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	2^376790+27	113426	Lelio R Paula	03/2013
6502	2^376786-112701	113424	Enzo Doria	06/2014
6503	2^376731+21	113408	Lelio R Paula	03/2013
6504	9*10^113394-73	113395	Robert Price	01/2021
6505	29660^6651+6651^29660	113387	Hans Havermann	01/2021
6507	2^376634+1871245	113379	Enzo Doria	05/2016
6506	(4^188318+17)/3	113379	Robert Price	02/2017
6508	E(29532)/492842728006750534663978950979381235	113367	Thomas Ritschel	01/2021
6509	2^376576-344369	113361	Enzo Doria	07/2015
6510	2^376549-4543	113353	Yves Minet	03/2019
6511	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
6512	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
6513	(2^376350+3538)/2	113293	Stefano Morozzi	09/2020
6514	27265^14272+14272^27265	113273	Hans Havermann	02/2021
6515	32174^3315+3315^32174	113269	Hans Havermann	02/2021
6516	(2*10^113248+73)/3	113248	Robert Price	09/2020
6517	2^376128-21237	113226	Enzo Doria	06/2013
6518	5*10^113224-81	113225	Robert Price	01/2019
6519	10^113220+51409	113221	Patrick De Geest	02/2021
6521	10^113220-1000001	113220	Robert Price	08/2020
6520	10^113220-61779	113220	Patrick De Geest	02/2021
6522	(2^376102+1578)/2	113218	Stefano Morozzi	09/2020
6523	(2^375996+3102)/2	113186	Stefano Morozzi	09/2020
6524	37258^1091+1091^37258	113184	Hans Havermann	02/2021
6525	(94*10^113176+11)/3	113178	Robert Price	04/2020
6526	(46*10^113162+521)/9	113163	Robert Price	02/2019
6527	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
6528	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
6529	3*10^113137+23	113138	Robert Price	03/2022
6530	(8*10^113135-269)/9	113135	Robert Price	09/2021
6531	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
6532	26050^21959+21959^26050	113100	Hans Havermann	02/2021
6533	2^375638-1787171	113079	Enzo Doria	03/2016
6534	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
6535	2^375537+4847	113048	Yves Minet	02/2011
6536	(17^91837+16^91837)/33	113000	Robert Price	08/2013
6537	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
6538	2^375350-3221	112992	Yves Minet	07/2011
6539	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
6540	2^375305+76757	112979	Enzo Doria	05/2016
6541	2^375258+1874989	112964	Enzo Doria	07/2016
6542	(29^77237-1)/28	112950	Robert Price	04/2012
6543	26620^17483+17483^26620	112939	Hans Havermann	01/2021
6544	2^375154+74959	112933	Enzo Doria	04/2016
6545	(266*10^112930-17)/3	112932	Robert Price	07/2020
6546	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
6547	(85*10^112919+293)/9	112920	Robert Price	12/2019
6548	29412^6899+6899^29412	112907	Hans Havermann	02/2021
6549	(191*10^112903-17)/3	112905	Robert Price	11/2021
6550	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
6551	25992^22039+22039^25992	112889	Hans Havermann	02/2021
6552	2^374993-2787163	112885	Enzo Doria	11/2015
6553	(697*10^112869+23)/9	112871	Robert Price	04/2021
6554	(19*10^112851+377)/9	112852	Alfred Reich	11/2022
6555	30420^5111+5111^30420	112813	Hans Havermann	02/2021
6556	13699^27268+27268^13699	112800	Norbert Schneider	12/2020
6557	123^53970+2	112793	Lelio R Paula	06/2013
6558	12308*27^78796+23	112790	Eric Chen	07/2023
6559	28942^7887+7887^28942	112785	Hans Havermann	01/2021
6560	2^374640-4685	112778	Yves Minet	05/2019
6561	12^104501-11	112776	Riley Fisher	12/2023
6562	57290^93+93^57290	112775	Hans Havermann	01/2021
6563	115^54726-54726^115	112774	Norman Luhn	09/2024
6564	13608^27277-27277^13608	112758	Norbert Schneider	12/2022
6565	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
6566	p(22852)#/2+512	112745	Robert Price	05/2017
6567	(11*10^112742-131)/3	112743	Robert Price	09/2018
6568	2^374441-21049	112718	Enzo Doria	06/2013
6569	4*10^112706-93	112707	Robert Price	07/2020
6570	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
6571	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
6572	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
6573	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
6574	3^236011-8828	112606	Enzo Doria	05/2014
6575	31854^3427+3427^31854	112602	Hans Havermann	02/2021
6576	(85*10^112530-373)/9	112531	Robert Price	05/2021
6577	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
6578	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
6579	27618^11821+11821^27618	112479	Hans Havermann	01/2021
6580	U(602921)/4823369	112479	Serge Batalov	07/2024
6581	26343^18580+18580^26343	112460	Hans Havermann	01/2021
6582	39^70666+2	112435	Lelio R Paula	11/2013
6583	(134*10^112400+7)/3	112402	Robert Price	02/2020
6584	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
6585	(2^373350-7)/3	112390	Lelio R Paula	03/2014
6586	2^373306-1840931	112377	Enzo Doria	06/2015
6587	8*10^112371-37	112372	Robert Price	03/2022
6588	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
6589	6*10^112359-79	112360	Robert Price	03/2022
6590	34409^1842+1842^34409	112356	Hans Havermann	02/2021
6591	(142*10^112352-7)/9	112354	Robert Price	12/2019
6592	25580^24633+24633^25580	112336	Hans Havermann	01/2021
6593	2^373117+1872107	112320	Enzo Doria	05/2016
6594	(2^373083+2226)/2	112309	Stefano Morozzi	01/2021
6595	(35*10^112308+37)/9	112309	Robert Price	05/2022
6596	27963^10376+10376^27963	112301	Hans Havermann	01/2021
6597	2^373040+2792761	112297	Enzo Doria	03/2016
6598	(156^51203-1)/155	112293	Anonymous	06/2024
6599	EPrime(112280)	112280	Eric W. Weisstein	10/2010
6600	2^372950+7	112270	Lelio R Paula	03/2013
6601	2^372945+1872167	112268	Enzo Doria	05/2016
6602	36274^1243+1243^36274	112249	Hans Havermann	02/2021
6603	(55*10^112246+629)/9	112247	Robert Price	01/2022
6604	(2^372872+3798)/2	112246	Stefano Morozzi	02/2021
6605	25513^25060+25060^25513	112232	Hans Havermann	02/2021
6606	(53*10^112229-611)/9	112230	Robert Price	02/2022
6607	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020
6608	6*10^112208+43	112209	Robert Price	07/2020
6609	(2^372728+3058)/2	112203	Stefano Morozzi	09/2020
6610	32061^3158+3158^32061	112195	Hans Havermann	02/2021
6611	2^372695+72113	112193	Enzo Doria	04/2016
6612	2^372689-2563	112191	Yves Minet	07/2014
6613	2^372638-1859441	112176	Enzo Doria	03/2016
6614	3^235074-113056	112159	Enzo Doria	07/2014
6615	-E(29242)/489848365125303139750087	112140	Thomas Ritschel	01/2021
6616	(2^372514+1822)/2	112138	Stefano Morozzi	02/2021
6617	29468^6387+6387^29468	112135	Hans Havermann	02/2021
6618	(2^372428+3742)/2	112112	Stefano Morozzi	01/2021
6619	25375^25454-25454^25375	112110	Norbert Schneider	01/2021
6620	131^52949-130	112108	Norbert Schneider	02/2019
6621	(91*10^112098-1)/9	112100	Robert Price	04/2015
6622	(68*10^112087-149)/9	112088	Robert Price	07/2022
6623	2^372314+212419	112078	Enzo Doria	08/2023
6624	2^372310-85061	112077	Paul Bourdelais	02/2012
6625	(10^112067+53)/9	112067	Serge Batalov	07/2015
6626	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
6627	75^59760+2	112054	Lelio R Paula	08/2013
6628	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
6629	(10^112048+7)/8747/373157	112039	Alfred Reich	06/2021
6630	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
6631	F(536233)/825798821/1102495049/5641839306317	112036	Serge Batalov	07/2024
6632	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
6633	8*10^112018-49	112019	Robert Price	08/2019
6635	2^372108+74221	112016	Enzo Doria	04/2016
6634	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
6636	8*10^112011-73	112012	Robert Price	01/2022
6637	(184*10^112007-1)/3	112009	Robert Price	02/2020
6638	5*10^112003+81	112004	Robert Price	03/2019
6639	215^48018+48018^215	112000	Norbert Schneider	10/2018
6640	25549^24148+24148^25549	111979	Hans Havermann	02/2021
6641	2^371970-459491	111975	Enzo Doria	05/2015
6642	41^69427-40^69427	111971	Robert Price	07/2012
6643	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
6644	15*25^80056+446	111915	Eric Chen	10/2023
6645	(34*10^111902-547)/9	111903	Robert Price	03/2021
6646	(10^111902+71)/9	111902	Serge Batalov	07/2015
6647	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
6648	29080^7027+7027^29080	111865	Hans Havermann	01/2021
6649	31307^3730+3730^31307	111820	Hans Havermann	02/2021
6650	2^371440-112865	111815	Enzo Doria	06/2014
6651	2^371426-459161	111811	Enzo Doria	05/2015
6652	25768^21771+21771^25768	111779	Hans Havermann	02/2021
6653	28022^9747+9747^28022	111777	Hans Havermann	02/2021
6654	(94*10^111770+11)/3	111772	Robert Price	04/2020
6655	2^371276-461267	111766	Enzo Doria	07/2015
6656	6*10^111760+43	111761	Robert Price	07/2020
6657	98079!4-1024	111747	Robert Price	11/2019
6658	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
6659	10^(255862+1)-410^55862-1	111725	Robert Price	07/2023
6660	2^371098-113261	111712	Enzo Doria	07/2014
6661	(7*10^111706-61)/9	111706	Erik Branger	01/2011
6662	2^371044+1869391	111696	Enzo Doria	05/2016
6663	26310^17581+17581^26310	111688	Hans Havermann	01/2021
6664	88^57416+87	111645	Norbert Schneider	11/2015
6665	2^370829-109693	111631	Enzo Doria	04/2014
6666	15^94906-2	111619	Lelio R Paula	11/2013
6667	25835^20904+20904^25835	111614	Hans Havermann	02/2021
6668	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
6669	27758^10479+10479^27758	111597	Hans Havermann	02/2021
6670	2^370695-4627	111591	Yves Minet	05/2019
6671	7*10^111579-87	111580	Robert Price	06/2020
6672	2^370643-37	111575	Yves Minet	01/2012
6673	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
6674	2^370610-3911	111565	Yves Minet	04/2017
6675	(154*10^111549+17)/9	111551	Robert Price	06/2022
6676	26200^18097+18097^26200	111550	Hans Havermann	01/2021
6677	286^45405+45405^286	111532	Norbert Schneider	04/2015
6678	4*5^159563-9	111531	Lelio R Paula	11/2014
6679	5*10^111528-21	111529	Robert Price	12/2021
6680	(4^185225+23)/3	111517	Robert Price	10/2018
6681	2^370393-2797093	111500	Enzo Doria	03/2016
6682	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
6683	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
6684	6^143273-5	111489	Paul Bourdelais	01/2021
6685	2^370292-2791979	111469	Enzo Doria	03/2016
6686	(14*10^111443-11)/3	111444	Robert Price	08/2022
6687	2^370177-461551	111435	Enzo Doria	07/2015
6688	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
6689	109^54683-108	111413	Norbert Schneider	02/2017
6691	(83*10^111406-173)/9	111407	Robert Price	04/2021
6690	959^37362-37362^959	111407	Henri Lifchitz	10/2024
6692	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
6693	32961^2396+2396^32961	111392	Hans Havermann	10/2020
6694	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
6695	(19*10^111385+11)/3	111386	Robert Price	07/2023
6696	(23*10^111380-29)/3	111381	Robert Price	03/2022
6697	2^369974+733	111374	Lelio R Paula	05/2013
6698	121^53470+120	111367	Norbert Schneider	10/2018
6699	2^369915-286267	111356	Enzo Doria	07/2015
6700	(62*10^111347-629)/9	111348	Robert Price	07/2021
6701	2^369855-1615	111338	Lelio R Paula	05/2017
6702	7*10^111325+3	111326	Robert Price	08/2015
6703	51^65176+2	111293	Lelio R Paula	08/2013
6704	2^369643-1865767	111274	Enzo Doria	03/2016
6705	2^369603+885	111262	Lelio R Paula	05/2017
6706	25555^22564+22564^25555	111252	Hans Havermann	10/2020
6707	F(532391)/89441689/1425422598617	111243	Serge Batalov	07/2024
6708	L(532277)	111240	Renaud Lifchitz	03/2004
6709	105^55033-2	111233	Lelio R Paula	10/2017
6710	(35*10^111232-737)/9	111233	Robert Price	07/2018
6711	26970^13307+13307^26970	111227	Hans Havermann	10/2020
6712	25419^23716+23716^25419	111210	Hans Havermann	10/2020
6713	(26^78593-3^78593)/23	111206	Robert Price	02/2025
6714	9*10^111201-29	111202	Robert Price	09/2019
6715	2^369392+29835	111199	Lelio R Paula	05/2017
6716	3^233059+16	111198	Robert Price	03/2020
6717	2^369354-3413	111187	Yves Minet	12/2016
6718	2^369296-27	111170	Lelio R Paula	02/2013
6719	(2468^40960+1)/(2468^8192+1)	111161	Martin Hopf	08/2024
6720	2^369239-109837	111153	Enzo Doria	05/2014
6721	2^369224-291839	111148	Enzo Doria	07/2015
6722	2^369216+2798881	111146	Enzo Doria	04/2016
6723	26842^13817+13817^26842	111137	Hans Havermann	11/2020
6724	(5*10^111119-191)/3	111120	Robert Price	05/2021
6725	(29*10^111112-23)/3	111113	Robert Price	03/2022
6726	10^111111+163849	111112	Patrick De Geest	03/2017
6727	10^111111-312911	111111	Patrick De Geest	03/2017
6728	2^369092-216923	111108	Enzo Doria	05/2014
6729	2^369081-55	111105	Lelio R Paula	02/2013
6730	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
6731	88^57124-87	111077	Norbert Schneider	11/2015
6732	2^368980+753	111075	Lelio R Paula	05/2013
6733	2^368946-3623	111064	Yves Minet	03/2017
6734	2^368929+29835	111059	Lelio R Paula	05/2017
6735	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
6736	111^54298+110	111057	Norbert Schneider	04/2017
6737	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
6738	(29*10^111020-41)/3	111021	Tyler Busby	03/2024
6739	35799^1262+1262^35799	111015	Hans Havermann	10/2020
6740	(298*10^111004+11)/3	111006	Robert Price	11/2020
6741	27648^10349+10349^27648	111004	Hans Havermann	11/2020
6742	28899^6932+6932^28899	110997	Hans Havermann	11/2020
6743	(749^38809+1)/(749^197+1)	110990	Martin Hopf	11/2023
6744	2^368641-460303	110972	Enzo Doria	06/2015
6745	2^368619-109087	110966	Enzo Doria	04/2014
6746	(74*10^110961+313)/9	110962	Robert Price	06/2019
6747	25258^24711+24711^25258	110956	Hans Havermann	11/2020
6748	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
6749	3*2^368489+7	110927	Lelio R Paula	09/2014
6750	(14*10^110922+61)/3	110923	Robert Price	12/2018

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301421 PRPs in the top)