Havermann	03/2021
4526	2^410997+39	123723	Lelio R Paula	05/2014
4527	(649^43987-1)/648	123700	Michael Stocker	05/2020
4528	(148*10^123688-1)/3	123690	Robert Price	03/2020
4529	36825^2284+2284^36825	123684	Hans Havermann	03/2021
4530	29582^15171+15171^29582	123683	Hans Havermann	03/2021
4531	10^123671+3593037	123672	Paul Bourdelais	10/2021
4532	8*10^123657+87	123658	Robert Price	10/2019
4533	30505^11302+11302^30505	123642	Hans Havermann	03/2021
4534	29956^13401+13401^29956	123633	Hans Havermann	03/2021
4535	155^56438+154	123618	Norbert Schneider	01/2019
4536	2^410596-39	123602	Lelio R Paula	05/2014
4537	(41*10^123600-221)/9	123601	Robert Price	10/2021
4538	28995^18302+18302^28995	123592	Hans Havermann	03/2021
4539	28302^23269+23269^28302	123589	Hans Havermann	03/2021
4540	2^410540-115079	123585	Enzo Doria	06/2015
4541	(7*10^123563+107)/3	123564	Robert Price	02/2018
4542	9*10^123549+89	123550	Robert Price	11/2019
4543	(197*10^123545+7)/3	123547	Robert Price	12/2020
4544	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
4545	2^410342+212449	123526	Enzo Doria	08/2023
4546	(29*10^123510+277)/9	123511	Robert Price	11/2021
4547	28118^24687+24687^28118	123508	Hans Havermann	03/2021
4548	39994^1225+1225^39994	123507	Hans Havermann	03/2021
4549	2^410206-113081	123485	Enzo Doria	07/2014
4550	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
4551	28974^18215+18215^28974	123442	Hans Havermann	03/2021
4552	28901^18618+18618^28901	123406	Hans Havermann	03/2021
4553	2^409909-189	123395	Enzo Doria	05/2014
4554	2^409896-109043	123391	Enzo Doria	04/2014
4555	2^409890+75409	123390	Enzo Doria	04/2016
4556	81254^33+33^81254	123386	Hans Havermann	03/2021
4557	33463^4854+4854^33463	123348	Hans Havermann	03/2021
4558	34061^4182+4182^34061	123348	Hans Havermann	03/2021
4559	133^58076-2	123345	Lelio R Paula	10/2017
4560	F(590041)	123311	Henri Lifchitz	01/2005
4561	(82*10^123299+377)/9	123300	Robert Price	03/2022
4562	2^409566-113501	123292	Enzo Doria	08/2014
4563	2^409533+77747	123282	Enzo Doria	05/2016
4564	2^409436-112799	123253	Enzo Doria	06/2014
4565	28212^23321+23321^28212	123223	Hans Havermann	03/2021
4566	2^409225+1873787	123189	Enzo Doria	06/2016
4567	2^409174+73009	123174	Enzo Doria	04/2016
4568	2^409058-112685	123139	Enzo Doria	06/2014
4569	(13*10^123137-61)/3	123138	Robert Price	11/2018
4570	4*10^123113+21	123114	Robert Price	12/2018
4571	2^408778+77689	123055	Enzo Doria	05/2016
4572	2^408690-75	123028	Lelio R Paula	11/2013
4573	28327^22032+22032^28327	123026	Hans Havermann	03/2021
4574	(29*10^122996+673)/9	122997	Robert Price	12/2018
4575	(65*10^122994-101)/9	122995	Robert Price	01/2022
4576	2^408574-2787341	122994	Enzo Doria	03/2016
4577	3*10^122977+37	122978	Robert Price	08/2018
4578	(7*10^122976-67)/3	122977	Robert Price	10/2021
4579	Phi(157825,10)	122961	Maksym Voznyy	06/2015
4580	(68*10^122933-419)/9	122934	Robert Price	07/2019
4581	29712^13721+13721^29712	122931	Hans Havermann	03/2021
4582	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
4583	(266*10^122872-17)/3	122874	Robert Price	07/2020
4584	(16*10^122871+77)/3	122872	Robert Price	03/2019
4585	30395^11022+11022^30395	122865	Hans Havermann	03/2021
4586	4*10^122859-69	122860	Robert Price	01/2022
4587	(10^122857+167)/3	122857	Robert Price	05/2021
4588	33331^4852+4852^33331	122856	Hans Havermann	03/2021
4589	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
4590	(19*10^122836-43)/3	122837	Robert Price	05/2019
4591	28420^20969+20969^28420	122820	Hans Havermann	03/2021
4592	(16*10^122818+179)/3	122819	Robert Price	11/2021
4593	29865^12934+12934^29865	122797	Hans Havermann	03/2021
4594	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
4595	(32*10^122733-77)/9	122734	Robert Price	06/2018
4596	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
4598	(22*10^122681+161)/3	122682	Robert Price	05/2019
4597	29513^14350+14350^29513	122682	Hans Havermann	03/2021
4599	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
4600	(26*10^122625-131)/3	122626	Robert Price	10/2019
4601	27925^24562+24562^27925	122599	Hans Havermann	03/2021
4602	(73*10^122592-1)/9	122593	Robert Price	01/2015
4603	(5*10^122592+91)/3	122593	Robert Price	04/2018
4604	36751^2166+2166^36751	122589	Hans Havermann	03/2021
4605	(85*10^122585-1)/3	122587	Robert Price	02/2020
4606	29368^14931+14931^29368	122585	Hans Havermann	03/2021
4607	2^407179-112075	122574	Enzo Doria	06/2014
4608	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
4609	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
4610	(646*10^122533+11)/9	122535	Robert Price	10/2021
4611	2^407008-1867919	122522	Enzo Doria	04/2016
4612	11^117642-300	122512	Enzo Doria	10/2012
4613	(F(397700+1)^2+L(397700+1)^2)/2	122509	Henri Lifchitz	10/2017
4614	2^406949+72197	122504	Enzo Doria	04/2016
4615	(19*10^122501+149)/3	122502	Robert Price	05/2019
4616	28632^18977+18977^28632	122495	Hans Havermann	03/2021
4617	31815^7076+7076^31815	122481	Hans Havermann	03/2021
4618	2^406826-65	122467	Lelio R Paula	11/2013
4619	2^406821-2797363	122466	Enzo Doria	04/2016
4620	(7*10^122456-331)/9	122456	Robert Price	03/2022
4621	2^406758-17	122447	Lelio R Paula	11/2013
4622	29941^12282+12282^29941	122437	Hans Havermann	03/2021
4623	(30^82883-1)/29	122427	Robert Price	12/2011
4624	27496^27577+27577^27496	122422	Norbert Schneider	12/2020
4625	28732^18215+18215^28732	122411	Hans Havermann	03/2021
4626	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
4627	4*10^122377+19	122378	Robert Price	10/2018
4628	28227^21634+21634^28227	122368	Hans Havermann	03/2021
4629	Phi(246362,10)	122365	Makoto Kamada	09/2019
4630	3*10^122345-97	122346	Robert Price	07/2018
4631	97^61575-2	122336	Lelio R Paula	12/2014
4632	2*10^122319+47	122320	Robert Price	12/2021
4633	208^52765+52765^208	122313	Norbert Schneider	11/2020
4635	2^406298+2799109	122308	Enzo Doria	04/2016
4634	2^406296+213691	122308	Enzo Doria	09/2023
4636	7*10^122294+57	122295	Robert Price	06/2019
4637	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
4638	2^406229-1849993	122288	Enzo Doria	08/2015
4639	3*10^122274+7	122275	Robert Price	07/2015
4640	2^406117+1876577	122254	Enzo Doria	07/2016
4641	29308^14835+14835^29308	122253	Hans Havermann	03/2021
4642	28119^22268+22268^28119	122253	Hans Havermann	03/2021
4643	32167^6312+6312^32167	122240	Hans Havermann	03/2021
4644	3^256199-2^256199	122238	Mike Oakes	06/2005
4645	27678^26053+26053^27678	122223	Hans Havermann	03/2021
4646	2^405992-78557	122216	Jorge Menendez	03/2018
4647	(8*10^122203+43)/3	122204	Robert Price	06/2018
4648	(58*10^122170+329)/9	122171	Robert Price	05/2019
4649	2^405774+179149	122151	Enzo Doria	06/2016
4650	2^405693+20417	122126	Enzo Doria	07/2023
4651	(218*10^122109+7)/9	122111	Robert Price	06/2022
4652	29189^15246+15246^29189	122103	Hans Havermann	03/2021
4654	34*10^122082-9	122084	Robert Price	06/2020
4653	33442^4473+4473^33442	122084	Hans Havermann	03/2021
4655	5*10^122082+41	122083	Robert Price	03/2019
4656	31849^6808+6808^31849	122078	Hans Havermann	03/2021
4658	2^405514-3311	122072	Yves Minet	12/2014
4659	2^405514-115511	122072	Enzo Doria	07/2015
4657	23*10^122070-7	122072	Robert Price	02/2020
4660	2^405422-113261	122045	Enzo Doria	07/2014
4661	2^405173+71237	121970	Enzo Doria	04/2016
4662	fibonacci(583574)+2	121960	Jon Grantham	08/2023
4663	(154*10^121953+17)/9	121955	Robert Price	06/2022
4664	(34*10^121924+191)/9	121925	Robert Price	08/2021
4665	(2^405016+1)/257	121920	Lelio R Paula	04/2014
4666	28557^18590+18590^28557	121918	Hans Havermann	03/2021
4667	28641^18002+18002^28641	121877	Hans Havermann	03/2021
4668	2^404858+71329	121875	Enzo Doria	04/2016
4669	2^404813-114703	121861	Enzo Doria	04/2015
4670	2^404764+77791	121847	Enzo Doria	05/2016
4671	28830^16841+16841^28830	121847	Hans Havermann	03/2021
4672	(4*10^121825+89)/3	121826	Robert Price	08/2021
4673	317^48694+48694^317	121787	Norbert Schneider	08/2015
4674	2^404536-115259	121778	Enzo Doria	06/2015
4675	2^404501-631	121767	Yves Minet	07/2012
4676	5*10^121764-69	121765	Robert Price	02/2021
4677	28236^20485+20485^28236	121738	Hans Havermann	02/2021
4678	(382*10^121694-31)/9	121696	Robert Price	06/2022
4679	63^67620+2	121672	Lelio R Paula	08/2015
4680	(25*34^79445-28062367)/33	121669	Eric Chen	08/2023
4681	(16*10^121633+167)/3	121634	Robert Price	06/2019
4682	29955^11494+11494^29955	121632	Hans Havermann	02/2021
4683	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
4684	31088^8163+8163^31088	121612	Hans Havermann	02/2021
4685	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
4686	(10^121543-79)/3	121543	Robert Price	01/2018
4687	2^403676+76831	121519	Enzo Doria	05/2016
4688	(7*10^121487+143)/3	121488	Robert Price	03/2018
4689	27965^22086+22086^27965	121484	Hans Havermann	02/2021
4690	(893*10^121470+7)/9	121472	Robert Price	06/2021
4691	(206*10^121462-11)/3	121464	Robert Price	02/2022
4692	(77*10^121455+67)/9	121456	Robert Price	12/2021
4693	2^403363-113635	121425	Enzo Doria	08/2014
4694	(17*10^121418-113)/3	121419	Robert Price	06/2021
4695	2^403336-1861469	121417	Enzo Doria	03/2016
4696	27929^22186+22186^27929	121382	Hans Havermann	02/2021
4697	p(24442)#/2-64	121381	Robert Price	04/2017
4698	11^116555-720	121380	Enzo Doria	11/2012
4699	2^403100-461267	121346	Enzo Doria	07/2015
4700	2^403093-112213	121344	Enzo Doria	06/2014
4701	29404^13385+13385^29404	121340	Hans Havermann	02/2021
4702	28106^20745+20745^28106	121332	Hans Havermann	02/2021
4703	(316^48539+1)/317	121330	Eric Chen	10/2017
4704	(23*10^121320-71)/3	121321	Robert Price	07/2020
4705	2^403004+1866361	121317	Enzo Doria	03/2016
4706	2^402953+89	121301	Lelio R Paula	10/2013
4707	2^402944-2788319	121299	Enzo Doria	03/2016
4708	(44*10^121297-719)/9	121298	Robert Price	12/2018
4709	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
4710	2^402828-113183	121264	Enzo Doria	07/2014
4711	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
4712	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
4714	2^402715+1874223	121230	Enzo Doria	06/2016
4713	(35*10^121229-593)/9	121230	Robert Price	07/2018
4715	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
4716	28719^16568+16568^28719	121174	Hans Havermann	02/2021
4717	7*10^121144+9	121145	Robert Price	09/2015
4718	27490^25467+25467^27490	121121	Hans Havermann	02/2021
4719	34575^3182+3182^34575	121106	Hans Havermann	02/2021
4720	5*10^121100-37	121101	Robert Price	11/2021
4721	29954^10935+10935^29954	120979	Hans Havermann	02/2021
4722	33585^3992+3992^33585	120946	Hans Havermann	02/2021
4723	40296^1003+1003^40296	120941	Hans Havermann	02/2021
4724	2^401725-113251	120932	Enzo Doria	07/2014
4725	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
4726	2^401652+73711	120910	Enzo Doria	04/2016
4727	(2^401632+3)/79	120902	Lelio R Paula	04/2014
4728	40450^973+973^40450	120870	Hans Havermann	01/2021
4729	(8*10^120851-11)/3	120852	Robert Price	07/2023
4730	10^120841+88417	120842	Patrick De Geest	04/2020
4731	10^120841-123456789	120841	Robert Price	02/2020
4732	10^120841-176853	120841	Patrick De Geest	04/2020
4733	2^401406-2791331	120836	Enzo Doria	03/2016
4734	(28^83497+1)/29	120832	Robert Price	07/2013
4735	(22*10^120828+161)/3	120829	Robert Price	05/2019
4736	2^401369+1867367	120825	Enzo Doria	03/2016
4737	(5*10^120821+43)/3	120822	Robert Price	12/2021
4738	(10^120782+29)/3	120782	Serge Batalov	12/2014
4739	2^401215-1657	120778	Yves Minet	07/2014
4740	2^401159+53	120761	Lelio R Paula	10/2013
4741	27782^22179+22179^27782	120739	Hans Havermann	01/2021
4742	32974^4585+4585^32974	120730	Hans Havermann	02/2021
4743	2^401031-113047	120723	Enzo Doria	07/2014
4744	30598^8813+8813^30598	120713	Hans Havermann	02/2021
4745	(71*10^120703-287)/9	120704	Robert Price	09/2019
4746	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
4747	34793^2940+2940^34793	120675	Hans Havermann	02/2021
4748	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
4749	(166*10^120654+11)/3	120656	Robert Price	03/2021
4750	34066^3481+3481^34066	120652	Hans Havermann	02/2021

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