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 ?
6251	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
6252	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
6253	(23^119099)%(10^119099)	119099	Henri Lifchitz	05/2025
6254	29548^10725+10725^29548	119091	Hans Havermann	02/2021
6255	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
6256	(30^80599+1)/31	119054	Robert Price	07/2013
6257	(232*10^119047+17)/3	119049	Robert Price	04/2021
6258	(43*10^119024-403)/9	119025	Robert Price	01/2019
6259	(4*10^119021+47)/3	119022	Robert Price	01/2022
6260	fibonacci(569433)+3	119005	Jon Grantham	08/2023
6261	26603^26888-26888^26603	118978	Norbert Schneider	07/2021
6262	912^40193-40193^912	118972	Norman Luhn	09/2024
6263	681^41992-41992^681	118970	Norman Luhn	09/2024
6264	6*10^118964+43	118965	Robert Price	07/2020
6265	(8*10^118960+49)/3	118961	Robert Price	05/2020
6266	31253^6402+6402^31253	118959	Hans Havermann	02/2021
6267	(194*10^118925-17)/3	118927	Robert Price	09/2020
6268	2^395062-109121	118926	Enzo Doria	04/2014
6269	2^395055-4627	118924	Yves Minet	05/2019
6270	(2^395054+702)/2	118923	Stefano Morozzi	09/2020
6271	2^395018-224141	118913	Harrison Mesh	06/2022
6272	(2^395011+2526)/2	118910	Stefano Morozzi	09/2020
6273	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
6274	25771^26948-26948^25771	118872	Frank Doornink	02/2024
6275	374^46201-46201^374	118870	Norman Luhn	09/2024
6276	(2^394858+1018)/2	118864	Stefano Morozzi	09/2020
6277	(77*10^118862-149)/9	118863	Robert Price	03/2022
6278	(16*10^118852+77)/3	118853	Robert Price	03/2019
6279	fibonacci(568658)-2	118843	Jon Grantham	08/2023
6280	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
6281	10^118772+163599	118773	Patrick De Geest	02/2021
6283	10^118772-40000000001	118772	Robert Price	09/2020
6282	10^118772-207603	118772	Patrick De Geest	02/2021
6284	26842^26577+26577^26842	118763	Hans Havermann	02/2021
6285	(2^394513+2034)/2	118760	Stefano Morozzi	09/2020
6286	(2^394473+2774)/2	118748	Stefano Morozzi	02/2021
6287	27949^17710+17710^27949	118734	Hans Havermann	02/2021
6288	2^394266+71389	118686	Enzo Doria	04/2016
6289	(10^118681-3^118681)/7	118681	Jon Grantham	08/2023
6290	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
6291	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
6292	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
6293	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
6294	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
6295	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
6296	29201^11568+11568^29201	118652	Hans Havermann	02/2021
6297	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
6298	(2^394131+2214)/2	118645	Stefano Morozzi	09/2020
6299	(17*10^118635+13)/3	118636	Robert Price	01/2019
6300	5^169727+2	118635	Lelio R Paula	08/2013
6301	2^394034-3	118617	M. Frind & P. Underwood	09/2002
6302	(7*10^118607+179)/3	118608	Robert Price	09/2018
6303	3^248572-6242	118599	Enzo Doria	05/2014
6304	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
6305	(49*10^118576-319)/9	118577	Robert Price	10/2021
6306	7^140303-6	118570	Robert Price	11/2014
6307	(2^393864+2686)/2	118565	Stefano Morozzi	09/2020
6308	(2^393862+3150)/2	118564	Stefano Morozzi	09/2020
6309	(2^393849+3762)/2	118561	Stefano Morozzi	01/2021
6310	(529*10^118554-7)/9	118556	Robert Price	08/2021
6311	26712^26777-26777^26712	118534	Norbert Schneider	07/2021
6312	(2^393661+2666)/2	118504	Stefano Morozzi	09/2020
6313	(2^393650+1614)/2	118501	Stefano Morozzi	09/2020
6314	27655^19264+19264^27655	118495	Hans Havermann	02/2021
6315	10^118485+469413	118486	Patrick De Geest	05/2021
6316	10^118485-50001	118485	Robert Price	08/2020
6317	(2^393528+1030)/2	118464	Stefano Morozzi	09/2020
6318	2^393427+75683	118434	Enzo Doria	04/2016
6319	2^393376-114749	118418	Enzo Doria	04/2015
6320	(65*10^118417+493)/9	118418	Robert Price	08/2021
6321	30960^6671+6671^30960	118397	Hans Havermann	02/2021
6322	(2^393234+2010)/2	118375	Stefano Morozzi	09/2020
6323	(2^393205+3030)/2	118367	Stefano Morozzi	09/2020
6324	(2^393191+2174)/2	118362	Stefano Morozzi	09/2020
6325	2^393180+73	118359	Lelio R Paula	04/2013
6326	3*2^393125+5	118343	Jon Grantham	07/2023
6327	27546^19771+19771^27546	118339	Hans Havermann	02/2021
6328	822^40595-40595^822	118330	Norman Luhn	09/2024
6329	p(23881)#/2+256	118328	Robert Price	05/2017
6330	(10^118324+359)/9	118324	Serge Batalov	12/2014
6331	(2^393048+570)/2	118319	Stefano Morozzi	09/2020
6332	p(23879)#/2+64	118317	Robert Price	03/2017
6333	2^393033+20147	118315	Enzo Doria	08/2023
6334	8*10^118308+59	118309	Robert Price	11/2021
6335	9*10^118282+29	118283	Robert Price	03/2022
6336	(9*35^76602+12877)/34	118279	Eric Chen	05/2025
6337	(238*10^118265-1)/3	118267	Robert Price	04/2020
6339	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
6338	(2^392707+1710)/2	118217	Stefano Morozzi	09/2020
6340	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
6341	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
6342	(2^392567+2750)/2	118175	Stefano Morozzi	01/2021
6343	55*10^118172+3	118174	Robert Price	07/2022
6344	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
6345	27185^22222+22222^27185	118168	Hans Havermann	01/2021
6346	2^392516-29219	118160	Enzo Doria	07/2015
6347	66*10^118155+7	118157	Robert Price	07/2020
6348	Phi(177231,10)	118152	Maksym Voznyy	09/2015
6349	2^392413-112123	118129	Enzo Doria	06/2014
6350	27491^19798+19798^27491	118119	Hans Havermann	02/2021
6351	(49*10^118109-319)/9	118110	Robert Price	10/2021
6352	(2^392342+5)/27	118106	Lelio R Paula	04/2014
6353	(2^392333+1782)/2	118104	Stefano Morozzi	01/2021
6354	2^392300-1841429	118095	Enzo Doria	06/2015
6355	3*2^392260-5	118083	Jon Grantham	07/2023
6356	2^392220+75241	118070	Enzo Doria	04/2016
6357	27836^17409+17409^27836	118047	Hans Havermann	02/2021
6358	(13^118026)%(10^118026)	118026	Henri Lifchitz	05/2025
6359	10^118009+664447	118010	Patrick De Geest	07/2018
6360	10^118009-20001	118009	Robert Price	01/2018
6361	(14*10^117991+61)/3	117992	Robert Price	12/2018
6362	2^391933+5897	117984	Yves Minet	02/2011
6363	2^391912-1849259	117978	Enzo Doria	08/2015
6364	(2*34^77029+1043)/11	117968	Eric Chen	08/2023
6365	5*2^391836-3	117956	Jon Grantham	07/2023
6366	28357^14440+14440^28357	117953	Hans Havermann	02/2021
6367	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
6368	85^61124-61124^85	117934	Norman Luhn	09/2024
6369	(7*10^117930-79)/9	117930	Robert Price	01/2021
6370	27531^19168+19168^27531	117904	Hans Havermann	02/2021
6371	(46*10^117902+683)/9	117903	Robert Price	03/2019
6372	26349^26668-26668^26349	117893	Frank Doornink	03/2024
6373	27670^18189+18189^27670	117869	Hans Havermann	02/2021
6374	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
6375	(56*10^117856+583)/9	117857	Robert Price	08/2021
6376	32169^4606+4606^32169	117846	Hans Havermann	02/2021
6377	(71*10^117803-143)/9	117804	Robert Price	10/2021
6378	2^391324+90901	117801	Yves Minet	02/2011
6379	2^391301-1859923	117794	Enzo Doria	03/2016
6380	2^391261-4131	117782	Yves Minet	02/2018
6381	(2^391211+554)/2	117766	Stefano Morozzi	09/2020
6382	816^40445-40445^816	117764	Norman Luhn	09/2024
6383	38434^1157+1157^38434	117737	Hans Havermann	01/2021
6384	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
6385	(85*10^117719+473)/9	117720	Robert Price	01/2020
6386	(2^391049+582)/2	117718	Stefano Morozzi	09/2020
6387	(21*23^86445-197)/22	117715	Eric Chen	08/2023
6388	31083^6122+6122^31083	117709	Hans Havermann	02/2021
6389	2^390960+1880881	117691	Enzo Doria	11/2016
6390	(71*10^117685+91)/9	117686	Robert Price	04/2022
6392	2^390897-1860553	117672	Enzo Doria	11/2015
6391	(61*10^117671+47)/9	117672	Robert Price	07/2022
6393	2^390889-115003	117670	Enzo Doria	06/2015
6394	12^109010+35	117642	Riley Fisher	08/2023
6395	2^390779-30337	117637	Paul Bourdelais	02/2012
6396	(2^390735+378)/2	117623	Stefano Morozzi	02/2021
6397	11^112916-780	117590	Enzo Doria	12/2012
6398	27641^17916+17916^27641	117564	Hans Havermann	02/2021
6399	27906^16321+16321^27906	117561	Hans Havermann	02/2021
6400	27294^20275+20275^27294	117555	Hans Havermann	02/2021
6401	(2^390473+1002)/2	117544	Stefano Morozzi	09/2020
6402	35912^1875+1875^35912	117541	Hans Havermann	02/2021
6403	(16^97613-5^97613)/11	117537	Robert Price	07/2013
6404	(2^390438+1774)/2	117534	Stefano Morozzi	01/2021
6405	(2^390418+1722)/2	117528	Stefano Morozzi	09/2020
6406	(2^390403+654)/2	117523	Stefano Morozzi	09/2020
6407	(2^390343+2246)/2	117505	Stefano Morozzi	01/2021
6408	28043^15478+15478^28043	117493	Hans Havermann	02/2021
6409	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
6410	37077^1474+1474^37077	117479	Hans Havermann	01/2021
6411	31^78759-30	117459	Theodore Burton	02/2007
6412	(2^390176+1222)/2	117455	Stefano Morozzi	09/2020
6413	(2^390133+1242)/2	117442	Stefano Morozzi	09/2020
6414	(2^390013+2634)/2	117406	Stefano Morozzi	09/2020
6415	3*10^117402+61	117403	Robert Price	09/2020
6416	2^389998+37	117402	Lelio R Paula	03/2013
6417	(2^389977+314)/2	117395	Stefano Morozzi	09/2020
6418	(2^389921+342)/2	117378	Stefano Morozzi	01/2021
6419	71830^43+43^71830	117333	Hans Havermann	01/2021
6420	(2^389768+1582)/2	117332	Stefano Morozzi	09/2020
6421	33802^2951+2951^33802	117292	Hans Havermann	02/2021
6422	(2^561185)%L(561185)	117281	Henri Lifchitz	05/2025
6423	26789^23866+23866^26789	117277	Hans Havermann	02/2021
6424	29^80192-1*80192^29	117273	Dylan Delgado	12/2019
6425	(101*10^117260+7)/9	117262	Robert Price	02/2022
6426	(13*10^117249+161)/3	117250	Robert Price	11/2018
6427	2^389478+43	117245	Lelio R Paula	03/2013
6428	(298*10^117229-7)/3	117231	Robert Price	06/2020
6429	(2^389416+342)/2	117226	Stefano Morozzi	01/2021
6430	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
6431	5*10^117205+23	117206	Robert Price	03/2019
6432	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
6433	27272^19827+19827^27272	117195	Hans Havermann	01/2021
6434	(2^389276+2650)/2	117184	Stefano Morozzi	09/2020
6435	(844*10^117175-7)/9	117177	Robert Price	05/2021
6436	10^117142+209223	117143	Patrick De Geest	04/2018
6438	10^117142-1000000001	117142	Robert Price	03/2018
6437	10^117142-966057	117142	Patrick De Geest	04/2018
6439	10^117135+360577	117136	Patrick De Geest	07/2018
6440	10^117135-401	117135	Robert Price	01/2018
6441	26415^26488-26488^26415	117126	Norbert Schneider	05/2021
6442	4*10^117123+79	117124	Robert Price	08/2018
6443	2^389033-12797413	117111	Enzo Doria	04/2016
6444	(2^388987+2634)/2	117097	Stefano Morozzi	09/2020
6445	2^388960-109505	117089	Enzo Doria	04/2014
6446	7*10^117082-57	117083	Robert Price	06/2020
6447	791^40398-40398^791	117081	Norman Luhn	09/2024
6448	(2^388928-5)/569	117077	Lelio R Paula	03/2014
6449	2^388888-1529	117067	Yves Minet	01/2013
6450	10^117059+28879	117060	Patrick De Geest	05/2016
6451	(10^117059-71)/1	117059	Serge Batalov	12/2014
6452	(2^388854+3630)/2	117057	Stefano Morozzi	09/2020
6453	(2^388842+2098)/2	117053	Stefano Morozzi	09/2020
6454	(2^388789+3150)/2	117037	Stefano Morozzi	09/2020
6455	(2^388748+378)/2	117025	Stefano Morozzi	02/2021
6456	(693^41189-1)/692	117005	Michael Stocker	05/2020
6457	(26*10^116999-503)/9	117000	Robert Price	07/2018
6458	20^89917-21	116985	Anonymous	09/2024
6459	(2^388609+1554)/2	116983	Stefano Morozzi	09/2020
6460	38496^1093+1093^38496	116975	Hans Havermann	02/2021
6461	3^245154-6256	116969	Enzo Doria	05/2014
6462	5*10^116966-43	116967	Robert Price	01/2019
6463	2^388536-113495	116961	Enzo Doria	08/2014
6464	(2^388512+382)/2	116954	Stefano Morozzi	02/2021
6465	(8*32^77701+271)/31	116952	Eric Chen	11/2023
6466	2^388469-43	116941	Lelio R Paula	03/2013
6467	27417^18416+18416^27417	116939	Hans Havermann	02/2021
6468	(2^388438+1842)/2	116932	Stefano Morozzi	02/2021
6469	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
6470	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
6471	2^388180+93	116854	Donovan Johnson	07/2008
6472	(2^388167+2510)/2	116850	Stefano Morozzi	09/2020
6473	(85*10^116842+293)/9	116843	Robert Price	12/2019
6474	35296^2043+2043^35296	116840	Hans Havermann	02/2021
6475	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
6476	38633^1056+1056^38633	116814	Hans Havermann	02/2021
6477	2^387946-113261	116784	Enzo Doria	07/2014
6478	28*36^75009+305	116739	Eric Chen	12/2022
6479	28363^13056+13056^28363	116737	Hans Havermann	02/2021
6480	2^387745+75557	116723	Enzo Doria	04/2016
6481	(29*10^116719+313)/9	116720	Robert Price	04/2021
6482	29622^8699+8699^29622	116695	Hans Havermann	02/2021
6483	(206*10^116687-17)/9	116689	Robert Price	01/2020
6484	(7*10^116684+179)/3	116685	Robert Price	09/2018
6485	2^387554+71455	116666	Enzo Doria	04/2016
6486	(602*10^116647-71)/9	116649	Robert Price	12/2021
6487	3^244461-10	116638	Tyler NeSmith	09/2022
6488	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
6489	(2*10^116620+43)/9	116620	Serge Batalov	11/2022
6490	(19*10^116617+287)/9/12893	116614	Alfred Reich	11/2022
6491	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
6492	(25*10^116601-331)/9	116602	Robert Price	08/2018
6493	25791^26428-26428^25791	116587	Frank Doornink	03/2024
6495	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
6494	(2^387284+3726)/2	116584	Stefano Morozzi	09/2020
6496	2^387211+111546435	116563	Paul Bourdelais	10/2021
6497	10^116557+987654321	116558	Robert Price	12/2019
6498	10^116557+9141	116558	Patrick De Geest	02/2020
6499	10^116557-609431	116557	Patrick De Geest	02/2020
6500	209^50234-50234^209	116551	Norman Luhn	09/2024

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PRP Records

Probable Primes Top 10000

(301822 PRPs in the top)