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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(444^49408+1)/(444^256+1)	130125	Martin Hopf	12/2023
5252	2^432217+41	130111	Lelio R Paula	06/2017
5253	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
5254	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
5255	97^65480-2	130094	Lelio R Paula	05/2017
5256	36007^4102+4102^36007	130094	Hans Havermann	04/2021
5257	4*10^130088-89	130089	Robert Price	11/2018
5258	2^432117-113215	130081	Enzo Doria	07/2014
5259	(4*10^130080+41)/9	130080	Serge Batalov	11/2022
5260	9583*29^88890+736	129997	Eric Chen	06/2025
5261	2^431804+72511	129986	Enzo Doria	04/2016
5262	27902^29237-29237^27902	129978	Frank Doornink	03/2024
5263	(2313^38809-1)/(2313^197-1)	129898	Ryan Propper	11/2023
5264	(13*10^129896+137)/3	129897	Robert Price	06/2021
5265	(13*10^129890+71)/3	129891	Robert Price	06/2021
5266	29048^29101-29101^29048	129882	Norbert Schneider	03/2022
5267	37832^2709+2709^37832	129871	Hans Havermann	04/2021
5268	31055^15184+15184^31055	129853	Hans Havermann	04/2021
5270	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
5269	Phi(1632846L,3)	129844	Anonymous	03/2025
5271	31385^13702+13702^31385	129833	Hans Havermann	04/2021
5272	(13*10^129826+41)/9	129827	Tyler Busby	02/2023
5273	28901^29102-29102^28901	129822	Norbert Schneider	03/2022
5274	(47*10^129789-119)/9	129790	Robert Price	05/2019
5275	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
5276	25999^29384-29384^25999	129730	Frank Doornink	03/2024
5277	25771^29408-29408^25771	129723	Frank Doornink	02/2024
5278	(166*10^129712+17)/3	129714	Robert Price	07/2022
5279	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
5280	2^430807+1869563	129686	Enzo Doria	05/2016
5281	2^430721-21429	129660	Enzo Doria	07/2013
5282	(4*10^129618+89)/3	129619	Robert Price	08/2021
5283	(142^60223-1)/141	129616	Anonymous	06/2024
5284	(10^129587-7^129587)/3	129587	Jon Grantham	07/2023
5285	2^430415-276271	129568	Enzo Doria	07/2015
5286	32282^10311+10311^32282	129558	Hans Havermann	04/2021
5287	29486^24741+24741^29486	129545	Hans Havermann	04/2021
5288	(29*10^129543+313)/9	129544	Robert Price	04/2021
5289	37095^3104+3104^37095	129533	Hans Havermann	04/2021
5290	31132^14459+14459^31132	129514	Hans Havermann	04/2021
5291	32582^9435+9435^32582	129506	Hans Havermann	03/2021
5292	30442^17953+17953^30442	129505	Hans Havermann	03/2021
5293	(199*10^129487-7)/3	129489	Robert Price	05/2020
5294	2^430142-2791721	129486	Enzo Doria	03/2016
5295	(7*10^129472-13)/3	129473	Robert Price	07/2018
5296	(8*10^129469+79)/3	129470	Robert Price	10/2020
5297	31678^12213+12213^31678	129463	Hans Havermann	04/2021
5298	10620^32143-10619^32143	129412	Norbert Schneider	08/2023
5299	(772*10^129406-7)/9	129408	Robert Price	06/2022
5300	(535^47431-1)/534	129406	Tom Wu	09/2024
5301	((320425-8193)F(618977)-(20425-8193)*L(618977))/2	129363	Yaroslav Berezhko	03/2025
5302	31100^14439+14439^31100	129362	Hans Havermann	04/2021
5303	33009^8288+8288^33009	129345	Hans Havermann	04/2021
5304	25895^29306-29306^25895	129334	Frank Doornink	03/2024
5305	(44^78697+43^78697)/87	129333	Aurel Gibier	11/2023
5306	29675^22804+22804^29675	129324	Hans Havermann	04/2021
5307	29068^28099+28099^29068	129315	Hans Havermann	04/2021
5308	2^429568-21017	129313	Enzo Doria	07/2013
5309	(10^129295+83)/3	129295	Robert Price	08/2021
5310	(853*10^129274-7)/9	129276	Robert Price	07/2021
5311	30958^14961+14961^30958	129249	Hans Havermann	04/2021
5312	(11*10^129239-179)/3	129240	Robert Price	09/2018
5313	28659^28988+28988^28659	129208	Norbert Schneider	02/2021
5314	29423^24616+24616^29423	129203	Hans Havermann	03/2021
5315	2^429194-112685	129201	Enzo Doria	06/2014
5316	31*35^83672+17398	129197	Eric Chen	05/2025
5317	2^429145-2780449	129186	Enzo Doria	04/2016
5318	32500^9427+9427^32500	129168	Hans Havermann	04/2021
5319	33577^7014+7014^33577	129136	Hans Havermann	03/2021
5320	2^428892-113453	129110	Enzo Doria	07/2014
5321	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
5322	2^428727-113959	129060	Enzo Doria	10/2014
5323	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
5324	(10^129051-31)/3	129051	Serge Batalov	12/2014
5325	(3^732836)/(2^732836)	129047	Henri Lifchitz	05/2025
5326	(134*10^129038+7)/3	129040	Robert Price	02/2020
5327	2^428564+71161	129011	Enzo Doria	04/2016
5328	28781^28930+28930^28781	129002	Norbert Schneider	02/2021
5329	29065^27424+27424^29065	128995	Hans Havermann	04/2021
5330	2^428502-113285	128992	Enzo Doria	07/2014
5331	2^428421-21373	128968	Enzo Doria	06/2013
5332	L(616787)	128901	Henri Lifchitz	09/2008
5333	(765^44701-1)/764	128900	Tom Wu	07/2024
5334	20^99055-3	128874	Paul Bourdelais	12/2020
5335	91^65772-2	128851	Lelio R Paula	05/2017
5336	2^428022+43	128848	Lelio R Paula	05/2017
5337	2^427999-459397	128841	Enzo Doria	05/2015
5338	2^427993+76847	128839	Enzo Doria	05/2016
5339	31059^14060+14060^31059	128833	Hans Havermann	03/2021
5340	10^128805+152871	128806	Patrick De Geest	05/2021
5341	10^128805-10001	128805	Robert Price	02/2021
5342	2^427824-1851507	128788	Enzo Doria	08/2015
5343	2^427807-21469	128783	Enzo Doria	07/2013
5344	29082^26783+26783^29082	128772	Hans Havermann	04/2021
5345	40055^1638+1638^40055	128750	Hans Havermann	04/2021
5346	(923^43411-1)/922	128720	Tom Wu	07/2024
5347	11^123594-240	128710	Enzo Doria	09/2012
5348	2^427504-21503	128692	Enzo Doria	07/2013
5349	37727^2574+2574^37727	128673	Hans Havermann	04/2021
5350	29686^21591+21591^29686	128668	Hans Havermann	04/2021
5351	10^128668-70000000001	128668	Robert Price	08/2021
5352	10^128668-350729	128668	Alfred Reich	08/2024
5353	2^427420+91	128667	Lelio R Paula	05/2017
5354	8*10^128651-37	128652	Robert Price	03/2022
5355	(68*10^128645-257)/9	128646	Robert Price	07/2019
5356	2^427269-113635	128621	Enzo Doria	08/2014
5357	2^427130+1877569	128579	Enzo Doria	08/2016
5358	2^427068+20011	128561	Enzo Doria	06/2023
5359	2^427016-115349	128545	Enzo Doria	07/2015
5360	2^427001+1334025	128541	Henri Lifchitz	11/2024
5361	(4*10^128510+137)/3	128511	Robert Price	03/2018
5362	2^426889-112879	128507	Enzo Doria	06/2014
5363	2^426804+1869931	128481	Enzo Doria	05/2016
5364	2^426750+77635	128465	Enzo Doria	05/2016
5365	27708^28913-28913^27708	128450	Frank Doornink	03/2024
5366	36988^2969+2969^36988	128445	Hans Havermann	03/2021
5367	36664^3185+3185^36664	128439	Hans Havermann	03/2021
5368	32618^8649+8649^32618	128416	Hans Havermann	04/2021
5369	28883^27874+27874^28883	128391	Hans Havermann	04/2021
5370	2^426425-91	128367	Lelio R Paula	05/2017
5371	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
5372	2^426352+74971	128345	Enzo Doria	04/2016
5373	(199*10^128343-7)/3	128345	Robert Price	05/2020
5374	4*10^128343-21	128344	Robert Price	09/2018
5375	(65*10^128338+493)/9	128339	Robert Price	08/2021
5376	35632^3997+3997^35632	128337	Hans Havermann	04/2021
5377	2^426300-1863689	128330	Enzo Doria	03/2016
5378	2^426293+1881017	128327	Enzo Doria	11/2016
5379	(88*10^128324-637)/9	128325	Robert Price	11/2020
5380	(491*10^128285+31)/9	128287	Robert Price	04/2022
5381	39103^1908+1908^39103	128281	Hans Havermann	04/2021
5382	2^426043+35	128252	Robert Price	11/2015
5383	(4*10^128244-19)/3	128245	Robert Price	03/2018
5384	26220^29021-29021^26220	128234	Frank Doornink	03/2024
5385	35489^4102+4102^35489	128222	Hans Havermann	04/2021
5386	34721^4926+4926^34721	128208	Hans Havermann	04/2021
5387	(305*10^128198+1)/9	128200	Robert Price	02/2020
5388	2^425808-459959	128181	Enzo Doria	06/2015
5389	30632^15291+15291^30632	128178	Hans Havermann	04/2021
5390	U(623603)	128177	Serge Batalov	07/2024
5391	35981^3648+3648^35981	128167	Hans Havermann	04/2021
5392	2^425627-113605	128127	Enzo Doria	08/2014
5393	(4*10^128109+119)/3	128110	Robert Price	12/2021
5394	(22*10^128094+53)/3	128095	Robert Price	07/2019
5395	(86*10^128086-221)/9	128087	Robert Price	09/2019
5396	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
5397	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
5398	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
5399	Phi(149401,10)/30037901719561	128003	Makoto Kamada	07/2022
5400	2^425205+4911	128000	Marek Hubal	02/2017
5401	29241^23836+23836^29241	127995	Hans Havermann	04/2021
5402	2^425118-113663	127974	Enzo Doria	08/2014
5403	(86*10^127967-329)/9	127968	Robert Price	01/2020
5404	2^425061+1869761	127957	Enzo Doria	05/2016
5405	746^44541+44541^746	127955	Norbert Schneider	07/2019
5406	30236^17043+17043^30236	127946	Hans Havermann	03/2021
5407	2^424938+212419	127920	Enzo Doria	08/2023
5408	2^424918-21141	127914	Enzo Doria	07/2013
5409	(62*10^127903+91)/9	127904	Robert Price	07/2021
5410	2^424864-29489	127897	Enzo Doria	08/2015
5411	30438^15893+15893^30438	127877	Hans Havermann	02/2021
5412	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
5413	28929^26258+26258^28929	127845	Hans Havermann	03/2021
5414	30563^15220+15220^30563	127828	Hans Havermann	03/2021
5415	2^424632-2786639	127827	Enzo Doria	03/2016
5416	10^127821-700001	127821	Robert Price	08/2021
5417	2^424577-113755	127811	Enzo Doria	09/2014
5418	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
5419	(56*10^127752+691)/9	127753	Robert Price	05/2019
5420	11^122629-720	127705	Enzo Doria	11/2012
5421	22*10^127645+3	127647	Robert Price	01/2020
5422	28715^27844+27844^28715	127631	Hans Havermann	03/2021
5423	(56*10^127612+187)/9	127613	Robert Price	10/2021
5424	(5*36^81995+821)/7	127609	Eric Chen	01/2021
5425	4*10^127562-39	127563	Robert Price	09/2020
5426	32595^8186+8186^32595	127547	Hans Havermann	03/2021
5427	2^423696-21429	127546	Enzo Doria	07/2013
5428	2^423664-1864559	127536	Enzo Doria	03/2016
5429	37889^2322+2322^37889	127530	Hans Havermann	03/2021
5430	37668^2429+2429^37668	127523	Hans Havermann	03/2021
5431	3^267267-4	127519	Henri Lifchitz	10/2014
5432	fibonacci(610144)-2	127513	Jon Grantham	08/2023
5433	26253^28852-28852^26253	127503	Frank Doornink	03/2024
5434	(103*10^127491+17)/3	127493	Robert Price	08/2020
5435	29376^21869+21869^29376	127487	Hans Havermann	03/2021
5436	31186^12241+12241^31186	127483	Hans Havermann	02/2021
5437	(19^99689+5^99689)/24	127477	Robert Price	09/2013
5438	27069^28754-28754^27069	127452	Frank Doornink	01/2024
5439	(21*2^423372+1)/101	127447	Lelio R Paula	05/2014
5440	30594^14645+14645^30594	127446	Hans Havermann	03/2021
5441	2^423328-21537	127435	Enzo Doria	07/2013
5442	(67*10^127413-7)/3	127415	Robert Price	01/2020
5443	(5*34^83193+700233)/11	127408	Eric Chen	08/2023
5444	(2*10^127407+73)/3	127407	Robert Price	09/2020
5445	(2^423165-7)/25	127384	Lelio R Paula	05/2015
5446	(7726^32768+1)/13917994151414876602369	127379	Kellen Shenton	04/2021
5447	(4*10^127349+17)/3	127350	Tyler Busby	01/2023
5448	29512^20647+20647^29512	127341	Hans Havermann	03/2021
5449	2^422987-3001935	127332	Paul Bourdelais	07/2023
5450	(112*10^127324+17)/3	127326	Robert Price	03/2020
5452	29565^20252+20252^29565	127321	Hans Havermann	03/2021
5451	232^232^232+1831^1831	127321	Henri Lifchitz	03/2025
5453	fibonacci(609165)-3	127308	Jon Grantham	08/2023
5455	(F(5)^182099-F(4)^182099)/F(3)	127282	Wayne Halsdorf	08/2013
5454	(5^182099-3^182099)/2	127282	Kellen Shenton	05/2022
5456	(16*10^127259+197)/3	127260	Robert Price	04/2019
5457	(26*10^127240+61)/3	127241	Robert Price	10/2019
5458	(234483*27^88884-145)/26	127230	Curtis Bright	05/2015
5459	2^422515-114997	127190	Enzo Doria	06/2015
5460	5*10^127179-3	127180	Robert Price	07/2015
5461	31678^10343+10343^31678	127176	Hans Havermann	03/2021
5462	(44*10^127169-233)/9	127170	Robert Price	01/2019
5463	34947^4352+4352^34947	127162	Hans Havermann	03/2021
5464	6*10^127158+19	127159	Robert Price	11/2021
5465	30469^14902+14902^30469	127155	Hans Havermann	03/2021
5466	5*10^127153+77	127154	Robert Price	12/2018
5467	29941^17620+17620^29941	127130	Hans Havermann	02/2021
5468	31607^10516+10516^31607	127119	Hans Havermann	03/2021
5469	(19*10^127118-97)/3	127119	Robert Price	10/2021
5470	(29*10^127111+691)/9	127112	Robert Price	08/2021
5471	736^44335+44335^736	127104	Norbert Schneider	07/2019
5472	33040^7023+7023^33040	127090	Hans Havermann	03/2021
5473	(4*10^127081+167)/9	127081	Robert Price	03/2022
5474	29748^18661+18661^29748	127052	Hans Havermann	03/2021
5475	27905^28578-28578^27905	127049	Frank Doornink	03/2024
5476	-516776642557847117490*Bern(37960)/34256837217082767928421792453	127042	Thomas Ritschel	06/2017
5477	(78^67141-1)/77	127036	Paul Bourdelais	09/2017
5478	(14*10^127014-137)/3	127015	Robert Price	04/2021
5479	31436^10965+10965^31436	127002	Hans Havermann	03/2021
5480	28905^24758+24758^28905	127001	Hans Havermann	03/2021
5481	2^421860-113285	126993	Enzo Doria	07/2014
5482	(10^127030+7)/81234833/9230384921/6092460488946445358851	126991	Alfred Reich	07/2021
5483	(2^421827-7)/11	126982	Lelio R Paula	05/2015
5484	26268^28729-28729^26268	126966	Frank Doornink	03/2024
5485	11^121910-840	126957	Enzo Doria	12/2012
5486	(56*10^126935+187)/9	126936	Robert Price	10/2021
5487	28915^24538+24538^28915	126933	Hans Havermann	03/2021
5488	(29*10^126928-77)/3	126929	Robert Price	02/2020
5489	(259*10^126919-1)/3	126921	Robert Price	12/2020
5490	10^126919+204567	126920	Patrick De Geest	05/2021
5491	(2^421617+100280245065)	126920	Paul Bourdelais	05/2022
5492	10^126919-100001	126919	Robert Price	07/2020
5493	28340^28503+28503^28340	126907	Norbert Schneider	02/2021
5494	2^421534-3001935	126895	Paul Bourdelais	07/2023
5495	(71^68539+1)/72	126882	Paul Bourdelais	09/2017
5496	(5*10^126871-119)/3	126872	Robert Price	03/2018
5497	331^50339-10004	126846	Enzo Doria	07/2012
5498	2^421363-2790757	126843	Enzo Doria	03/2016
5499	(106*10^126839-1)/3	126841	Serge Batalov	12/2014
5500	37938^2203+2203^37938	126828	Hans Havermann	03/2021

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301678 PRPs in the top)