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 ?
5251	2^420741-113659	126656	Enzo Doria	08/2014
5252	2^420694-21	126642	Lelio R Paula	05/2017
5253	(13*10^126638+437)/9	126639	Robert Price	04/2018
5254	(167*10^126637-17)/3	126639	Robert Price	03/2020
5255	4*10^126625+87	126626	Robert Price	08/2018
5256	(31*2^420556+1)/7	126601	Lelio R Paula	05/2014
5257	7*10^126600-99	126601	Robert Price	06/2019
5258	U(655247)/250330563881/206066063082749	126596	Serge Batalov	07/2024
5259	2^420424-59189	126561	Enzo Doria	10/2015
5260	28717^25534+25534^28717	126560	Hans Havermann	03/2021
5261	(86*10^126542+103)/9	126543	Robert Price	12/2021
5262	(19*10^126517-7)/3	126518	Robert Price	12/2023
5263	28922^23655+23655^28922	126503	Hans Havermann	03/2021
5264	2^420126+71893	126471	Enzo Doria	04/2016
5265	25982^28643-28643^25982	126450	Frank Doornink	03/2024
5266	(43*10^126441+47)/9	126442	Robert Price	12/2018
5267	8*10^126408+71	126409	Robert Price	05/2022
5268	2^419866+1877059	126393	Enzo Doria	07/2016
5269	29315^20484+20484^29315	126390	Hans Havermann	03/2021
5270	29433^19676+19676^29433	126384	Hans Havermann	03/2021
5271	F(604711)	126377	Henri Lifchitz	02/2005
5272	2^419757+72707	126360	Enzo Doria	04/2016
5273	2^419720-21569	126349	Enzo Doria	07/2013
5274	2^419637+29	126324	Henri Lifchitz	02/2006
5275	31004^11865+11865^31004	126319	Hans Havermann	03/2021
5276	2^419612+1876741	126316	Enzo Doria	07/2016
5277	2^419520+2793271	126289	Enzo Doria	03/2016
5278	(2^419447-5)/369	126264	Lelio R Paula	05/2014
5279	2^419328-1859939	126231	Enzo Doria	03/2016
5280	2^419282-1851507	126217	Enzo Doria	08/2015
5281	(133*10^126212+17)/3	126214	Robert Price	11/2021
5282	2^419251+1866143	126208	Enzo Doria	03/2016
5283	11^121185+2	126202	Robert Price	05/2014
5284	28203^28352+28352^28203	126175	Norbert Schneider	01/2021
5285	(23*2^419036-1)/1393	126141	Lelio R Paula	05/2014
5286	2^418851+23	126087	Robert Price	09/2015
5287	(2^418849-9)/2681	126083	Lelio R Paula	05/2014
5288	2^418829+167	126081	Lelio R Paula	01/2012
5289	31037^11530+11530^31037	126067	Hans Havermann	03/2021
5290	4*10^126064-69	126065	Robert Price	01/2022
5291	(31*2^418782-1)/75891	126063	Lelio R Paula	05/2014
5292	(19*2^418754-1)/15	126058	Lelio R Paula	05/2014
5293	(35*10^126048-323)/9	126049	Robert Price	10/2021
5294	33016^6551+6551^33016	126000	Hans Havermann	03/2021
5295	2^418548-111546435	125996	Paul Bourdelais	10/2021
5296	25134^28625-28625^25134	125958	Frank Doornink	12/2023
5297	34736^4227+4227^34736	125954	Hans Havermann	03/2021
5298	26197^28502-28502^26197	125930	Frank Doornink	03/2024
5299	2^418319-109501	125927	Enzo Doria	04/2014
5300	2^418316-112373	125926	Enzo Doria	06/2014
5301	40398^1309+1309^40398	125919	Hans Havermann	03/2021
5302	(8*10^125894-29)/3	125895	Robert Price	07/2018
5303	(26*10^125886-413)/9	125887	Robert Price	05/2018
5304	10^(262938+1)-710^62938-1	125877	Robert Price	07/2023
5305	55*10^125847+9	125849	Robert Price	03/2022
5306	4*10^125832+57	125833	Robert Price	05/2022
5307	2^417968+1869811	125821	Enzo Doria	06/2016
5308	2^417902+63	125802	Lelio R Paula	09/2015
5309	(10^125792-91)/9	125792	Serge Batalov	12/2014
5310	30438^13573+13573^30438	125791	Hans Havermann	03/2021
5311	32867^6714+6714^32867	125782	Hans Havermann	03/2021
5312	31155^10892+10892^31155	125777	Hans Havermann	03/2021
5313	(35*10^125754-593)/9	125755	Robert Price	07/2018
5314	30455^13464+13464^30455	125754	Hans Havermann	03/2021
5315	(32*10^125751-77)/9	125752	Robert Price	06/2018
5316	2^417704+77011	125742	Enzo Doria	05/2016
5317	29755^16816+16816^29755	125737	Hans Havermann	03/2021
5318	(22*10^125734+203)/9	125735	Robert Price	10/2021
5319	29918^15915+15915^29918	125710	Hans Havermann	03/2021
5320	(10^125706+149)/3	125706	Serge Batalov	12/2014
5321	28531^25368+25368^28531	125659	Hans Havermann	03/2021
5322	2^417419-115309	125656	Enzo Doria	07/2015
5323	(46*10^125642+593)/9	125643	Robert Price	04/2022
5324	2^417315+213953	125625	Enzo Doria	10/2023
5325	2^417300+77281	125620	Enzo Doria	05/2016
5326	30638^12537+12537^30638	125561	Hans Havermann	03/2021
5327	2^417095-1657	125559	Yves Minet	07/2014
5328	30162^14525+14525^30162	125538	Hans Havermann	03/2021
5329	(56*10^125535+583)/9	125536	Robert Price	08/2021
5330	(23*10^125517-179)/3	125518	Robert Price	06/2022
5331	9*10^125516+29	125517	Robert Price	03/2022
5332	(88*10^125492-637)/9	125493	Robert Price	11/2020
5333	28958^21525+21525^28958	125474	Hans Havermann	02/2021
5336	2^416773-25	125462	Lelio R Paula	09/2015
5334	(10^125482+7)/162685667/1639829194459	125462	Alfred Reich	07/2021
5335	26078^28409-28409^26078	125462	Frank Doornink	03/2024
5337	33889^5032+5032^33889	125449	Hans Havermann	03/2021
5338	(289511#+292834)/(2^3*146417)	125444	Makoto Morimoto	10/2017
5339	(2861^36481+1)/(2861^191+1)	125438	Martin Hopf	12/2023
5340	(11*2^416691+1)/43	125436	Lelio R Paula	05/2014
5341	(289511#+1896)/(23^3797801939911849)	125434	Makoto Morimoto	06/2019
5342	2^416641-2*416641+1	125422	Robert Price	05/2018
5343	33392^5697+5697^33392	125409	Hans Havermann	03/2021
5344	(21*2^416566-1)/17	125399	Lelio R Paula	05/2014
5345	2^416530+1870429	125389	Enzo Doria	05/2016
5346	(56*10^125385+691)/9	125386	Robert Price	05/2019
5347	27953^28198+28198^27953	125381	Norbert Schneider	01/2021
5348	31074^10837+10837^31074	125381	Hans Havermann	03/2021
5349	33745^5194+5194^33745	125380	Hans Havermann	03/2021
5350	2^416490+1875109	125376	Enzo Doria	09/2016
5351	28360^26331+26331^28360	125365	Hans Havermann	03/2021
5352	2^416416-114929	125354	Enzo Doria	05/2015
5353	25805^28412-28412^25805	125346	Frank Doornink	03/2024
5354	(77*10^125330-293)/9	125331	Robert Price	09/2019
5355	(172*10^125292-1)/9	125294	Serge Batalov	12/2014
5356	2^416134+1865899	125269	Enzo Doria	03/2016
5357	153^57337-152	125264	Norbert Schneider	12/2018
5358	(599*10^125224+13)/9	125226	Robert Price	02/2022
5359	(9*2^415992+1)/13560845	125220	Lelio R Paula	05/2014
5360	30054^14657+14657^30054	125207	Hans Havermann	03/2021
5361	(23^91943-1)/22	125201	Robert Price	01/2012
5362	2^415884-933075	125194	Paul Bourdelais	06/2021
5363	43125^27010-106	125185	Enzo Doria	08/2012
5364	(38*10^125166+349)/9	125167	Robert Price	10/2018
5365	10^125166-5001	125166	Robert Price	12/2021
5366	2^415765-112603	125158	Enzo Doria	06/2014
5367	8*10^125088-13	125089	Robert Price	08/2019
5368	(25*10^125076-13)/3	125077	Robert Price	09/2019
5369	(11*10^125054+73)/3	125055	Robert Price	08/2021
5370	(29*10^125021-113)/3	125022	Robert Price	10/2019
5371	2^415290-113591	125015	Enzo Doria	08/2014
5372	2^415276-460919	125011	Enzo Doria	06/2015
5373	2^415259+77243	125006	Enzo Doria	05/2016
5374	(67*10^124990+77)/9	124991	Robert Price	10/2021
5375	2^415144-3683	124971	Yves Minet	10/2011
5376	2^415092+111546435	124956	Paul Bourdelais	10/2021
5377	31936^8173+8173^31936	124946	Hans Havermann	03/2021
5378	27458^28145-28145^27458	124927	Frank Doornink	03/2024
5379	5^178715-4	124917	Tyler NeSmith	07/2021
5380	29767^15700+15700^29767	124900	Hans Havermann	03/2021
5381	(310^50131-1)/309	124892	Tom Wu	07/2024
5382	2^414874+79	124890	Lelio R Paula	01/2015
5383	25292^28361-28361^25292	124874	Frank Doornink	01/2024
5384	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
5385	2^414618+79459	124813	Enzo Doria	06/2016
5386	(61*10^124809-1)/3	124811	Robert Price	01/2020
5387	(29*10^124765-71)/3	124766	Robert Price	07/2021
5388	2^414432-1846709	124757	Enzo Doria	07/2015
5389	2*10^124751-51	124752	Robert Price	04/2018
5390	(56*10^124735+367)/9	124736	Robert Price	06/2019
5391	27362^28111-28111^27362	124733	Frank Doornink	03/2024
5392	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
5393	(23*10^124690+37)/3	124691	Robert Price	02/2022
5394	p(25046)#-p(25046+1)	124675	Henri Lifchitz	11/2024
5395	56*10^124656-3	124658	Robert Price	03/2020
5396	(7*10^124648+197)/3	124649	Robert Price	07/2018
5398	2^414032-5	124637	Henri Lifchitz	07/2006
5397	2^414032+1872331	124637	Enzo Doria	05/2016
5399	37373^2158+2158^37373	124604	Hans Havermann	03/2021
5400	29811^15112+15112^29811	124590	Hans Havermann	03/2021
5401	(22^92791-3^92791)/19	124564	Robert Price	02/2025
5402	F(596093)/36870605281541	124563	Serge Batalov	07/2024
5403	2^413781-2023	124561	Riley Fisher	09/2023
5404	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
5405	29757^15296+15296^29757	124521	Hans Havermann	03/2021
5406	35056^3561+3561^35056	124504	Hans Havermann	03/2021
5407	40588^1167+1167^40588	124487	Hans Havermann	02/2021
5408	(85*10^124485-49)/9	124486	Robert Price	12/2020
5409	64^68909-63^68909	124463	Robert Price	07/2013
5410	35016^3581+3581^35016	124448	Hans Havermann	03/2021
5411	2^413387+76253	124442	Enzo Doria	04/2016
5412	28749^21298+21298^28749	124436	Hans Havermann	03/2021
5413	2^413352+524287	124432	Paul Underwood	09/2018
5414	287117#+391613	124424	Nicolas PALAU	01/2017
5415	(4*10^124420+83)/3	124421	Robert Price	02/2018
5416	34578^3965+3965^34578	124421	Hans Havermann	03/2021
5417	(68*10^124392-329)/9	124393	Robert Price	03/2021
5418	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
5419	10^124383+58407	124384	Patrick De Geest	08/2021
5421	10^124383-8000001	124383	Robert Price	04/2021
5420	10^124383-5801	124383	Patrick De Geest	08/2021
5422	26091^28154-28154^26091	124342	Frank Doornink	03/2024
5423	(41*10^124335-383)/9	124336	Robert Price	11/2018
5424	(304*10^124329-43)/9	124331	Robert Price	02/2020
5425	34716^3811+3811^34716	124320	Hans Havermann	03/2021
5426	26892^28063-28063^26892	124309	Frank Doornink	03/2024
5427	2^412868-120599	124286	Paul Bourdelais	02/2012
5428	10^124248+899089	124249	Patrick De Geest	05/2021
5430	10^124248-1000001	124248	Robert Price	08/2020
5429	10^124248-501903	124248	Patrick De Geest	05/2021
5431	45^75145-2	124231	Lelio R Paula	08/2015
5432	29901^14272+14272^29901	124224	Hans Havermann	03/2021
5433	2^412645-112213	124219	Enzo Doria	06/2014
5434	29837^14500+14500^29837	124163	Hans Havermann	03/2021
5435	28074^26455+26455^28074	124158	Hans Havermann	03/2021
5436	954^41669-41669^954	124155	Norman Luhn	10/2024
5437	432^47093-47093^432	124113	Norman Luhn	10/2024
5438	2^412285+213317	124111	Enzo Doria	09/2023
5439	2^412248+74611	124100	Enzo Doria	04/2016
5440	(22*10^124096-13)/9	124097	Robert Price	06/2018
5441	(455*10^124093+31)/9	124095	Robert Price	06/2021
5442	2^412192-3329	124083	Yves Minet	12/2014
5443	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
5445	(25*10^124076-67)/3	124077	Robert Price	06/2019
5444	28132^25735+25735^28132	124077	Hans Havermann	03/2021
5446	F(593689)	124074	Henri Lifchitz	01/2005
5447	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
5448	1232^40143-40143^1232	124067	Norman Luhn	10/2024
5449	26372^28057-28057^26372	124045	Frank Doornink	03/2024
5450	27528^27937-27937^27528	124034	Frank Doornink	03/2024
5451	35364^3215+3215^35364	124028	Hans Havermann	03/2021
5453	(266*10^124022-11)/3	124024	Robert Price	04/2020
5452	29987^13674+13674^29987	124024	Hans Havermann	03/2021
5454	2^411932-111546435	124004	Paul Bourdelais	10/2021
5455	2^411884-113279	123990	Enzo Doria	07/2014
5456	(2^411832+1)/257	123972	Lelio R Paula	05/2014
5457	(2^411833+2)/514	123972	Stefano Morozzi	03/2020
5458	(26*10^123970-89)/9	123971	Robert Price	06/2018
5459	2^411790-1853531	123962	Enzo Doria	08/2015
5460	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
5461	(101*10^123950+7)/9	123952	Robert Price	02/2022
5462	2^411711-113257	123938	Enzo Doria	07/2014
5463	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
5464	36289^2598+2598^36289	123914	Hans Havermann	03/2021
5465	(11*10^123899-179)/3	123900	Robert Price	09/2018
5466	32276^6879+6879^32276	123860	Hans Havermann	02/2021
5467	2^411325-351103	123822	Enzo Doria	06/2015
5468	(646*10^123817+11)/9	123819	Robert Price	10/2021
5469	30738^10643+10643^30738	123784	Hans Havermann	03/2021
5470	31074^9607+9607^31074	123755	Hans Havermann	03/2021
5471	2^411052+1872481	123739	Enzo Doria	05/2016
5472	34365^3986+3986^34365	123733	Hans Havermann	03/2021
5473	2^410997+39	123723	Lelio R Paula	05/2014
5474	(649^43987-1)/648	123700	Michael Stocker	05/2020
5475	(148*10^123688-1)/3	123690	Robert Price	03/2020
5476	36825^2284+2284^36825	123684	Hans Havermann	03/2021
5477	29582^15171+15171^29582	123683	Hans Havermann	03/2021
5478	10^123671+3593037	123672	Paul Bourdelais	10/2021
5479	8*10^123657+87	123658	Robert Price	10/2019
5480	30505^11302+11302^30505	123642	Hans Havermann	03/2021
5481	29956^13401+13401^29956	123633	Hans Havermann	03/2021
5482	155^56438+154	123618	Norbert Schneider	01/2019
5483	2^410596-39	123602	Lelio R Paula	05/2014
5484	(41*10^123600-221)/9	123601	Robert Price	10/2021
5485	28995^18302+18302^28995	123592	Hans Havermann	03/2021
5486	28302^23269+23269^28302	123589	Hans Havermann	03/2021
5487	(41^76630+40)/37	123587	Alfred Reich	06/2024
5488	2^410540-115079	123585	Enzo Doria	06/2015
5489	(7*10^123563+107)/3	123564	Robert Price	02/2018
5490	9*10^123549+89	123550	Robert Price	11/2019
5491	(197*10^123545+7)/3	123547	Robert Price	12/2020
5492	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
5493	2^410342+212449	123526	Enzo Doria	08/2023
5494	(29*10^123510+277)/9	123511	Robert Price	11/2021
5495	28118^24687+24687^28118	123508	Hans Havermann	03/2021
5496	39994^1225+1225^39994	123507	Hans Havermann	03/2021
5497	2^410206-113081	123485	Enzo Doria	07/2014
5498	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
5499	28974^18215+18215^28974	123442	Hans Havermann	03/2021
5500	28901^18618+18618^28901	123406	Hans Havermann	03/2021

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