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	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
6252	(10^119836+77)/3	119836	Robert Price	01/2018
6253	26681^27074-27074^26681	119835	Frank Doornink	03/2024
6254	28179^17870+17870^28179	119821	Hans Havermann	02/2021
6255	2^398029+1872527	119819	Enzo Doria	05/2016
6256	33142^4119+4119^33142	119802	Hans Havermann	01/2021
6257	2^397897-113541	119779	Enzo Doria	08/2014
6258	28636^15171+15171^28636	119728	Hans Havermann	02/2021
6259	87^61730-61730^87	119727	Norman Luhn	09/2024
6260	(10556^29929-1)/(10556^173-1)	119724	Ryan Propper	11/2023
6261	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
6263	(19*10^119716+101)/3	119717	Robert Price	09/2019
6262	29563^11208+11208^29563	119717	Hans Havermann	02/2021
6264	458^44991-44991^458	119715	Norman Luhn	09/2024
6265	2^397655-933075	119707	Paul Bourdelais	06/2021
6266	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
6267	28243^17308+17308^28243	119701	Hans Havermann	02/2021
6268	77*10^119688+3	119690	Robert Price	06/2020
6269	586*25^85601+3717	119668	Eric Chen	10/2023
6270	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
6271	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
6272	2^397426+73849	119638	Enzo Doria	04/2016
6273	8*10^119509+29	119510	Robert Price	11/2021
6274	2^396933-112723	119489	Enzo Doria	06/2014
6275	11^114738-150	119488	Enzo Doria	10/2012
6276	(4*10^119474+149)/9	119474	Robert Price	04/2018
6277	26964^26964-13^13	119472	Henri Lifchitz	08/2024
6278	2^396790-21	119446	Lelio R Paula	04/2013
6279	32061^5300+5300^32061	119405	Hans Havermann	01/2021
6280	(2^396633-7)/5	119398	Lelio R Paula	04/2014
6281	27382^22913+22913^27382	119388	Hans Havermann	03/2021
6282	(2^396577+2522)/2	119382	Stefano Morozzi	09/2020
6283	(2^396492+2230)/2	119356	Stefano Morozzi	01/2021
6284	(47*10^119354+259)/9	119355	Robert Price	03/2022
6286	105^59050+104	119352	Norbert Schneider	11/2016
6285	126^56824-125	119352	Norbert Schneider	12/2018
6287	2^396469+111546435	119350	Paul Bourdelais	10/2021
6288	139^55690-138	119345	Norbert Schneider	04/2019
6289	790^41179+41179^790	119322	Norbert Schneider	04/2019
6290	2^396374+73729	119321	Enzo Doria	04/2016
6292	88*10^119295+3	119297	Robert Price	05/2020
6291	21*29^81575+129664	119297	Eric Chen	06/2025
6293	2^396258-459491	119286	Enzo Doria	05/2015
6294	(2^396248+3126)/2	119283	Stefano Morozzi	09/2020
6295	2^396128-396128-1	119247	Karsten Bonath	06/2018
6296	(893*10^119228+7)/9	119230	Robert Price	06/2021
6297	(31*10^119229+257)/9	119230	Robert Price	12/2021
6298	(28*10^119206-67)/3	119207	Robert Price	10/2020
6299	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
6300	11^114458+6	119196	Paul Bourdelais	02/2021
6301	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
6302	(2^395902+202)/2	119179	Stefano Morozzi	09/2020
6303	(2^395825+582)/2	119155	Stefano Morozzi	09/2020
6304	(2^395733+1130)/2	119128	Stefano Morozzi	09/2020
6305	(23^119099)%(10^119099)	119099	Henri Lifchitz	05/2025
6306	29548^10725+10725^29548	119091	Hans Havermann	02/2021
6307	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
6308	(30^80599+1)/31	119054	Robert Price	07/2013
6309	(232*10^119047+17)/3	119049	Robert Price	04/2021
6310	(43*10^119024-403)/9	119025	Robert Price	01/2019
6311	(4*10^119021+47)/3	119022	Robert Price	01/2022
6312	fibonacci(569433)+3	119005	Jon Grantham	08/2023
6313	26603^26888-26888^26603	118978	Norbert Schneider	07/2021
6314	912^40193-40193^912	118972	Norman Luhn	09/2024
6315	681^41992-41992^681	118970	Norman Luhn	09/2024
6316	6*10^118964+43	118965	Robert Price	07/2020
6317	(8*10^118960+49)/3	118961	Robert Price	05/2020
6318	31253^6402+6402^31253	118959	Hans Havermann	02/2021
6319	(194*10^118925-17)/3	118927	Robert Price	09/2020
6320	2^395062-109121	118926	Enzo Doria	04/2014
6321	2^395055-4627	118924	Yves Minet	05/2019
6322	(2^395054+702)/2	118923	Stefano Morozzi	09/2020
6323	2^395018-224141	118913	Harrison Mesh	06/2022
6324	(2^395011+2526)/2	118910	Stefano Morozzi	09/2020
6325	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
6326	25771^26948-26948^25771	118872	Frank Doornink	02/2024
6327	374^46201-46201^374	118870	Norman Luhn	09/2024
6328	(2^394858+1018)/2	118864	Stefano Morozzi	09/2020
6329	(77*10^118862-149)/9	118863	Robert Price	03/2022
6330	(16*10^118852+77)/3	118853	Robert Price	03/2019
6331	fibonacci(568658)-2	118843	Jon Grantham	08/2023
6332	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
6333	10^118772+163599	118773	Patrick De Geest	02/2021
6335	10^118772-40000000001	118772	Robert Price	09/2020
6334	10^118772-207603	118772	Patrick De Geest	02/2021
6336	26842^26577+26577^26842	118763	Hans Havermann	02/2021
6337	(2^394513+2034)/2	118760	Stefano Morozzi	09/2020
6338	(2^394473+2774)/2	118748	Stefano Morozzi	02/2021
6339	27949^17710+17710^27949	118734	Hans Havermann	02/2021
6340	2^394266+71389	118686	Enzo Doria	04/2016
6341	(10^118681-3^118681)/7	118681	Jon Grantham	08/2023
6342	2^394215-51261	118671	Tony Prest / Never Odd Or Even	04/2018
6343	(2^394215-48793)/5/5	118670	Tony Prest / Never Odd Or Even	04/2018
6344	(2^394215-17063)/3/3/5	118669	Tony Prest / Never Odd Or Even	04/2018
6345	(2^394215-24393)/5/5/5/5/5	118668	Tony Prest / Never Odd Or Even	04/2018
6346	(2^394215-35885)/3/71/173	118666	Tony Prest / Never Odd Or Even	04/2018
6347	(2^394215-47925)/353/2269	118665	Tony Prest / Never Odd Or Even	04/2018
6348	29201^11568+11568^29201	118652	Hans Havermann	02/2021
6349	(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673	118650	Tony Prest / Never Odd Or Even	04/2018
6350	(2^394131+2214)/2	118645	Stefano Morozzi	09/2020
6351	(17*10^118635+13)/3	118636	Robert Price	01/2019
6352	5^169727+2	118635	Lelio R Paula	08/2013
6353	2^394034-3	118617	M. Frind & P. Underwood	09/2002
6354	(7*10^118607+179)/3	118608	Robert Price	09/2018
6355	3^248572-6242	118599	Enzo Doria	05/2014
6356	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
6357	(49*10^118576-319)/9	118577	Robert Price	10/2021
6358	7^140303-6	118570	Robert Price	11/2014
6359	(2^393864+2686)/2	118565	Stefano Morozzi	09/2020
6360	(2^393862+3150)/2	118564	Stefano Morozzi	09/2020
6361	(2^393849+3762)/2	118561	Stefano Morozzi	01/2021
6362	(529*10^118554-7)/9	118556	Robert Price	08/2021
6363	26712^26777-26777^26712	118534	Norbert Schneider	07/2021
6364	(2^393661+2666)/2	118504	Stefano Morozzi	09/2020
6365	(2^393650+1614)/2	118501	Stefano Morozzi	09/2020
6366	27655^19264+19264^27655	118495	Hans Havermann	02/2021
6367	10^118485+469413	118486	Patrick De Geest	05/2021
6368	10^118485-50001	118485	Robert Price	08/2020
6369	(2^393528+1030)/2	118464	Stefano Morozzi	09/2020
6370	2^393427+75683	118434	Enzo Doria	04/2016
6371	2^393376-114749	118418	Enzo Doria	04/2015
6372	(65*10^118417+493)/9	118418	Robert Price	08/2021
6373	30960^6671+6671^30960	118397	Hans Havermann	02/2021
6374	(2^393234+2010)/2	118375	Stefano Morozzi	09/2020
6375	(2^393205+3030)/2	118367	Stefano Morozzi	09/2020
6376	(2^393191+2174)/2	118362	Stefano Morozzi	09/2020
6377	2^393180+73	118359	Lelio R Paula	04/2013
6378	3*2^393125+5	118343	Jon Grantham	07/2023
6379	27546^19771+19771^27546	118339	Hans Havermann	02/2021
6380	822^40595-40595^822	118330	Norman Luhn	09/2024
6381	p(23881)#/2+256	118328	Robert Price	05/2017
6382	(10^118324+359)/9	118324	Serge Batalov	12/2014
6383	(2^393048+570)/2	118319	Stefano Morozzi	09/2020
6384	p(23879)#/2+64	118317	Robert Price	03/2017
6385	2^393033+20147	118315	Enzo Doria	08/2023
6386	8*10^118308+59	118309	Robert Price	11/2021
6387	9*10^118282+29	118283	Robert Price	03/2022
6388	(9*35^76602+12877)/34	118279	Eric Chen	05/2025
6389	(238*10^118265-1)/3	118267	Robert Price	04/2020
6391	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
6390	(2^392707+1710)/2	118217	Stefano Morozzi	09/2020
6392	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
6393	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
6394	(2^392567+2750)/2	118175	Stefano Morozzi	01/2021
6395	55*10^118172+3	118174	Robert Price	07/2022
6396	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
6397	27185^22222+22222^27185	118168	Hans Havermann	01/2021
6398	2^392516-29219	118160	Enzo Doria	07/2015
6399	66*10^118155+7	118157	Robert Price	07/2020
6400	Phi(177231,10)	118152	Maksym Voznyy	09/2015
6401	2^392413-112123	118129	Enzo Doria	06/2014
6402	27491^19798+19798^27491	118119	Hans Havermann	02/2021
6403	(49*10^118109-319)/9	118110	Robert Price	10/2021
6404	(2^392342+5)/27	118106	Lelio R Paula	04/2014
6405	(2^392333+1782)/2	118104	Stefano Morozzi	01/2021
6406	2^392300-1841429	118095	Enzo Doria	06/2015
6407	3*2^392260-5	118083	Jon Grantham	07/2023
6408	2^392220+75241	118070	Enzo Doria	04/2016
6409	27836^17409+17409^27836	118047	Hans Havermann	02/2021
6410	(13^118026)%(10^118026)	118026	Henri Lifchitz	05/2025
6411	10^118009+664447	118010	Patrick De Geest	07/2018
6412	10^118009-20001	118009	Robert Price	01/2018
6413	(14*10^117991+61)/3	117992	Robert Price	12/2018
6414	2^391933+5897	117984	Yves Minet	02/2011
6415	2^391912-1849259	117978	Enzo Doria	08/2015
6416	(2*34^77029+1043)/11	117968	Eric Chen	08/2023
6417	5*2^391836-3	117956	Jon Grantham	07/2023
6418	28357^14440+14440^28357	117953	Hans Havermann	02/2021
6419	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
6420	85^61124-61124^85	117934	Norman Luhn	09/2024
6421	(7*10^117930-79)/9	117930	Robert Price	01/2021
6422	27531^19168+19168^27531	117904	Hans Havermann	02/2021
6423	(46*10^117902+683)/9	117903	Robert Price	03/2019
6424	26349^26668-26668^26349	117893	Frank Doornink	03/2024
6425	27670^18189+18189^27670	117869	Hans Havermann	02/2021
6426	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
6427	(56*10^117856+583)/9	117857	Robert Price	08/2021
6428	32169^4606+4606^32169	117846	Hans Havermann	02/2021
6429	(71*10^117803-143)/9	117804	Robert Price	10/2021
6430	2^391324+90901	117801	Yves Minet	02/2011
6431	2^391301-1859923	117794	Enzo Doria	03/2016
6432	2^391261-4131	117782	Yves Minet	02/2018
6433	(2^391211+554)/2	117766	Stefano Morozzi	09/2020
6434	816^40445-40445^816	117764	Norman Luhn	09/2024
6435	38434^1157+1157^38434	117737	Hans Havermann	01/2021
6436	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
6437	(85*10^117719+473)/9	117720	Robert Price	01/2020
6438	(2^391049+582)/2	117718	Stefano Morozzi	09/2020
6439	(21*23^86445-197)/22	117715	Eric Chen	08/2023
6440	31083^6122+6122^31083	117709	Hans Havermann	02/2021
6441	2^390960+1880881	117691	Enzo Doria	11/2016
6442	(71*10^117685+91)/9	117686	Robert Price	04/2022
6444	2^390897-1860553	117672	Enzo Doria	11/2015
6443	(61*10^117671+47)/9	117672	Robert Price	07/2022
6445	2^390889-115003	117670	Enzo Doria	06/2015
6446	12^109010+35	117642	Riley Fisher	08/2023
6447	2^390779-30337	117637	Paul Bourdelais	02/2012
6448	(2^390735+378)/2	117623	Stefano Morozzi	02/2021
6449	11^112916-780	117590	Enzo Doria	12/2012
6450	27641^17916+17916^27641	117564	Hans Havermann	02/2021
6451	27906^16321+16321^27906	117561	Hans Havermann	02/2021
6452	27294^20275+20275^27294	117555	Hans Havermann	02/2021
6453	(2^390473+1002)/2	117544	Stefano Morozzi	09/2020
6454	35912^1875+1875^35912	117541	Hans Havermann	02/2021
6455	(16^97613-5^97613)/11	117537	Robert Price	07/2013
6456	(2^390438+1774)/2	117534	Stefano Morozzi	01/2021
6457	(2^390418+1722)/2	117528	Stefano Morozzi	09/2020
6458	(2^390403+654)/2	117523	Stefano Morozzi	09/2020
6459	(2^390343+2246)/2	117505	Stefano Morozzi	01/2021
6460	28043^15478+15478^28043	117493	Hans Havermann	02/2021
6461	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
6462	37077^1474+1474^37077	117479	Hans Havermann	01/2021
6463	31^78759-30	117459	Theodore Burton	02/2007
6464	(2^390176+1222)/2	117455	Stefano Morozzi	09/2020
6465	(2^390133+1242)/2	117442	Stefano Morozzi	09/2020
6466	(2^390013+2634)/2	117406	Stefano Morozzi	09/2020
6467	3*10^117402+61	117403	Robert Price	09/2020
6468	2^389998+37	117402	Lelio R Paula	03/2013
6469	(2^389977+314)/2	117395	Stefano Morozzi	09/2020
6470	(2^389921+342)/2	117378	Stefano Morozzi	01/2021
6471	71830^43+43^71830	117333	Hans Havermann	01/2021
6472	(2^389768+1582)/2	117332	Stefano Morozzi	09/2020
6473	33802^2951+2951^33802	117292	Hans Havermann	02/2021
6474	(2^561185)%L(561185)	117281	Henri Lifchitz	05/2025
6475	26789^23866+23866^26789	117277	Hans Havermann	02/2021
6476	29^80192-1*80192^29	117273	Dylan Delgado	12/2019
6477	(101*10^117260+7)/9	117262	Robert Price	02/2022
6478	(13*10^117249+161)/3	117250	Robert Price	11/2018
6479	2^389478+43	117245	Lelio R Paula	03/2013
6480	(298*10^117229-7)/3	117231	Robert Price	06/2020
6481	(2^389416+342)/2	117226	Stefano Morozzi	01/2021
6482	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
6483	5*10^117205+23	117206	Robert Price	03/2019
6484	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
6485	27272^19827+19827^27272	117195	Hans Havermann	01/2021
6486	(2^389276+2650)/2	117184	Stefano Morozzi	09/2020
6487	(844*10^117175-7)/9	117177	Robert Price	05/2021
6488	10^117142+209223	117143	Patrick De Geest	04/2018
6490	10^117142-1000000001	117142	Robert Price	03/2018
6489	10^117142-966057	117142	Patrick De Geest	04/2018
6491	10^117135+360577	117136	Patrick De Geest	07/2018
6492	10^117135-401	117135	Robert Price	01/2018
6493	26415^26488-26488^26415	117126	Norbert Schneider	05/2021
6494	4*10^117123+79	117124	Robert Price	08/2018
6495	2^389033-12797413	117111	Enzo Doria	04/2016
6496	(2^388987+2634)/2	117097	Stefano Morozzi	09/2020
6497	2^388960-109505	117089	Enzo Doria	04/2014
6498	7*10^117082-57	117083	Robert Price	06/2020
6499	791^40398-40398^791	117081	Norman Luhn	09/2024
6500	(2^388928-5)/569	117077	Lelio R Paula	03/2014

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PRP Records

Probable Primes Top 10000

(301901 PRPs in the top)