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	2^240617-3645	72433	Lelio R Paula	05/2013
7252	11^69531-24000	72410	Enzo Doria	12/2012
7253	18714^7367+7367^18714	72373	Hans Havermann	11/2019
7254	(22699*2^240396+1)/55	72370	Lelio R Paula	06/2014
7255	6^92995+13	72365	Lelio R Paula	01/2015
7256	(11*10^72362-149)/3	72363	Robert Price	01/2017
7257	18567^7892+7892^18567	72360	Hans Havermann	11/2019
7258	(2^240381+3)/51655	72358	Lelio R Paula	05/2012
7259	6^92974-55	72348	Lelio R Paula	01/2015
7260	2^240295+11	72337	Lelio R Paula	02/2012
7261	(14*10^72326-53)/3	72327	Robert Price	12/2016
7262	15^61493-46	72322	Lelio R Paula	01/2015
7263	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
7264	5*10^72302+9	72303	Dmitry Domanov	11/2010
7265	(9787*2^240179-1)/265	72303	Lelio R Paula	04/2015
7266	11^69419-3120	72293	Enzo Doria	12/2012
7267	18069^10016+10016^18069	72289	Hans Havermann	11/2019
7268	4*10^72274-83	72275	Robert Price	10/2017
7269	10^72267+33	72268	Robert Price	01/2011
7270	10^72267-553947	72267	Patrick De Geest	05/2013
7271	11^69389-1380	72262	Enzo Doria	12/2012
7272	(16^60013-5^60013)/11	72262	Robert Price	07/2013
7273	7^85507-30	72262	Lelio R Paula	08/2014
7274	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
7275	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
7276	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
7277	2^239863-112267	72206	Enzo Doria	06/2014
7278	2^239853-114853	72203	Enzo Doria	05/2015
7279	(4*10^72174+149)/9	72174	Robert Price	03/2017
7281	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
7280	2^239651-110665	72143	Enzo Doria	05/2014
7282	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
7283	241^30280+30280^241	72128	Norbert Schneider	11/2014
7284	(68*10^72120-23)/9	72121	Robert Price	10/2015
7285	(9^75571+8^75571)/17	72112	Robert Price	12/2012
7286	(15*2^239530-1)/173	72105	Lelio R Paula	01/2014
7287	2^239513-112519	72101	Enzo Doria	06/2014
7288	(10^72097+149)/3	72097	Serge Batalov	12/2014
7289	2^239442-6555	72080	Lelio R Paula	05/2012
7290	2*5^103106+3	72069	Lelio R Paula	10/2014
7291	2^239402-197	72068	Lelio R Paula	02/2012
7292	2^239356-111875	72054	Enzo Doria	05/2014
7293	(38*10^72050-119)/9	72051	Robert Price	11/2016
7294	2^239339+15015	72049	Lelio R Paula	01/2013
7295	159^32728+2	72048	Lelio R Paula	05/2013
7296	15^61259-38	72047	Lelio R Paula	01/2015
7297	92^36683-91^36683	72038	Robert Price	08/2015
7298	2^239280+54615	72031	Lelio R Paula	05/2012
7299	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015
7300	(85*10^72025-1)/3	72027	Robert Price	07/2017
7301	2^239236-97305	72018	Lelio R Paula	05/2012
7302	144^33361-143	72006	Norbert Schneider	11/2018
7303	2^239169+59	71998	Lelio R Paula	02/2012
7304	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
7305	(15*2^239171-1)/106301	71994	Lelio R Paula	01/2014
7307	(29^49211-1)/28	71965	Robert Price	04/2012
7306	(299*10^71963+1)/3	71965	Robert Price	11/2017
7308	L(344293)	71953	Renaud Lifchitz	09/2003
7309	V(344293)	71953	Serge Batalov	03/2015
7310	6*10^71951+7	71952	Dmitry Domanov	11/2010
7311	3^150798+40	71949	Lelio R Paula	01/2015
7312	2^238961+95	71935	Lelio R Paula	02/2012
7313	12511^17556+17556^12511	71933	Norbert Schneider	09/2019
7314	2^238936-407	71927	Yves Minet	02/2012
7315	2^238923-28635	71923	Lelio R Paula	05/2012
7316	10^71910+25119	71911	Patrick De Geest	05/2016
7317	10^71910-801	71910	Robert Price	04/2016
7318	2^238845-112651	71900	Enzo Doria	06/2014
7319	2^238792-111245	71884	Enzo Doria	05/2014
7320	6*7^85059+5	71884	Lelio R Paula	10/2014
7321	19312^5273+5273^19312	71881	Hans Havermann	11/2019
7322	19176^5603+5603^19176	71880	Hans Havermann	11/2019
7323	2^238752-110589	71872	Enzo Doria	05/2014
7324	12^66581+7	71853	Lelio R Paula	07/2014
7325	(7*2^238691+1)/41229	71850	Lelio R Paula	06/2012
7326	4*3^150568-5	71840	Lelio R Paula	04/2014
7327	6^92301+67	71825	Lelio R Paula	01/2015
7328	2^238568+98765331	71817	Jason Earls	01/2009
7329	2^238541-112723	71808	Enzo Doria	06/2014
7330	2^238529-15949	71805	Enzo Doria	04/2013
7331	9*5^102721-8	71800	Lelio R Paula	10/2014
7332	2^238494-165	71794	Lelio R Paula	02/2012
7333	18035^9562+9562^18035	71790	Hans Havermann	10/2019
7334	18390^7993+7993^18390	71771	Hans Havermann	11/2019
7335	2^238389-110905	71763	Enzo Doria	05/2014
7336	(145*10^71760-1)/9	71762	Serge Batalov	12/2014
7337	7^84913+5062	71760	Mike Oakes	02/2010
7338	21218^2409+2409^21218	71756	Hans Havermann	10/2019
7339	(F(11446)^31-F(11445)^31)/F(11444)	71753	Wayne Halsdorf	03/2012
7340	2^238268-97305	71726	Lelio R Paula	05/2012
7341	gcd(V(1330365),5F(266073)(F(266073)-1)+1)	71724	Serge Batalov	04/2015
7342	2^238235-113247	71716	Enzo Doria	07/2014
7343	2*12^66450-5^66450	71712	Mike Oakes	11/2010
7344	(2^238213+lucasV(1,2,238213)+1)/4	71709	Mike Oakes	11/2016
7345	2^238199-111817	71706	Enzo Doria	05/2014
7346	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
7347	2^238144+98765331	71689	Jason Earls	01/2009
7348	18^57102-4265	71679	Enzo Doria	03/2013
7349	(73*10^71670-1)/9	71671	Robert Price	01/2015
7350	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
7351	2^238067-111925	71666	Enzo Doria	05/2014
7352	19143^5528+5528^19143	71644	Hans Havermann	10/2019
7353	65401!4+128	71638	Robert Price	09/2019
7354	36^46030+35	71637	Norbert Schneider	04/2014
7355	(74*10^71621+313)/9	71622	Robert Price	11/2017
7356	2^237905-91	71617	Lelio R Paula	02/2012
7357	(31*2^237902-1)/123	71616	Lelio R Paula	01/2014
7358	(15185*2^237866-1)/43967	71605	Lelio R Paula	04/2015
7359	16696^16957+16957^16696	71603	Norbert Schneider	09/2019
7360	(24737*2^237841+1)/25	71601	Lelio R Paula	06/2014
7361	2^237846+1299	71599	Lelio R Paula	05/2012
7362	6^92004+199801	71594	Mike Oakes	02/2011
7363	159^32516+2	71581	Lelio R Paula	05/2013
7364	2^237781+855	71580	Lelio R Paula	05/2012
7365	2^237720-4079	71561	Yves Minet	06/2011
7366	2^237698-110945	71555	Enzo Doria	05/2014
7367	2^237695-113239	71554	Enzo Doria	07/2014
7368	8*5^102362-9	71549	Lelio R Paula	10/2014
7369	(4*10^71546-31)/9	71546	Erik Branger	05/2011
7370	2^237650+37	71540	Lelio R Paula	02/2012
7371	18^56977-4391	71522	Enzo Doria	03/2013
7373	(22699*2^237565+1)/4136637	71512	Lelio R Paula	06/2014
7372	((1+sqrt(7)+sqrt(6))^48479-1)((1+sqrt(7)-sqrt(6))^48479-1)((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(7	71512	Mike Oakes	05/2009
7374	(26*10^71503+7)/3	71504	Erik Branger	11/2013
7375	(4*10^71498+173)/3	71499	Robert Price	01/2017
7376	3^149848+110	71496	Lelio R Paula	11/2014
7377	2^237498+513	71495	Lelio R Paula	05/2012
7378	2^237485+107	71491	Lelio R Paula	02/2012
7379	(2^237465+9)/2419	71481	Lelio R Paula	05/2012
7380	2^237439-112237	71477	Enzo Doria	06/2014
7381	2^237407-9787	71467	Lelio R Paula	11/2009
7382	2^237383+72953	71460	Enzo Doria	04/2016
7383	19768^4119+4119^19768	71458	Hans Havermann	11/2019
7384	82^37337-81^37337	71457	Robert Price	01/2015
7385	(1017*2^237313-1)/19	71441	Lelio R Paula	04/2015
7386	2^237311+191	71438	Lelio R Paula	02/2012
7387	11699^17560+17560^11699	71437	Norbert Schneider	09/2019
7388	2^237280-59	71429	Lelio R Paula	02/2012
7389	11^68564-98	71403	Lelio R Paula	01/2015
7390	2^237173+74801	71397	Enzo Doria	04/2016
7391	15^60697+56	71386	Lelio R Paula	01/2015
7392	2^237118+177	71380	Lelio R Paula	02/2012
7393	2^237110+69	71378	Lelio R Paula	02/2012
7394	15^60690-58	71377	Lelio R Paula	01/2015
7395	(5*2^237125-1)/599851191	71374	Lelio R Paula	01/2014
7396	20311^3262+3262^20311	71363	Hans Havermann	11/2019
7397	(3^149567+2)/539	71359	Lelio R Paula	06/2012
7398	(5*10^71357-143)/3	71358	Robert Price	04/2016
7399	2^237039-114621	71356	Enzo Doria	05/2015
7400	12^66116-37	71352	Lelio R Paula	02/2015
7401	(3^149497+2^149497)/5	71328	Jean-Louis Charton	10/2010
7402	2^236941-66945	71327	Lelio R Paula	05/2012
7403	2^236911-1147	71318	Yves Minet	10/2009
7404	65^39337+42	71315	Lelio R Paula	01/2016
7405	6*10^71299+7	71300	Dmitry Domanov	11/2010
7406	(25*2^236843+1)/3753	71295	Lelio R Paula	06/2012
7407	10^71291+15187	71292	Patrick De Geest	03/2016
7409	10^71291-5587309119	71291	Robert Price	03/2015
7408	10^71291-273581	71291	Patrick De Geest	03/2016
7410	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
7411	15105^17054+17054^15105	71271	Norbert Schneider	08/2018
7412	(2^236738+9)/13	71265	Lelio R Paula	05/2012
7413	5^101949+42	71260	Lelio R Paula	07/2014
7414	5*10^71237+9	71238	Dmitry Domanov	11/2010
7415	2^236634-16025	71234	Enzo Doria	04/2013
7416	71^38478+70	71233	Norbert Schneider	12/2014
7417	9*7^84280+8	71226	Lelio R Paula	10/2014
7418	(10^71223+59)/3	71223	Serge Batalov	12/2014
7419	23260^1153+1153^23260	71219	Hans Havermann	10/2019
7420	(15185*2^236569-1)/453	71216	Lelio R Paula	04/2015
7421	51829#+(216091#)/(51829#)	71208	Makoto Morimoto	03/2016
7422	2^236528-173	71203	Lelio R Paula	02/2012
7423	3*2^236511-5	71198	Lelio R Paula	04/2014
7424	2^236477-99	71187	Lelio R Paula	02/2012
7425	11^68356-2130	71186	Enzo Doria	12/2012
7426	15128^17031+17031^15128	71186	Norbert Schneider	08/2018
7427	11^68355-3120	71185	Enzo Doria	12/2012
7428	36^45737-35^45737	71181	Robert Price	10/2012
7429	(3^149183-lucasV(1,3,149183)+1)/3	71178	Paul Vanderveen	12/2017
7430	2^236432+25	71174	Lelio R Paula	02/2012
7431	5^101818-12806	71168	Enzo Doria	02/2013
7432	(7*10^71166-457)/9	71166	Robert Price	09/2017
7433	65^39253+62	71163	Lelio R Paula	01/2016
7434	39^44718+38	71150	Norbert Schneider	05/2014
7435	18996^5557+5557^18996	71137	Hans Havermann	10/2019
7436	64983!4-256	71135	Robert Price	11/2019
7437	2^236296-407	71133	Yves Minet	02/2012
7438	2^236286-117	71130	Lelio R Paula	02/2012
7439	2^236257-111193	71121	Enzo Doria	05/2014
7440	7^84149-36	71115	Lelio R Paula	08/2014
7441	164176#-p(164176)	71108	Henri Lifchitz	12/2018
7442	2^236209-112123	71106	Enzo Doria	06/2014
7443	18^56644-4985	71104	Enzo Doria	03/2013
7444	(46*10^71077+521)/9	71078	Robert Price	08/2017
7445	21^53753+2	71074	Ray Chandler	08/2011
7446	(86*10^71068-311)/9	71069	Robert Price	10/2017
7447	2^236081-110923	71068	Enzo Doria	05/2014
7448	(293*27^49642-1736)/13	71058	Curtis Bright	05/2015
7449	65^39192+22	71052	Lelio R Paula	01/2016
7450	(439#+1)^397-439#^397	71038	Mike Oakes	11/2010
7451	7^84050-2	71031	Lelio R Paula	09/2013
7452	15813^16916+16916^15813	71031	Norbert Schneider	09/2019
7453	64877!4+128	71007	Robert Price	09/2019
7454	18562^6681+6681^18562	70997	Hans Havermann	10/2019
7455	20^54558-23	70982	Lelio R Paula	01/2015
7456	2^235793-112555	70981	Enzo Doria	06/2014
7457	49936!3-3^49936	70981	Robert Price	08/2015
7458	2^235787-78795	70979	Lelio R Paula	05/2012
7459	Perrin(581132)	70970	Eric W. Weisstein	02/2011
7460	14^61913-97	70961	Lelio R Paula	01/2015
7462	2^235720+16321	70959	Yves Minet	03/2010
7461	2^235718+16095	70959	Lelio R Paula	05/2012
7463	163841#+349933	70957	Nicolas PALAU	11/2016
7464	2^235710+7	70956	Lelio R Paula	02/2012
7465	(175^31627+1)/176	70939	Eric Chen	10/2017
7466	2^235635-112087	70934	Enzo Doria	06/2014
7467	153^32467+152	70931	Norbert Schneider	11/2018
7469	2^235575-1965	70916	Lelio R Paula	05/2012
7468	6^91133+101	70916	Lelio R Paula	01/2015
7470	(21181*2^235505+1)/3	70898	Lelio R Paula	06/2014
7471	(14*10^70896+211)/9	70897	Robert Price	11/2017
7472	5^101425+84	70894	Lelio R Paula	07/2014
7473	177^31536+2	70893	Lelio R Paula	05/2013
7474	43*71^38292+4	70891	Serge Batalov	03/2016
7475	(29*2^235506-1)/112029785	70888	Lelio R Paula	01/2014
7476	11^68045-1530	70862	Enzo Doria	12/2012
7477	5*10^70858+21	70859	Robert Price	01/2017
7479	2^235326+3	70841	Donovan Johnson	02/2006
7478	34523!2+4	70841	Robert Price	02/2015
7480	(31*2^235307+1)/3	70836	Lelio R Paula	06/2012
7481	2^235308+135	70835	Lelio R Paula	02/2012
7482	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
7483	2^235274+159	70825	Lelio R Paula	02/2012
7484	3^148409+70	70810	Lelio R Paula	11/2014
7485	(19*10^70794+17)/9	70795	Robert Price	03/2015
7486	2^235108-232709	70775	Paul Bourdelais	03/2013
7487	22995^1196+1196^22995	70773	Hans Havermann	11/2019
7488	(2^235099-2^117550+1)/5	70772		11/2006
7489	19^55325-6	70748	Lelio R Paula	08/2014
7490	257^29356+29356^257	70746	Norbert Schneider	10/2014
7491	22*10^70729+3	70731	Robert Price	10/2017
7492	2^234956+11715	70729	Lelio R Paula	05/2012
7493	(7*10^70727-43)/9	70727	Robert Price	10/2014
7494	2^234890-30341	70709	Enzo Doria	11/2012
7495	17^57461+14	70703	Lelio R Paula	01/2015
7496	18281^7366+7366^18281	70697	Hans Havermann	09/2019
7497	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
7498	2*10^70688+51	70689	Robert Price	10/2017
7499	123^33822-122	70685	Norbert Schneider	01/2015
7500	7*10^70680-99	70681	Robert Price	11/2017

Find by discoverer :

PRP Records

Probable Primes Top 10000

(255312 PRPs in the top)