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 ?
6501	2^405992-78557	122216	Jorge Menendez	03/2018
6502	(8*10^122203+43)/3	122204	Robert Price	06/2018
6503	(58*10^122170+329)/9	122171	Robert Price	05/2019
6504	2^405774+179149	122151	Enzo Doria	06/2016
6505	2^405693+20417	122126	Enzo Doria	07/2023
6506	(218*10^122109+7)/9	122111	Robert Price	06/2022
6507	29189^15246+15246^29189	122103	Hans Havermann	03/2021
6508	(42^75217-5^75217)/37	122095	Robert Price	06/2026
6510	34*10^122082-9	122084	Robert Price	06/2020
6509	33442^4473+4473^33442	122084	Hans Havermann	03/2021
6511	5*10^122082+41	122083	Robert Price	03/2019
6512	31849^6808+6808^31849	122078	Hans Havermann	03/2021
6514	2^405514-3311	122072	Yves Minet	12/2014
6515	2^405514-115511	122072	Enzo Doria	07/2015
6513	23*10^122070-7	122072	Robert Price	02/2020
6516	2^405422-113261	122045	Enzo Doria	07/2014
6517	95^61698-61698^95	122022	Norman Luhn	10/2024
6518	2^405173+71237	121970	Enzo Doria	04/2016
6519	fibonacci(583574)+2	121960	Jon Grantham	08/2023
6520	(154*10^121953+17)/9	121955	Robert Price	06/2022
6521	(34*10^121924+191)/9	121925	Robert Price	08/2021
6522	(2^405016+1)/257	121920	Lelio R Paula	04/2014
6523	28557^18590+18590^28557	121918	Hans Havermann	03/2021
6524	28641^18002+18002^28641	121877	Hans Havermann	03/2021
6525	2^404858+71329	121875	Enzo Doria	04/2016
6526	2^404813-114703	121861	Enzo Doria	04/2015
6527	2^404764+77791	121847	Enzo Doria	05/2016
6528	28830^16841+16841^28830	121847	Hans Havermann	03/2021
6529	(4*10^121825+89)/3	121826	Robert Price	08/2021
6530	317^48694+48694^317	121787	Norbert Schneider	08/2015
6531	2^404536-115259	121778	Enzo Doria	06/2015
6532	2^404501-631	121767	Yves Minet	07/2012
6533	5*10^121764-69	121765	Robert Price	02/2021
6534	(34^79493-3^79493)/31	121741	Robert Price	07/2025
6535	28236^20485+20485^28236	121738	Hans Havermann	02/2021
6536	(382*10^121694-31)/9	121696	Robert Price	06/2022
6537	63^67620+2	121672	Lelio R Paula	08/2015
6538	(25*34^79445-28062367)/33	121669	Eric Chen	08/2023
6539	(13*33^80110-121453)/32	121648	Eric Chen	12/2023
6540	(16*10^121633+167)/3	121634	Robert Price	06/2019
6541	29955^11494+11494^29955	121632	Hans Havermann	02/2021
6542	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
6543	31088^8163+8163^31088	121612	Hans Havermann	02/2021
6544	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
6545	(211^52301-1)/210	121560	Anonymous	04/2024
6546	(10^121543-79)/3	121543	Robert Price	01/2018
6547	Phi(85408,1105)	121540	Henri Lifchitz	12/2025
6548	801^41852-41852^801	121523	Norman Luhn	10/2024
6549	2^403676+76831	121519	Enzo Doria	05/2016
6550	(41^75337-1)/98233421080	121492	Paul Vanderveen	05/2025
6551	715^42564-42564^715	121491	Norman Luhn	10/2024
6552	(7*10^121487+143)/3	121488	Robert Price	03/2018
6553	27965^22086+22086^27965	121484	Hans Havermann	02/2021
6554	(893*10^121470+7)/9	121472	Robert Price	06/2021
6555	(206*10^121462-11)/3	121464	Robert Price	02/2022
6556	26282^27481-27481^26282	121457	Frank Doornink	03/2024
6557	(77*10^121455+67)/9	121456	Robert Price	12/2021
6558	2^403363-113635	121425	Enzo Doria	08/2014
6559	25531^27552-27552^25531	121424	Frank Doornink	02/2024
6560	(17*10^121418-113)/3	121419	Robert Price	06/2021
6561	2^403336-1861469	121417	Enzo Doria	03/2016
6562	27929^22186+22186^27929	121382	Hans Havermann	02/2021
6563	p(24442)#/2-64	121381	Robert Price	04/2017
6564	11^116555-720	121380	Enzo Doria	11/2012
6565	(873^41263+1)/874	121353	Jinyuan Wang	12/2024
6566	2^403100-461267	121346	Enzo Doria	07/2015
6567	2^403093-112213	121344	Enzo Doria	06/2014
6568	29404^13385+13385^29404	121340	Hans Havermann	02/2021
6569	28106^20745+20745^28106	121332	Hans Havermann	02/2021
6570	(316^48539+1)/317	121330	Eric Chen	10/2017
6571	(23*10^121320-71)/3	121321	Robert Price	07/2020
6572	2^403004+1866361	121317	Enzo Doria	03/2016
6573	2^402953+89	121301	Lelio R Paula	10/2013
6574	2^402944-2788319	121299	Enzo Doria	03/2016
6575	(44*10^121297-719)/9	121298	Robert Price	12/2018
6576	Phi(171913,7)	121289	Henri Lifchitz	12/2025
6577	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
6578	2^402828-113183	121264	Enzo Doria	07/2014
6579	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
6580	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
6581	282^49477-49477^282	121231	Norman Luhn	10/2024
6583	2^402715+1874223	121230	Enzo Doria	06/2016
6582	(35*10^121229-593)/9	121230	Robert Price	07/2018
6584	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
6585	291^49190-49190^291	121199	Norman Luhn	10/2024
6586	981^40512+980	121199	Alfred Reich	05/2026
6587	(10^121243)/(121243^10)	121193	Henri Lifchitz	05/2025
6588	28719^16568+16568^28719	121174	Hans Havermann	02/2021
6589	Phi(24773,-17#)	121170	Henri Lifchitz	12/2025
6590	7*10^121144+9	121145	Robert Price	09/2015
6591	27490^25467+25467^27490	121121	Hans Havermann	02/2021
6592	34575^3182+3182^34575	121106	Hans Havermann	02/2021
6593	5*10^121100-37	121101	Robert Price	11/2021
6594	F(579521)/516247738177	121101	Serge Batalov	07/2024
6595	25592^27467-27467^25592	121078	Frank Doornink	02/2024
6596	29954^10935+10935^29954	120979	Hans Havermann	02/2021
6597	33585^3992+3992^33585	120946	Hans Havermann	02/2021
6598	40296^1003+1003^40296	120941	Hans Havermann	02/2021
6599	2^401725-113251	120932	Enzo Doria	07/2014
6600	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
6601	2^401652+73711	120910	Enzo Doria	04/2016
6602	(2^401632+3)/79	120902	Lelio R Paula	04/2014
6603	40450^973+973^40450	120870	Hans Havermann	01/2021
6604	(8*10^120851-11)/3	120852	Robert Price	07/2023
6605	10^120841+88417	120842	Patrick De Geest	04/2020
6606	10^120841-123456789	120841	Robert Price	02/2020
6607	10^120841-176853	120841	Patrick De Geest	04/2020
6608	2^401406-2791331	120836	Enzo Doria	03/2016
6609	(28^83497+1)/29	120832	Robert Price	07/2013
6610	(22*10^120828+161)/3	120829	Robert Price	05/2019
6611	2^401369+1867367	120825	Enzo Doria	03/2016
6612	(5*10^120821+43)/3	120822	Robert Price	12/2021
6613	26990^27263-27263^26990	120808	Frank Doornink	03/2024
6614	(10^120782+29)/3	120782	Serge Batalov	12/2014
6615	2^401215-1657	120778	Yves Minet	07/2014
6616	2^401159+53	120761	Lelio R Paula	10/2013
6617	27782^22179+22179^27782	120739	Hans Havermann	01/2021
6618	242^50649-50649^242	120738	Norman Luhn	09/2024
6619	32974^4585+4585^32974	120730	Hans Havermann	02/2021
6620	2^401031-113047	120723	Enzo Doria	07/2014
6621	30598^8813+8813^30598	120713	Hans Havermann	02/2021
6622	(71*10^120703-287)/9	120704	Robert Price	09/2019
6623	25671^27370-27370^25671	120687	Frank Doornink	02/2024
6624	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
6625	34793^2940+2940^34793	120675	Hans Havermann	02/2021
6626	26028^27329-27329^26028	120670	Frank Doornink	03/2024
6627	(2^400846+538)/2	120667	Stefano Morozzi	09/2020
6628	(166*10^120654+11)/3	120656	Robert Price	03/2021
6629	34066^3481+3481^34066	120652	Hans Havermann	02/2021
6630	8*10^120637-27	120638	Robert Price	10/2021
6631	(2^400709+3546)/2	120626	Stefano Morozzi	09/2020
6632	(2^400700+3126)/2	120623	Stefano Morozzi	09/2020
6633	(2^400693+2634)/2	120621	Stefano Morozzi	09/2020
6634	9*10^120617-61	120618	Robert Price	06/2021
6635	(29*10^120590-71)/3	120591	Robert Price	07/2021
6636	2^400571-15	120584	Lelio R Paula	10/2013
6637	(10^120574+359)/9	120574	Serge Batalov	12/2014
6638	(8*10^120552-17)/9	120552	Serge Batalov	11/2022
6639	27431^24810+24810^27431	120550	Hans Havermann	02/2021
6640	2^400424-216413	120540	Enzo Doria	04/2013
6641	29090^13911+13911^29090	120531	Hans Havermann	02/2021
6642	(2^400346+1722)/2	120516	Stefano Morozzi	09/2020
6643	27899^20868+20868^27899	120510	Hans Havermann	02/2021
6644	33740^3729+3729^33740	120506	Hans Havermann	02/2021
6645	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
6646	17228^28437-28437^17228	120466	Norbert Schneider	08/2025
6647	1069^39770-39770^1069	120463	Norbert Schneider	05/2025
6649	2^400166+1874899	120462	Enzo Doria	06/2016
6648	(2^400165+1602)/2	120462	Stefano Morozzi	09/2020
6650	2739^35038-35038^2739	120447	Norbert Schneider	05/2025
6651	37078^1771+1771^37078	120438	Hans Havermann	02/2021
6652	(2^400084+1638)/2	120437	Stefano Morozzi	09/2020
6653	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
6654	12857^29306-29306^12857	120423	Norbert Schneider	07/2025
6655	2^399999+54173	120412	Norman Luhn	08/2023
6656	(2^399974+2790)/2	120404	Stefano Morozzi	02/2021
6657	2^399966+73759	120402	Enzo Doria	04/2016
6658	(2^399961+2306)/2	120400	Stefano Morozzi	02/2021
6659	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
6660	2^399918-95	120388	Lelio R Paula	04/2013
6661	2^399918+214009	120388	Enzo Doria	10/2023
6662	(28*10^120381-67)/3	120382	Robert Price	10/2020
6663	(49*10^120380-139)/9	120381	Robert Price	03/2019
6664	(2^399874+2194)/2	120374	Stefano Morozzi	09/2020
6665	2^399792-1849259	120350	Enzo Doria	08/2015
6666	9*10^120342-7	120343	Robert Price	09/2015
6667	(2^399751+786)/2	120337	Stefano Morozzi	09/2020
6668	(331*10^120332-7)/9	120334	Robert Price	04/2022
6669	14609^28890-28890^14609	120316	Norbert Schneider	09/2025
6670	(13*10^120306-37)/3	120307	Robert Price	01/2019
6671	(23*10^120299+37)/3	120300	Robert Price	02/2022
6672	25935^27254-27254^25935	120297	Frank Doornink	03/2024
6673	(2^399604+3070)/2	120293	Stefano Morozzi	09/2020
6674	(2^399549+1062)/2	120276	Stefano Morozzi	09/2020
6675	2^399526-1861721	120270	Enzo Doria	11/2015
6676	12199^29430-29430^12199	120261	Norbert Schneider	08/2025
6677	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
6678	32016^5687+5687^32016	120217	Hans Havermann	01/2021
6679	(205*10^120212-1)/3	120214	Robert Price	11/2021
6680	13302^29149-29149^13302	120209	Norbert Schneider	08/2025
6681	2^399322-2798111	120208	Enzo Doria	04/2016
6682	30438^8867+8867^30438	120163	Hans Havermann	02/2021
6683	3^251841-5*2^251841	120159	Jon Grantham	08/2023
6685	72^64693-71^64693	120157	Robert Price	03/2014
6684	(17*10^120156-161)/9	120157	Robert Price	02/2021
6686	Phi(81997,-5#)	120150	Henri Lifchitz	12/2025
6687	2^399111-28489	120145	Enzo Doria	08/2015
6688	2958^34607-34607^2958	120121	Norbert Schneider	04/2025
6689	(2^399014+1318)/2	120115	Stefano Morozzi	02/2021
6690	30254^9333+9333^30254	120110	Hans Havermann	02/2021
6691	2^398972+6561	120103	Henri Lifchitz	10/2024
6692	30882^7745+7745^30882	120101	Hans Havermann	02/2021
6693	23687^27452-27452^23687	120090	Norbert Schneider	08/2025
6695	2^398877+105	120074	Donovan Johnson	01/2006
6694	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
6696	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
6697	U(686581)/4280145953	120067	Serge Batalov	07/2024
6698	16651^28442-28442^16651	120067	Norbert Schneider	07/2025
6699	12284^29359-29359^12284	120059	Norbert Schneider	06/2025
6700	3207^34240-34240^3207	120049	Norbert Schneider	04/2025
6701	2^398710+57	120024	Lelio R Paula	04/2013
6702	(2^398698+1138)/2	120020	Stefano Morozzi	09/2020
6703	2^398691-115057	120018	Enzo Doria	06/2015
6704	12134^29385-29385^12134	120009	Norbert Schneider	06/2025
6705	6089^31710-31710^6089	120008	Norbert Schneider	05/2025
6706	L(574219)	120005	Renaud Lifchitz	03/2004
6707	2^398571+60413	119982	Yves Minet	03/2011
6708	28623^15538+15538^28623	119971	Hans Havermann	02/2021
6709	p(24179)#/2-64	119949	Robert Price	04/2017
6710	2^398448+1872001	119945	Enzo Doria	05/2016
6711	(10^119946*19-91)/6093	119944	Alfred Reich	10/2023
6712	(19*10^119946-91)/9/677	119944	Alfred Reich	11/2023
6713	(191*10^119941-17)/3	119943	Robert Price	11/2021
6714	634^42803+42803^634	119938	Norbert Schneider	07/2019
6715	31083^7220+7220^31083	119935	Hans Havermann	01/2021
6716	(68*10^119931-11)/3	119933	Robert Price	01/2020
6717	8*10^119930-3	119931	Ray Chandler	04/2011
6718	(2^398398+774)/2	119930	Stefano Morozzi	09/2020
6719	(10^119880+179)/9	119880	Serge Batalov	12/2014
6720	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
6721	(10^119836+77)/3	119836	Robert Price	01/2018
6722	26681^27074-27074^26681	119835	Frank Doornink	03/2024
6723	28179^17870+17870^28179	119821	Hans Havermann	02/2021
6724	2^398029+1872527	119819	Enzo Doria	05/2016
6725	33142^4119+4119^33142	119802	Hans Havermann	01/2021
6726	2^397897-113541	119779	Enzo Doria	08/2014
6727	28636^15171+15171^28636	119728	Hans Havermann	02/2021
6728	87^61730-61730^87	119727	Norman Luhn	09/2024
6729	(10556^29929-1)/(10556^173-1)	119724	Ryan Propper	11/2023
6730	(2^397696+1042)/2	119719	Stefano Morozzi	09/2020
6732	(19*10^119716+101)/3	119717	Robert Price	09/2019
6731	29563^11208+11208^29563	119717	Hans Havermann	02/2021
6733	458^44991-44991^458	119715	Norman Luhn	09/2024
6734	2^397655-933075	119707	Paul Bourdelais	06/2021
6735	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
6736	28243^17308+17308^28243	119701	Hans Havermann	02/2021
6737	77*10^119688+3	119690	Robert Price	06/2020
6738	586*25^85601+3717	119668	Eric Chen	10/2023
6739	(2^397504+1698)/2	119661	Stefano Morozzi	09/2020
6740	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
6741	2^397426+73849	119638	Enzo Doria	04/2016
6742	8*10^119509+29	119510	Robert Price	11/2021
6743	2^396933-112723	119489	Enzo Doria	06/2014
6744	11^114738-150	119488	Enzo Doria	10/2012
6745	(4*10^119474+149)/9	119474	Robert Price	04/2018
6746	26964^26964-13^13	119472	Henri Lifchitz	08/2024
6747	11^114702+10	119450	Alfred Reich	04/2026
6748	2^396790-21	119446	Lelio R Paula	04/2013
6749	8^132246+45045	119431	Enzo Doria	08/2026
6750	32061^5300+5300^32061	119405	Hans Havermann	01/2021

Find by discoverer :

PRP Records

Probable Primes Top 10000

(303390 PRPs in the top)