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 ?
6251	p(23879)#/2+64	118317	Robert Price	03/2017
6252	2^393033+20147	118315	Enzo Doria	08/2023
6253	8*10^118308+59	118309	Robert Price	11/2021
6254	9*10^118282+29	118283	Robert Price	03/2022
6255	(9*35^76602+12877)/34	118279	Eric Chen	05/2025
6256	(238*10^118265-1)/3	118267	Robert Price	04/2020
6258	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
6257	(2^392707+1710)/2	118217	Stefano Morozzi	09/2020
6259	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
6260	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
6261	(2^392567+2750)/2	118175	Stefano Morozzi	01/2021
6262	55*10^118172+3	118174	Robert Price	07/2022
6263	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
6264	27185^22222+22222^27185	118168	Hans Havermann	01/2021
6265	2^392516-29219	118160	Enzo Doria	07/2015
6266	66*10^118155+7	118157	Robert Price	07/2020
6267	Phi(177231,10)	118152	Maksym Voznyy	09/2015
6268	2^392413-112123	118129	Enzo Doria	06/2014
6269	27491^19798+19798^27491	118119	Hans Havermann	02/2021
6270	(49*10^118109-319)/9	118110	Robert Price	10/2021
6271	(2^392342+5)/27	118106	Lelio R Paula	04/2014
6272	(2^392333+1782)/2	118104	Stefano Morozzi	01/2021
6273	2^392300-1841429	118095	Enzo Doria	06/2015
6274	3*2^392260-5	118083	Jon Grantham	07/2023
6275	2^392220+75241	118070	Enzo Doria	04/2016
6276	27836^17409+17409^27836	118047	Hans Havermann	02/2021
6277	(13^118026)%(10^118026)	118026	Henri Lifchitz	05/2025
6278	10^118009+664447	118010	Patrick De Geest	07/2018
6279	10^118009-20001	118009	Robert Price	01/2018
6280	(14*10^117991+61)/3	117992	Robert Price	12/2018
6281	2^391933+5897	117984	Yves Minet	02/2011
6282	2^391912-1849259	117978	Enzo Doria	08/2015
6283	(2*34^77029+1043)/11	117968	Eric Chen	08/2023
6284	5*2^391836-3	117956	Jon Grantham	07/2023
6285	28357^14440+14440^28357	117953	Hans Havermann	02/2021
6286	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
6287	85^61124-61124^85	117934	Norman Luhn	09/2024
6288	(7*10^117930-79)/9	117930	Robert Price	01/2021
6289	27531^19168+19168^27531	117904	Hans Havermann	02/2021
6290	(46*10^117902+683)/9	117903	Robert Price	03/2019
6291	26349^26668-26668^26349	117893	Frank Doornink	03/2024
6292	27670^18189+18189^27670	117869	Hans Havermann	02/2021
6293	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
6294	(56*10^117856+583)/9	117857	Robert Price	08/2021
6295	32169^4606+4606^32169	117846	Hans Havermann	02/2021
6296	(71*10^117803-143)/9	117804	Robert Price	10/2021
6297	2^391324+90901	117801	Yves Minet	02/2011
6298	2^391301-1859923	117794	Enzo Doria	03/2016
6299	2^391261-4131	117782	Yves Minet	02/2018
6300	(2^391211+554)/2	117766	Stefano Morozzi	09/2020
6301	816^40445-40445^816	117764	Norman Luhn	09/2024
6302	38434^1157+1157^38434	117737	Hans Havermann	01/2021
6303	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
6304	(85*10^117719+473)/9	117720	Robert Price	01/2020
6305	(2^391049+582)/2	117718	Stefano Morozzi	09/2020
6306	(21*23^86445-197)/22	117715	Eric Chen	08/2023
6307	31083^6122+6122^31083	117709	Hans Havermann	02/2021
6308	2^390960+1880881	117691	Enzo Doria	11/2016
6309	(71*10^117685+91)/9	117686	Robert Price	04/2022
6311	2^390897-1860553	117672	Enzo Doria	11/2015
6310	(61*10^117671+47)/9	117672	Robert Price	07/2022
6312	2^390889-115003	117670	Enzo Doria	06/2015
6313	12^109010+35	117642	Riley Fisher	08/2023
6314	2^390779-30337	117637	Paul Bourdelais	02/2012
6315	(2^390735+378)/2	117623	Stefano Morozzi	02/2021
6316	11^112916-780	117590	Enzo Doria	12/2012
6317	27641^17916+17916^27641	117564	Hans Havermann	02/2021
6318	27906^16321+16321^27906	117561	Hans Havermann	02/2021
6319	27294^20275+20275^27294	117555	Hans Havermann	02/2021
6320	(2^390473+1002)/2	117544	Stefano Morozzi	09/2020
6321	35912^1875+1875^35912	117541	Hans Havermann	02/2021
6322	(16^97613-5^97613)/11	117537	Robert Price	07/2013
6323	(2^390438+1774)/2	117534	Stefano Morozzi	01/2021
6324	(2^390418+1722)/2	117528	Stefano Morozzi	09/2020
6325	(2^390403+654)/2	117523	Stefano Morozzi	09/2020
6326	(2^390343+2246)/2	117505	Stefano Morozzi	01/2021
6327	28043^15478+15478^28043	117493	Hans Havermann	02/2021
6328	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
6329	37077^1474+1474^37077	117479	Hans Havermann	01/2021
6330	31^78759-30	117459	Theodore Burton	02/2007
6331	(2^390176+1222)/2	117455	Stefano Morozzi	09/2020
6332	(2^390133+1242)/2	117442	Stefano Morozzi	09/2020
6333	(2^390013+2634)/2	117406	Stefano Morozzi	09/2020
6334	3*10^117402+61	117403	Robert Price	09/2020
6335	2^389998+37	117402	Lelio R Paula	03/2013
6336	(2^389977+314)/2	117395	Stefano Morozzi	09/2020
6337	(2^389921+342)/2	117378	Stefano Morozzi	01/2021
6338	71830^43+43^71830	117333	Hans Havermann	01/2021
6339	(2^389768+1582)/2	117332	Stefano Morozzi	09/2020
6340	33802^2951+2951^33802	117292	Hans Havermann	02/2021
6341	(2^561185)%L(561185)	117281	Henri Lifchitz	05/2025
6342	26789^23866+23866^26789	117277	Hans Havermann	02/2021
6343	29^80192-1*80192^29	117273	Dylan Delgado	12/2019
6344	(101*10^117260+7)/9	117262	Robert Price	02/2022
6345	(13*10^117249+161)/3	117250	Robert Price	11/2018
6346	2^389478+43	117245	Lelio R Paula	03/2013
6347	(298*10^117229-7)/3	117231	Robert Price	06/2020
6348	(2^389416+342)/2	117226	Stefano Morozzi	01/2021
6349	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
6350	5*10^117205+23	117206	Robert Price	03/2019
6351	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
6352	27272^19827+19827^27272	117195	Hans Havermann	01/2021
6353	(2^389276+2650)/2	117184	Stefano Morozzi	09/2020
6354	(844*10^117175-7)/9	117177	Robert Price	05/2021
6355	10^117142+209223	117143	Patrick De Geest	04/2018
6357	10^117142-1000000001	117142	Robert Price	03/2018
6356	10^117142-966057	117142	Patrick De Geest	04/2018
6358	10^117135+360577	117136	Patrick De Geest	07/2018
6359	10^117135-401	117135	Robert Price	01/2018
6360	26415^26488-26488^26415	117126	Norbert Schneider	05/2021
6361	4*10^117123+79	117124	Robert Price	08/2018
6362	2^389033-12797413	117111	Enzo Doria	04/2016
6363	(2^388987+2634)/2	117097	Stefano Morozzi	09/2020
6364	2^388960-109505	117089	Enzo Doria	04/2014
6365	7*10^117082-57	117083	Robert Price	06/2020
6366	791^40398-40398^791	117081	Norman Luhn	09/2024
6367	(2^388928-5)/569	117077	Lelio R Paula	03/2014
6368	2^388888-1529	117067	Yves Minet	01/2013
6369	10^117059+28879	117060	Patrick De Geest	05/2016
6370	(10^117059-71)/1	117059	Serge Batalov	12/2014
6371	(2^388854+3630)/2	117057	Stefano Morozzi	09/2020
6372	(2^388842+2098)/2	117053	Stefano Morozzi	09/2020
6373	(2^388789+3150)/2	117037	Stefano Morozzi	09/2020
6374	(2^388748+378)/2	117025	Stefano Morozzi	02/2021
6375	(693^41189-1)/692	117005	Michael Stocker	05/2020
6376	(26*10^116999-503)/9	117000	Robert Price	07/2018
6377	20^89917-21	116985	Anonymous	09/2024
6378	(2^388609+1554)/2	116983	Stefano Morozzi	09/2020
6379	38496^1093+1093^38496	116975	Hans Havermann	02/2021
6380	3^245154-6256	116969	Enzo Doria	05/2014
6381	5*10^116966-43	116967	Robert Price	01/2019
6382	2^388536-113495	116961	Enzo Doria	08/2014
6383	(2^388512+382)/2	116954	Stefano Morozzi	02/2021
6384	(8*32^77701+271)/31	116952	Eric Chen	11/2023
6385	2^388469-43	116941	Lelio R Paula	03/2013
6386	27417^18416+18416^27417	116939	Hans Havermann	02/2021
6387	(2^388438+1842)/2	116932	Stefano Morozzi	02/2021
6388	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
6389	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
6390	2^388180+93	116854	Donovan Johnson	07/2008
6391	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
6392	(85*10^116842+293)/9	116843	Robert Price	12/2019
6393	35296^2043+2043^35296	116840	Hans Havermann	02/2021
6394	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
6395	38633^1056+1056^38633	116814	Hans Havermann	02/2021
6396	2^387946-113261	116784	Enzo Doria	07/2014
6397	28*36^75009+305	116739	Eric Chen	12/2022
6398	28363^13056+13056^28363	116737	Hans Havermann	02/2021
6399	2^387745+75557	116723	Enzo Doria	04/2016
6400	(29*10^116719+313)/9	116720	Robert Price	04/2021
6401	29622^8699+8699^29622	116695	Hans Havermann	02/2021
6402	(206*10^116687-17)/9	116689	Robert Price	01/2020
6403	(7*10^116684+179)/3	116685	Robert Price	09/2018
6404	2^387554+71455	116666	Enzo Doria	04/2016
6405	(602*10^116647-71)/9	116649	Robert Price	12/2021
6406	3^244461-10	116638	Tyler NeSmith	09/2022
6407	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
6408	(2*10^116620+43)/9	116620	Serge Batalov	11/2022
6409	(19*10^116617+287)/9/12893	116614	Alfred Reich	11/2022
6410	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
6411	(25*10^116601-331)/9	116602	Robert Price	08/2018
6412	25791^26428-26428^25791	116587	Frank Doornink	03/2024
6414	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
6413	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
6415	2^387211+111546435	116563	Paul Bourdelais	10/2021
6416	10^116557+987654321	116558	Robert Price	12/2019
6417	10^116557+9141	116558	Patrick De Geest	02/2020
6418	10^116557-609431	116557	Patrick De Geest	02/2020
6419	209^50234-50234^209	116551	Norman Luhn	09/2024
6420	(28*10^116546+41)/3	116547	Robert Price	07/2021
6421	(2^387123+1814)/2	116536	Stefano Morozzi	02/2021
6422	(2^387076+2046)/2	116522	Stefano Morozzi	09/2020
6423	(2^387073+2570)/2	116521	Stefano Morozzi	09/2020
6424	(7*10^116514-1)/3	116515	Robert Price	08/2022
6425	(26*32^77406-390071011)/31	116508	Eric Chen	11/2023
6426	28846^10931+10931^28846	116500	Hans Havermann	02/2021
6427	10^116496+3593037	116497	Paul Bourdelais	10/2021
6428	272^47851-47851^272	116497	Norman Luhn	09/2024
6429	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
6430	(944^39157+1)/945	116489	Jinyuan Wang	12/2024
6431	2^386947+1869143	116483	Enzo Doria	05/2016
6432	(30^78857-1)/29	116480	Robert Price	12/2011
6433	(2^386903-3)/5	116469	Lelio R Paula	03/2014
6434	28107^13892+13892^28107	116441	Hans Havermann	02/2021
6435	29110^9957+9957^29110	116386	Hans Havermann	02/2021
6436	26469^24838+24838^26469	116335	Hans Havermann	01/2021
6437	2^386389-1864783	116315	Enzo Doria	03/2016
6438	(8*32^77250-163)/31	116273	Eric Chen	11/2023
6439	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
6440	297^47012+47012^297	116250	Norbert Schneider	07/2018
6441	(35*10^116223-341)/9	116224	Robert Price	08/2021
6442	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
6443	(2^386054+714)/2	116214	Stefano Morozzi	09/2020
6444	(10^116201+7)/39623	116197	Alfred Reich	06/2021
6445	2^385969-823	116189	Yves Minet	05/2012
6446	57^66162+2	116173	Lelio R Paula	08/2013
6447	2^385854+75049	116154	Enzo Doria	04/2016
6448	(2^385832+2590)/2	116147	Stefano Morozzi	09/2020
6449	2^385775-109587	116130	Enzo Doria	04/2014
6450	(14*10^116112-101)/3	116113	Robert Price	02/2019
6451	Phi(236354,10)/24817171	116109	Makoto Kamada	08/2019
6452	3*10^116107+23	116108	Robert Price	03/2022
6453	28729^10990+10990^28729	116094	Hans Havermann	02/2021
6454	2^385622+71839	116084	Enzo Doria	04/2016
6455	2^385564+781	116067	Lelio R Paula	01/2012
6456	(2^385565+1562)/2	116067	Stefano Morozzi	09/2020
6457	(2^385563+378)/2	116066	Stefano Morozzi	02/2021
6458	(2^385557+2214)/2	116064	Stefano Morozzi	09/2020
6459	29431^8776+8776^29431	116056	Hans Havermann	01/2021
6460	(266*10^116024-17)/3	116026	Robert Price	07/2020
6461	30263^6820+6820^30263	116022	Hans Havermann	02/2021
6462	2^385410+71893	116020	Enzo Doria	04/2016
6463	38225^1084+1084^38225	116014	Hans Havermann	02/2021
6464	26548^23433+23433^26548	116011	Hans Havermann	02/2021
6465	12^107422-11	115928	Riley Fisher	12/2023
6466	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
6467	(11*10^115910-131)/3	115911	Robert Price	09/2018
6468	2^384953-111943	115883	Paul Bourdelais	02/2012
6469	43^70942-2	115882	Lelio R Paula	04/2014
6470	(94*10^115879-7)/3	115881	Robert Price	03/2020
6471	7*10^115863+3	115864	Robert Price	08/2015
6472	2^384834+93	115847	Donovan Johnson	07/2008
6473	2^384809+71297	115840	Enzo Doria	04/2016
6474	(55*10^115829+323)/9	115830	Robert Price	10/2021
6475	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
6476	31348^4951+4951^31348	115822	Hans Havermann	02/2021
6477	(793*10^115810+53)/9	115812	Robert Price	01/2022
6478	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
6479	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
6480	31115^5266+5266^31115	115794	Hans Havermann	02/2021
6481	2*10^115784-27	115785	Robert Price	05/2018
6482	10^115773+126739	115774	Patrick De Geest	04/2018
6484	10^115773-1000000001	115773	Robert Price	03/2018
6483	10^115773-396221	115773	Patrick De Geest	04/2018
6485	(2^384582+778)/2	115771	Stefano Morozzi	09/2020
6486	30537^6178+6178^30537	115762	Hans Havermann	01/2021
6487	2^384530+1874305	115756	Enzo Doria	06/2016
6488	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
6489	28275^12406+12406^28275	115748	Hans Havermann	01/2021
6490	(44*10^115697-413)/9	115698	Robert Price	03/2019
6491	31408^4825+4825^31408	115692	Hans Havermann	02/2021
6492	(2^384317+1026)/2	115691	Stefano Morozzi	09/2020
6493	2^384312+81091	115690	Yves Minet	02/2010
6494	(2^384265+2150)/2	115675	Stefano Morozzi	09/2020
6495	(2^384246+2182)/2	115670	Stefano Morozzi	09/2020
6496	(4*10^115668-79)/3	115669	Robert Price	02/2018
6497	(2^384193+242)/2	115654	Stefano Morozzi	09/2020
6498	(266947#+1267)/(7^2*181)	115647	Makoto Morimoto	06/2019
6499	(266947#+273808)/(2109157)	115646	Makoto Morimoto	10/2017
6500	18^92125-92125^18	115642	Dylan Delgado	08/2019

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301723 PRPs in the top)