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 ?
7251	13643^27572-27572^13643	114008	Norbert Schneider	12/2022
7253	(46*10^113969+683)/9	113970	Robert Price	03/2019
7252	(83*10^113969+133)/9	113970	Robert Price	08/2021
7254	32226^3439+3439^32226	113966	Hans Havermann	02/2021
7255	(77*10^113963-149)/9	113964	Robert Price	03/2022
7256	78*10^113954-7	113956	Robert Price	10/2020
7257	2*10^113941+9	113942	Dmitry Domanov	11/2010
7258	10^113933+145897	113934	Patrick De Geest	02/2021
7261	(2^378478+1642)/2	113933	Stefano Morozzi	09/2020
7259	10^113933-8000000001	113933	Robert Price	11/2020
7260	10^113933-66167	113933	Patrick De Geest	02/2021
7262	2339662057597*10^113903+9	113916	Robert Price	03/2021
7264	4*10^113905+91	113906	Robert Price	08/2018
7263	Phi(256695,7)	113906	Henri Lifchitz	02/2026
7265	10^113894+76609	113895	Patrick De Geest	02/2021
7267	10^113894-10000001	113894	Robert Price	09/2020
7266	10^113894-373947	113894	Patrick De Geest	02/2021
7268	33933^2270+2270^33933	113881	Hans Havermann	02/2021
7269	4*10^113874-21	113875	Robert Price	09/2018
7270	2^378272-16565	113872	Enzo Doria	04/2013
7271	2^378217-109075	113855	Enzo Doria	04/2014
7272	2^378198+67	113849	Lelio R Paula	03/2013
7273	2^378173-3249	113842	Yves Minet	12/2014
7274	(2^378155-5)/6597	113833	Lelio R Paula	03/2014
7275	2^378137+1334025	113831	Henri Lifchitz	10/2024
7276	92941#+(355049#)/(92941#)	113830	Makoto Morimoto	10/2017
7277	30030^6173+6173^30030	113829	Hans Havermann	01/2021
7278	2^378128-262977	113828	Enzo Doria	05/2014
7279	2^378123-113215	113827	Enzo Doria	07/2014
7280	6^146274-18893	113824	Enzo Doria	03/2013
7281	34596^1949+1949^34596	113815	Hans Havermann	02/2021
7282	2^378078+75	113813	Lelio R Paula	03/2013
7283	(28*10^113810+449)/9	113811	Robert Price	11/2021
7284	26273^21448+21448^26273	113799	Hans Havermann	02/2021
7285	2^377966+255255	113780	Paul Bourdelais	10/2021
7286	2^377940+63	113772	Lelio R Paula	03/2013
7287	2^377941-2785843	113772	Enzo Doria	04/2016
7288	(7*10^113757+11)/9	113757	Tyler Busby	01/2023
7289	2^377810+1875109	113733	Enzo Doria	09/2016
7290	2^377803-1838635	113731	Enzo Doria	05/2015
7291	2^377799+52223	113729	Yves Minet	08/2010
7292	(2^377791+3258)/2	113727	Stefano Morozzi	02/2021
7293	11^109190-270	113710	Enzo Doria	12/2012
7294	28206^10739+10739^28206	113698	Hans Havermann	01/2021
7295	7*10^113693+9	113694	Robert Price	09/2015
7296	13899^27442+27442^13899	113692	Norbert Schneider	12/2020
7297	(82*10^113681+161)/9	113682	Robert Price	10/2019
7298	26121^22478+22478^26121	113673	Hans Havermann	01/2021
7299	4*10^113658+49	113659	Robert Price	01/2019
7300	(10^113656+7)/40231/6439001	113645	Alfred Reich	06/2021
7301	(2*10^113631+529)/9	113631	Robert Price	01/2018
7302	2^377408-2798279	113612	Enzo Doria	04/2016
7303	(292^46336+1)/(292^256+1)	113605	Martin Hopf	12/2023
7304	13706^27459+27459^13706	113596	Norbert Schneider	12/2020
7305	5*10^113586+57	113587	Robert Price	12/2018
7306	Phi(150733,-7)	113582	Henri Lifchitz	12/2025
7307	(2^377242+2794)/2	113561	Stefano Morozzi	02/2021
7308	2^377222+93679	113556	Yves Minet	02/2011
7310	262147#+316847	113552	Makoto Morimoto	02/2016
7309	27172^15101+15101^27172	113552	Hans Havermann	01/2021
7311	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
7312	2^377026-458903	113497	Enzo Doria	04/2015
7313	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
7314	34791^1828+1828^34791	113488	Hans Havermann	02/2021
7315	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
7316	(29*10^113468-17)/3	113469	Robert Price	09/2019
7317	35^73477-34^73477	113454	Robert Price	05/2012
7318	(14*10^113451-89)/3	113452	Robert Price	05/2020
7319	2^376790+27	113426	Lelio R Paula	03/2013
7320	2^376786-112701	113424	Enzo Doria	06/2014
7321	2^376731+21	113408	Lelio R Paula	03/2013
7322	9*10^113394-73	113395	Robert Price	01/2021
7323	29660^6651+6651^29660	113387	Hans Havermann	01/2021
7325	2^376634+1871245	113379	Enzo Doria	05/2016
7324	(4^188318+17)/3	113379	Robert Price	02/2017
7326	E(29532)/492842728006750534663978950979381235	113367	Thomas Ritschel	01/2021
7327	2^376576-344369	113361	Enzo Doria	07/2015
7328	2^376549-4543	113353	Yves Minet	03/2019
7329	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
7330	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
7331	(2^376350+3538)/2	113293	Stefano Morozzi	09/2020
7332	27265^14272+14272^27265	113273	Hans Havermann	02/2021
7333	32174^3315+3315^32174	113269	Hans Havermann	02/2021
7334	(2*10^113248+73)/3	113248	Robert Price	09/2020
7335	2^376128-21237	113226	Enzo Doria	06/2013
7336	5*10^113224-81	113225	Robert Price	01/2019
7337	10^113220+51409	113221	Patrick De Geest	02/2021
7339	10^113220-1000001	113220	Robert Price	08/2020
7338	10^113220-61779	113220	Patrick De Geest	02/2021
7340	(2^376102+1578)/2	113218	Stefano Morozzi	09/2020
7341	(2^375996+3102)/2	113186	Stefano Morozzi	09/2020
7342	37258^1091+1091^37258	113184	Hans Havermann	02/2021
7343	(94*10^113176+11)/3	113178	Robert Price	04/2020
7344	(46*10^113162+521)/9	113163	Robert Price	02/2019
7345	14*29^77375+17875	113155	Eric Chen	06/2025
7346	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
7347	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
7348	3*10^113137+23	113138	Robert Price	03/2022
7349	(8*10^113135-269)/9	113135	Robert Price	09/2021
7350	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
7351	26050^21959+21959^26050	113100	Hans Havermann	02/2021
7352	2^375638-1787171	113079	Enzo Doria	03/2016
7353	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
7354	2^375537+4847	113048	Yves Minet	02/2011
7355	(17^91837+16^91837)/33	113000	Robert Price	08/2013
7356	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
7357	2^375350-3221	112992	Yves Minet	07/2011
7358	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
7359	2^375305+76757	112979	Enzo Doria	05/2016
7360	2^375258+1874989	112964	Enzo Doria	07/2016
7361	(29^77237-1)/28	112950	Robert Price	04/2012
7362	26620^17483+17483^26620	112939	Hans Havermann	01/2021
7363	2^375154+74959	112933	Enzo Doria	04/2016
7364	(266*10^112930-17)/3	112932	Robert Price	07/2020
7365	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
7366	(85*10^112919+293)/9	112920	Robert Price	12/2019
7367	29412^6899+6899^29412	112907	Hans Havermann	02/2021
7368	(191*10^112903-17)/3	112905	Robert Price	11/2021
7369	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
7370	25992^22039+22039^25992	112889	Hans Havermann	02/2021
7371	2^374993-2787163	112885	Enzo Doria	11/2015
7372	(697*10^112869+23)/9	112871	Robert Price	04/2021
7373	(19*10^112851+377)/9	112852	Alfred Reich	11/2022
7374	30420^5111+5111^30420	112813	Hans Havermann	02/2021
7375	13699^27268+27268^13699	112800	Norbert Schneider	12/2020
7376	123^53970+2	112793	Lelio R Paula	06/2013
7377	12308*27^78796+23	112790	Eric Chen	07/2023
7378	28942^7887+7887^28942	112785	Hans Havermann	01/2021
7379	2^374640-4685	112778	Yves Minet	05/2019
7380	12^104501-11	112776	Riley Fisher	12/2023
7381	57290^93+93^57290	112775	Hans Havermann	01/2021
7382	115^54726-54726^115	112774	Norman Luhn	09/2024
7383	13608^27277-27277^13608	112758	Norbert Schneider	12/2022
7384	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
7385	p(22852)#/2+512	112745	Robert Price	05/2017
7386	(11*10^112742-131)/3	112743	Robert Price	09/2018
7387	2^374441-21049	112718	Enzo Doria	06/2013
7388	(15056!^2+1)/(30113*454287444157)	112711	Michael Porter	09/2025
7389	4*10^112706-93	112707	Robert Price	07/2020
7391	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
7390	Phi(374321,-2)	112682	Henri Lifchitz	12/2025
7392	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
7393	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
7394	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
7395	3^236011-8828	112606	Enzo Doria	05/2014
7396	31854^3427+3427^31854	112602	Hans Havermann	02/2021
7397	2569^33013-2568^33013	112567	Norbert Schneider	01/2026
7398	Phi(442141,-2)	112561	Henri Lifchitz	12/2025
7399	(85*10^112530-373)/9	112531	Robert Price	05/2021
7400	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
7401	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
7402	27618^11821+11821^27618	112479	Hans Havermann	01/2021
7403	U(602921)/4823369	112479	Serge Batalov	07/2024
7404	26343^18580+18580^26343	112460	Hans Havermann	01/2021
7405	39^70666+2	112435	Lelio R Paula	11/2013
7406	(134*10^112400+7)/3	112402	Robert Price	02/2020
7407	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
7408	(2^373350-7)/3	112390	Lelio R Paula	03/2014
7409	3^235532-235532	112378	Anonymous	09/2025
7410	2^373306-1840931	112377	Enzo Doria	06/2015
7411	8*10^112371-37	112372	Robert Price	03/2022
7412	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
7413	6*10^112359-79	112360	Robert Price	03/2022
7414	34409^1842+1842^34409	112356	Hans Havermann	02/2021
7415	(142*10^112352-7)/9	112354	Robert Price	12/2019
7416	25580^24633+24633^25580	112336	Hans Havermann	01/2021
7417	2^373117+1872107	112320	Enzo Doria	05/2016
7418	(2^373083+2226)/2	112309	Stefano Morozzi	01/2021
7419	(35*10^112308+37)/9	112309	Robert Price	05/2022
7420	27963^10376+10376^27963	112301	Hans Havermann	01/2021
7421	2^373040+2792761	112297	Enzo Doria	03/2016
7422	(156^51203-1)/155	112293	Anonymous	06/2024
7423	EPrime(112280)	112280	Eric W. Weisstein	10/2010
7424	2^372950+7	112270	Lelio R Paula	03/2013
7425	2^372945+1872167	112268	Enzo Doria	05/2016
7426	36274^1243+1243^36274	112249	Hans Havermann	02/2021
7427	(55*10^112246+629)/9	112247	Robert Price	01/2022
7428	(2^372872+3798)/2	112246	Stefano Morozzi	02/2021
7429	25513^25060+25060^25513	112232	Hans Havermann	02/2021
7430	(53*10^112229-611)/9	112230	Robert Price	02/2022
7431	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020
7432	6*10^112208+43	112209	Robert Price	07/2020
7433	(2^372728+3058)/2	112203	Stefano Morozzi	09/2020
7434	32061^3158+3158^32061	112195	Hans Havermann	02/2021
7435	2^372695+72113	112193	Enzo Doria	04/2016
7436	2^372689-2563	112191	Yves Minet	07/2014
7437	2^372638-1859441	112176	Enzo Doria	03/2016
7438	3^235074-113056	112159	Enzo Doria	07/2014
7439	-E(29242)/489848365125303139750087	112140	Thomas Ritschel	01/2021
7440	(2^372514+1822)/2	112138	Stefano Morozzi	02/2021
7441	29468^6387+6387^29468	112135	Hans Havermann	02/2021
7442	(2^372428+3742)/2	112112	Stefano Morozzi	01/2021
7443	25375^25454-25454^25375	112110	Norbert Schneider	01/2021
7444	131^52949-130	112108	Norbert Schneider	02/2019
7445	(91*10^112098-1)/9	112100	Robert Price	04/2015
7446	(68*10^112087-149)/9	112088	Robert Price	07/2022
7447	2^372314+212419	112078	Enzo Doria	08/2023
7448	2^372310-85061	112077	Paul Bourdelais	02/2012
7449	(10^112067+53)/9	112067	Serge Batalov	07/2015
7450	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
7451	75^59760+2	112054	Lelio R Paula	08/2013
7452	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
7453	(10^112048+7)/8747/373157	112039	Alfred Reich	06/2021
7454	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
7455	F(536233)/825798821/1102495049/5641839306317	112036	Serge Batalov	07/2024
7456	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
7457	8*10^112018-49	112019	Robert Price	08/2019
7459	2^372108+74221	112016	Enzo Doria	04/2016
7458	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
7460	8*10^112011-73	112012	Robert Price	01/2022
7461	(184*10^112007-1)/3	112009	Robert Price	02/2020
7462	5*10^112003+81	112004	Robert Price	03/2019
7463	215^48018+48018^215	112000	Norbert Schneider	10/2018
7464	Phi(82303,5#)	111990	Henri Lifchitz	12/2025
7465	25549^24148+24148^25549	111979	Hans Havermann	02/2021
7466	2^371970-459491	111975	Enzo Doria	05/2015
7467	41^69427-40^69427	111971	Robert Price	07/2012
7468	(20^86027+19^86027)/39	111923	Robert Price	09/2025
7469	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
7470	15*25^80056+446	111915	Eric Chen	10/2023
7471	(34*10^111902-547)/9	111903	Robert Price	03/2021
7472	(10^111902+71)/9	111902	Serge Batalov	07/2015
7473	((385283-70250)F(535399)-(85283-70250)*L(535399))/2	111897	Yaroslav Berezhko	09/2025
7474	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
7475	29080^7027+7027^29080	111865	Hans Havermann	01/2021
7476	3^234408+531440	111842	Alfred Reich	03/2026
7477	31307^3730+3730^31307	111820	Hans Havermann	02/2021
7478	2^371440-112865	111815	Enzo Doria	06/2014
7479	2^371426-459161	111811	Enzo Doria	05/2015
7480	25768^21771+21771^25768	111779	Hans Havermann	02/2021
7481	28022^9747+9747^28022	111777	Hans Havermann	02/2021
7482	(94*10^111770+11)/3	111772	Robert Price	04/2020
7483	2^371276-461267	111766	Enzo Doria	07/2015
7484	6*10^111760+43	111761	Robert Price	07/2020
7485	98079!4-1024	111747	Robert Price	11/2019
7486	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
7487	10^(255862+1)-410^55862-1	111725	Robert Price	07/2023
7488	2^371098-113261	111712	Enzo Doria	07/2014
7489	(7*10^111706-61)/9	111706	Erik Branger	01/2011
7490	2^371044+1869391	111696	Enzo Doria	05/2016
7491	26310^17581+17581^26310	111688	Hans Havermann	01/2021
7492	88^57416+87	111645	Norbert Schneider	11/2015
7493	2^370829-109693	111631	Enzo Doria	04/2014
7494	15^94906-2	111619	Lelio R Paula	11/2013
7495	25835^20904+20904^25835	111614	Hans Havermann	02/2021
7496	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
7497	27758^10479+10479^27758	111597	Hans Havermann	02/2021
7498	2^370695-4627	111591	Yves Minet	05/2019
7499	7*10^111579-87	111580	Robert Price	06/2020
7500	2^370643-37	111575	Yves Minet	01/2012

Find by discoverer :

PRP Records

Probable Primes Top 10000

(303383 PRPs in the top)