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	2^432917+22217	130322	Enzo Doria	09/2023
5252	29387^27112+27112^29387	130278	Hans Havermann	04/2021
5253	2^432768+213181	130277	Enzo Doria	09/2023
5254	29577^25370+25370^29577	130267	Hans Havermann	04/2021
5255	31738^12685+12685^31738	130231	Hans Havermann	03/2021
5256	44235^878+878^44235	130206	Hans Havermann	04/2021
5257	32160^11171+11171^32160	130187	Hans Havermann	04/2021
5258	29489^25956+25956^29489	130172	Hans Havermann	04/2021
5259	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
5260	33005^8766+8766^33005	130133	Hans Havermann	04/2021
5261	(35*10^130132-611)/9	130133	Robert Price	02/2022
5262	(444^49408+1)/(444^256+1)	130125	Martin Hopf	12/2023
5263	2^432217+41	130111	Lelio R Paula	06/2017
5264	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
5265	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
5266	97^65480-2	130094	Lelio R Paula	05/2017
5267	36007^4102+4102^36007	130094	Hans Havermann	04/2021
5268	4*10^130088-89	130089	Robert Price	11/2018
5269	2^432117-113215	130081	Enzo Doria	07/2014
5270	(4*10^130080+41)/9	130080	Serge Batalov	11/2022
5271	9583*29^88890+736	129997	Eric Chen	06/2025
5272	2^431804+72511	129986	Enzo Doria	04/2016
5273	27902^29237-29237^27902	129978	Frank Doornink	03/2024
5274	(2313^38809-1)/(2313^197-1)	129898	Ryan Propper	11/2023
5275	(13*10^129896+137)/3	129897	Robert Price	06/2021
5276	(13*10^129890+71)/3	129891	Robert Price	06/2021
5277	29048^29101-29101^29048	129882	Norbert Schneider	03/2022
5278	37832^2709+2709^37832	129871	Hans Havermann	04/2021
5279	31055^15184+15184^31055	129853	Hans Havermann	04/2021
5281	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
5280	Phi(1632846L,3)	129844	Anonymous	03/2025
5282	31385^13702+13702^31385	129833	Hans Havermann	04/2021
5283	(13*10^129826+41)/9	129827	Tyler Busby	02/2023
5284	28901^29102-29102^28901	129822	Norbert Schneider	03/2022
5285	(47*10^129789-119)/9	129790	Robert Price	05/2019
5286	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
5287	25999^29384-29384^25999	129730	Frank Doornink	03/2024
5288	25771^29408-29408^25771	129723	Frank Doornink	02/2024
5289	(166*10^129712+17)/3	129714	Robert Price	07/2022
5290	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
5291	2^430807+1869563	129686	Enzo Doria	05/2016
5292	2^430721-21429	129660	Enzo Doria	07/2013
5293	(4*10^129618+89)/3	129619	Robert Price	08/2021
5294	(142^60223-1)/141	129616	Anonymous	06/2024
5295	(10^129587-7^129587)/3	129587	Jon Grantham	07/2023
5296	2^430415-276271	129568	Enzo Doria	07/2015
5297	32282^10311+10311^32282	129558	Hans Havermann	04/2021
5298	29486^24741+24741^29486	129545	Hans Havermann	04/2021
5299	(29*10^129543+313)/9	129544	Robert Price	04/2021
5300	37095^3104+3104^37095	129533	Hans Havermann	04/2021
5301	31132^14459+14459^31132	129514	Hans Havermann	04/2021
5302	32582^9435+9435^32582	129506	Hans Havermann	03/2021
5303	30442^17953+17953^30442	129505	Hans Havermann	03/2021
5304	(199*10^129487-7)/3	129489	Robert Price	05/2020
5305	2^430142-2791721	129486	Enzo Doria	03/2016
5306	(7*10^129472-13)/3	129473	Robert Price	07/2018
5307	(8*10^129469+79)/3	129470	Robert Price	10/2020
5308	31678^12213+12213^31678	129463	Hans Havermann	04/2021
5309	10620^32143-10619^32143	129412	Norbert Schneider	08/2023
5310	(772*10^129406-7)/9	129408	Robert Price	06/2022
5311	(535^47431-1)/534	129406	Tom Wu	09/2024
5312	((320425-8193)F(618977)-(20425-8193)*L(618977))/2	129363	Yaroslav Berezhko	03/2025
5313	31100^14439+14439^31100	129362	Hans Havermann	04/2021
5314	33009^8288+8288^33009	129345	Hans Havermann	04/2021
5315	25895^29306-29306^25895	129334	Frank Doornink	03/2024
5316	(44^78697+43^78697)/87	129333	Aurel Gibier	11/2023
5317	29675^22804+22804^29675	129324	Hans Havermann	04/2021
5318	29068^28099+28099^29068	129315	Hans Havermann	04/2021
5319	2^429568-21017	129313	Enzo Doria	07/2013
5320	(10^129295+83)/3	129295	Robert Price	08/2021
5321	(853*10^129274-7)/9	129276	Robert Price	07/2021
5322	30958^14961+14961^30958	129249	Hans Havermann	04/2021
5323	(11*10^129239-179)/3	129240	Robert Price	09/2018
5324	28659^28988+28988^28659	129208	Norbert Schneider	02/2021
5325	29423^24616+24616^29423	129203	Hans Havermann	03/2021
5326	2^429194-112685	129201	Enzo Doria	06/2014
5327	31*35^83672+17398	129197	Eric Chen	05/2025
5328	2^429145-2780449	129186	Enzo Doria	04/2016
5329	32500^9427+9427^32500	129168	Hans Havermann	04/2021
5330	33577^7014+7014^33577	129136	Hans Havermann	03/2021
5331	2^428892-113453	129110	Enzo Doria	07/2014
5332	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
5333	2^428727-113959	129060	Enzo Doria	10/2014
5334	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
5335	(10^129051-31)/3	129051	Serge Batalov	12/2014
5336	(3^732836)/(2^732836)	129047	Henri Lifchitz	05/2025
5337	(134*10^129038+7)/3	129040	Robert Price	02/2020
5338	2^428564+71161	129011	Enzo Doria	04/2016
5339	28781^28930+28930^28781	129002	Norbert Schneider	02/2021
5340	29065^27424+27424^29065	128995	Hans Havermann	04/2021
5341	2^428502-113285	128992	Enzo Doria	07/2014
5342	2^428421-21373	128968	Enzo Doria	06/2013
5343	L(616787)	128901	Henri Lifchitz	09/2008
5344	(765^44701-1)/764	128900	Tom Wu	07/2024
5345	20^99055-3	128874	Paul Bourdelais	12/2020
5346	91^65772-2	128851	Lelio R Paula	05/2017
5347	2^428022+43	128848	Lelio R Paula	05/2017
5348	2^427999-459397	128841	Enzo Doria	05/2015
5349	2^427993+76847	128839	Enzo Doria	05/2016
5350	31059^14060+14060^31059	128833	Hans Havermann	03/2021
5351	10^128805+152871	128806	Patrick De Geest	05/2021
5352	10^128805-10001	128805	Robert Price	02/2021
5353	2^427824-1851507	128788	Enzo Doria	08/2015
5354	2^427807-21469	128783	Enzo Doria	07/2013
5355	29082^26783+26783^29082	128772	Hans Havermann	04/2021
5356	40055^1638+1638^40055	128750	Hans Havermann	04/2021
5357	(923^43411-1)/922	128720	Tom Wu	07/2024
5358	11^123594-240	128710	Enzo Doria	09/2012
5359	2^427504-21503	128692	Enzo Doria	07/2013
5360	37727^2574+2574^37727	128673	Hans Havermann	04/2021
5361	29686^21591+21591^29686	128668	Hans Havermann	04/2021
5362	10^128668-70000000001	128668	Robert Price	08/2021
5363	10^128668-350729	128668	Alfred Reich	08/2024
5364	2^427420+91	128667	Lelio R Paula	05/2017
5365	8*10^128651-37	128652	Robert Price	03/2022
5366	(68*10^128645-257)/9	128646	Robert Price	07/2019
5367	2^427269-113635	128621	Enzo Doria	08/2014
5368	2^427130+1877569	128579	Enzo Doria	08/2016
5369	2^427068+20011	128561	Enzo Doria	06/2023
5370	2^427016-115349	128545	Enzo Doria	07/2015
5371	2^427001+1334025	128541	Henri Lifchitz	11/2024
5372	(4*10^128510+137)/3	128511	Robert Price	03/2018
5373	2^426889-112879	128507	Enzo Doria	06/2014
5374	2^426804+1869931	128481	Enzo Doria	05/2016
5375	2^426750+77635	128465	Enzo Doria	05/2016
5376	27708^28913-28913^27708	128450	Frank Doornink	03/2024
5377	36988^2969+2969^36988	128445	Hans Havermann	03/2021
5378	36664^3185+3185^36664	128439	Hans Havermann	03/2021
5379	32618^8649+8649^32618	128416	Hans Havermann	04/2021
5380	28883^27874+27874^28883	128391	Hans Havermann	04/2021
5381	2^426425-91	128367	Lelio R Paula	05/2017
5382	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
5383	2^426352+74971	128345	Enzo Doria	04/2016
5384	(199*10^128343-7)/3	128345	Robert Price	05/2020
5385	4*10^128343-21	128344	Robert Price	09/2018
5386	(65*10^128338+493)/9	128339	Robert Price	08/2021
5387	35632^3997+3997^35632	128337	Hans Havermann	04/2021
5388	2^426300-1863689	128330	Enzo Doria	03/2016
5389	2^426293+1881017	128327	Enzo Doria	11/2016
5390	(88*10^128324-637)/9	128325	Robert Price	11/2020
5391	(491*10^128285+31)/9	128287	Robert Price	04/2022
5392	39103^1908+1908^39103	128281	Hans Havermann	04/2021
5393	2^426043+35	128252	Robert Price	11/2015
5394	(4*10^128244-19)/3	128245	Robert Price	03/2018
5395	26220^29021-29021^26220	128234	Frank Doornink	03/2024
5396	35489^4102+4102^35489	128222	Hans Havermann	04/2021
5397	34721^4926+4926^34721	128208	Hans Havermann	04/2021
5398	(305*10^128198+1)/9	128200	Robert Price	02/2020
5399	2^425808-459959	128181	Enzo Doria	06/2015
5400	30632^15291+15291^30632	128178	Hans Havermann	04/2021
5401	U(623603)	128177	Serge Batalov	07/2024
5402	35981^3648+3648^35981	128167	Hans Havermann	04/2021
5403	2^425627-113605	128127	Enzo Doria	08/2014
5404	(4*10^128109+119)/3	128110	Robert Price	12/2021
5405	(22*10^128094+53)/3	128095	Robert Price	07/2019
5406	(86*10^128086-221)/9	128087	Robert Price	09/2019
5407	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
5408	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
5409	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
5410	Phi(149401,10)/30037901719561	128003	Makoto Kamada	07/2022
5411	2^425205+4911	128000	Marek Hubal	02/2017
5412	29241^23836+23836^29241	127995	Hans Havermann	04/2021
5413	2^425118-113663	127974	Enzo Doria	08/2014
5414	(86*10^127967-329)/9	127968	Robert Price	01/2020
5415	2^425061+1869761	127957	Enzo Doria	05/2016
5416	746^44541+44541^746	127955	Norbert Schneider	07/2019
5417	30236^17043+17043^30236	127946	Hans Havermann	03/2021
5418	2^424938+212419	127920	Enzo Doria	08/2023
5419	2^424918-21141	127914	Enzo Doria	07/2013
5420	(62*10^127903+91)/9	127904	Robert Price	07/2021
5421	2^424864-29489	127897	Enzo Doria	08/2015
5422	30438^15893+15893^30438	127877	Hans Havermann	02/2021
5423	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
5424	28929^26258+26258^28929	127845	Hans Havermann	03/2021
5425	30563^15220+15220^30563	127828	Hans Havermann	03/2021
5426	2^424632-2786639	127827	Enzo Doria	03/2016
5427	10^127821-700001	127821	Robert Price	08/2021
5428	2^424577-113755	127811	Enzo Doria	09/2014
5429	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
5430	(56*10^127752+691)/9	127753	Robert Price	05/2019
5431	11^122629-720	127705	Enzo Doria	11/2012
5432	22*10^127645+3	127647	Robert Price	01/2020
5433	28715^27844+27844^28715	127631	Hans Havermann	03/2021
5434	(56*10^127612+187)/9	127613	Robert Price	10/2021
5435	(5*36^81995+821)/7	127609	Eric Chen	01/2021
5436	4*10^127562-39	127563	Robert Price	09/2020
5437	32595^8186+8186^32595	127547	Hans Havermann	03/2021
5438	2^423696-21429	127546	Enzo Doria	07/2013
5439	2^423664-1864559	127536	Enzo Doria	03/2016
5440	37889^2322+2322^37889	127530	Hans Havermann	03/2021
5441	37668^2429+2429^37668	127523	Hans Havermann	03/2021
5442	3^267267-4	127519	Henri Lifchitz	10/2014
5443	fibonacci(610144)-2	127513	Jon Grantham	08/2023
5444	26253^28852-28852^26253	127503	Frank Doornink	03/2024
5445	(103*10^127491+17)/3	127493	Robert Price	08/2020
5446	29376^21869+21869^29376	127487	Hans Havermann	03/2021
5447	31186^12241+12241^31186	127483	Hans Havermann	02/2021
5448	(19^99689+5^99689)/24	127477	Robert Price	09/2013
5449	27069^28754-28754^27069	127452	Frank Doornink	01/2024
5450	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
5451	30594^14645+14645^30594	127446	Hans Havermann	03/2021
5452	2^423328-21537	127435	Enzo Doria	07/2013
5453	(67*10^127413-7)/3	127415	Robert Price	01/2020
5454	(5*34^83193+700233)/11	127408	Eric Chen	08/2023
5455	(2*10^127407+73)/3	127407	Robert Price	09/2020
5456	(2^423165-7)/25	127384	Lelio R Paula	05/2015
5457	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
5458	(4*10^127349+17)/3	127350	Tyler Busby	01/2023
5459	29512^20647+20647^29512	127341	Hans Havermann	03/2021
5460	2^422987-3001935	127332	Paul Bourdelais	07/2023
5461	(112*10^127324+17)/3	127326	Robert Price	03/2020
5463	29565^20252+20252^29565	127321	Hans Havermann	03/2021
5462	232^232^232+1831^1831	127321	Henri Lifchitz	03/2025
5464	fibonacci(609165)-3	127308	Jon Grantham	08/2023
5466	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
5465	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
5467	(16*10^127259+197)/3	127260	Robert Price	04/2019
5468	(26*10^127240+61)/3	127241	Robert Price	10/2019
5469	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
5470	2^422515-114997	127190	Enzo Doria	06/2015
5471	5*10^127179-3	127180	Robert Price	07/2015
5472	31678^10343+10343^31678	127176	Hans Havermann	03/2021
5473	(44*10^127169-233)/9	127170	Robert Price	01/2019
5474	34947^4352+4352^34947	127162	Hans Havermann	03/2021
5475	6*10^127158+19	127159	Robert Price	11/2021
5476	30469^14902+14902^30469	127155	Hans Havermann	03/2021
5477	5*10^127153+77	127154	Robert Price	12/2018
5478	29941^17620+17620^29941	127130	Hans Havermann	02/2021
5479	31607^10516+10516^31607	127119	Hans Havermann	03/2021
5480	(19*10^127118-97)/3	127119	Robert Price	10/2021
5481	(29*10^127111+691)/9	127112	Robert Price	08/2021
5482	736^44335+44335^736	127104	Norbert Schneider	07/2019
5483	33040^7023+7023^33040	127090	Hans Havermann	03/2021
5484	(4*10^127081+167)/9	127081	Robert Price	03/2022
5485	29748^18661+18661^29748	127052	Hans Havermann	03/2021
5486	27905^28578-28578^27905	127049	Frank Doornink	03/2024
5487	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
5488	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
5489	(14*10^127014-137)/3	127015	Robert Price	04/2021
5490	31436^10965+10965^31436	127002	Hans Havermann	03/2021
5491	28905^24758+24758^28905	127001	Hans Havermann	03/2021
5492	2^421860-113285	126993	Enzo Doria	07/2014
5493	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
5494	(2^421827-7)/11	126982	Lelio R Paula	05/2015
5495	26268^28729-28729^26268	126966	Frank Doornink	03/2024
5496	11^121910-840	126957	Enzo Doria	12/2012
5497	(56*10^126935+187)/9	126936	Robert Price	10/2021
5498	28915^24538+24538^28915	126933	Hans Havermann	03/2021
5499	(29*10^126928-77)/3	126929	Robert Price	02/2020
5500	(259*10^126919-1)/3	126921	Robert Price	12/2020

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Probable Primes Top 10000

(301692 PRPs in the top)