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	(29*2^230684+1)/1395	69442	Lelio R Paula	08/2012
7252	(19*10^69424+77)/3	69425	Robert Price	08/2016
7253	19^54287-96	69420	Lelio R Paula	09/2013
7254	2^230541+58905	69400	Lelio R Paula	04/2012
7255	2^230506+12705	69390	Lelio R Paula	02/2013
7256	8*6^89156-5	69378	Lelio R Paula	09/2014
7257	2^230438-111347	69369	Enzo Doria	05/2014
7258	2^230428-99	69366	Lelio R Paula	02/2012
7259	(62^38699+1)/63	69362	Paul Bourdelais	08/2017
7260	3*10^69354+17	69355	Robert Price	03/2017
7261	(493*10^69340-7)/9	69342	Robert Price	07/2016
7262	(41*10^69321+373)/9	69322	Robert Price	04/2017
7263	6^89072+53	69312	Lelio R Paula	09/2013
7264	155^31639+2	69300	Lelio R Paula	05/2013
7265	3*7^81965-4	69269	Lelio R Paula	09/2014
7266	(16*10^69265+41)/3	69266	Robert Price	10/2017
7267	(86*10^69260-77)/9	69261	Robert Price	05/2016
7268	9*5^99087+4	69260	Lelio R Paula	09/2014
7269	3^145145+2660	69252	Lelio R Paula	09/2013
7271	11^66492-1140	69245	Enzo Doria	11/2012
7270	5*3^145129-4	69245	Lelio R Paula	04/2014
7272	7*3^145126+8	69244	Lelio R Paula	04/2014
7273	11^66480-2370	69232	Enzo Doria	12/2012
7274	2^229962-65	69226	Lelio R Paula	02/2012
7275	2^229958-110733	69225	Enzo Doria	05/2014
7276	V(332407)	69225	Serge Batalov	03/2015
7277	6^88959+7	69224	Lelio R Paula	09/2013
7278	15^58855-94	69219	Lelio R Paula	09/2013
7279	159773#-p(159773)	69212	Henri Lifchitz	12/2018
7280	(2^229838+47)/12081	69185	Lelio R Paula	04/2012
7281	3^144952+98	69160	Lelio R Paula	09/2013
7282	5^98941-72	69157	Lelio R Paula	06/2013
7283	(17*2^229604-1)/229	69117	Lelio R Paula	01/2014
7284	2^229585-1063	69112	Yves Minet	11/2012
7285	(13*2^229567-1)/19	69107	Lelio R Paula	01/2014
7286	(13*2^229393-1)/5	69055	Lelio R Paula	01/2014
7287	(53*10^69050-17)/9	69051	Robert Price	09/2015
7288	(43*10^69048+47)/9	69049	Robert Price	12/2017
7289	2^229305-1868533	69028	Enzo Doria	04/2016
7290	2^229297+1385	69026	Lelio R Paula	04/2012
7291	18^54986-2441	69023	Enzo Doria	03/2013
7292	(34*10^69021-7)/9/3/67	69020	Makoto Morimoto	04/2016
7293	5^98736-14636	69014	Enzo Doria	02/2013
7294	(13^61949-5^61949)/8	69007	Robert Price	03/2013
7295	(2^229227+5)/611	69002	Lelio R Paula	04/2012
7296	2^229216-113279	69001	Enzo Doria	07/2014
7297	10^68994+51913	68995	Patrick De Geest	03/2016
7299	10^68994-10^5814-1	68994	Serge Batalov	01/2011
7298	10^68994-82947	68994	Patrick De Geest	03/2016
7300	(17*2^229136-1)/2381	68975	Lelio R Paula	01/2014
7301	2^229113+107	68970	Lelio R Paula	02/2012
7302	11^66202-4410	68943	Enzo Doria	01/2013
7303	12^63883+5	68942	Lelio R Paula	07/2013
7304	(9913*2^229002-1)/399903	68935	Lelio R Paula	04/2015
7305	2^228962-111581	68925	Enzo Doria	05/2014
7306	2^228944+81	68920	Henri Lifchitz	01/2007
7307	11^66174-54	68914	Lelio R Paula	09/2013
7308	2^228913-111265	68910	Enzo Doria	05/2014
7309	2^228902+73519	68907	Enzo Doria	04/2016
7310	(47*2^228884+1)/63	68901	Lelio R Paula	04/2015
7311	2^228821+76427	68882	Enzo Doria	05/2016
7312	3^144340+50	68868	Lelio R Paula	09/2013
7313	2^228758-112967	68864	Enzo Doria	06/2014
7314	2^228743-111379	68859	Enzo Doria	05/2014
7315	2^228741-110911	68858	Enzo Doria	05/2014
7317	lucasU(1926,1,20964)-lucasU(1926,1,20963)	68857	Mike Oakes	05/2009
7316	3*5^98511-8	68857	Lelio R Paula	09/2014
7318	2^228717+467	68851	Lelio R Paula	02/2011
7319	Phi(153218,10)/2211855049/23592660859/497714117291	68849	Maksym Voznyy	10/2011
7320	(509203*2^228665-1)/35	68840	Lelio R Paula	04/2015
7321	8^76213-7^76213	68828	Ananda Tallur & Jean-Louis Charton	11/2003
7322	11^66074-1050	68809	Enzo Doria	11/2012
7323	(68*10^68798-11)/3	68800	Robert Price	10/2017
7324	2^228484+181	68781	Lelio R Paula	02/2012
7325	2^228479-58695	68780	Lelio R Paula	04/2012
7326	2^228465-15853	68775	Enzo Doria	04/2013
7327	11^66040-5400	68774	Enzo Doria	01/2013
7328	(13*2^228441-1)/575	68766	Lelio R Paula	01/2014
7329	(17*2^228393+1)/295	68752	Lelio R Paula	08/2012
7330	2*10^68744+41	68745	Robert Price	01/2017
7331	11^66011-150	68744	Enzo Doria	08/2012
7332	(13*2^228304-1)/81	68726	Lelio R Paula	01/2014
7333	2^228295-111079	68724	Enzo Doria	05/2014
7335	(3^144039+7)/22	68723	Lelio R Paula	04/2012
7334	(8*10^68722+49)/3	68723	Robert Price	03/2016
7336	(35*10^68718+1)/9	68719	Serge Batalov	11/2010
7337	2^228271-228271	68717	Henri Lifchitz	11/2004
7338	2^228257+82875	68713	Lelio R Paula	02/2013
7339	3^144013+40	68712	Lelio R Paula	09/2013
7340	13^61671-86	68699	Lelio R Paula	09/2013
7341	(46*10^68698+683)/9	68699	Robert Price	12/2017
7342	17^55828-72	68694	Lelio R Paula	09/2013
7343	6^88259+61	68679	Lelio R Paula	09/2013
7344	18^54699-5	68663	Lelio R Paula	09/2013
7345	33^45216+2	68662	Lelio R Paula	05/2013
7347	(2^228073-5)/3	68657	Lelio R Paula	04/2012
7346	(2^(6*38012+1)-5)/3	68657	Kevin Acres	11/2013
7348	2^228055-111607	68652	Enzo Doria	05/2014
7349	2^228054-114761	68652	Enzo Doria	05/2015
7350	2^228041+1185	68648	Lelio R Paula	04/2012
7351	2^228040-1037	68647	Yves Minet	11/2012
7352	2*F(328450)-1	68642	Henri Lifchitz	12/2009
7353	5^98201-34	68640	Lelio R Paula	06/2013
7354	9^71910+38^71910-24^71910-3*2^71910	68620	Mike Oakes	12/2010
7355	7*2^227780-3	68570	Lelio R Paula	04/2014
7356	15327^16382-16382^15327	68567	Norbert Schneider	11/2018
7357	2^227733-121	68555	Lelio R Paula	02/2012
7358	2^227702-16967	68546	Enzo Doria	05/2013
7359	2^227689-111655	68542	Enzo Doria	05/2014
7360	gcd(V(823915),5F(164783)(F(164783)-1)+1)	68536	Serge Batalov	04/2015
7361	5^98051+2	68535	Ray Chandler	07/2011
7362	5*10^68524+51	68525	Robert Price	01/2017
7363	(11*10^68520-149)/3	68521	Robert Price	01/2017
7364	19^53573-78	68507	Lelio R Paula	09/2013
7365	(68*10^68504+13)/9	68505	Ray Chandler	10/2010
7366	9*5^98003+4	68503	Lelio R Paula	09/2014
7367	2^227528+51	68493	Lelio R Paula	02/2012
7368	(146*28^47316+1)/3	68476	Karsten Bonath	06/2018
7369	3^143497+8	68466	Lelio R Paula	04/2012
7370	2^227430-95	68464	Lelio R Paula	02/2012
7371	(8*10^68455+13)/3	68456	Robert Price	11/2017
7372	3*5^97934-2	68454	Lelio R Paula	09/2014
7373	20^52613+77	68452	Lelio R Paula	09/2013
7374	2^227371+32769	68446	Lelio R Paula	04/2012
7375	(3^143465+4)/21270420067	68440	Lelio R Paula	04/2012
7376	CopelandErdos(68433)	68433	Eric W. Weisstein	08/2013
7377	2^227323+75431	68432	Enzo Doria	04/2016
7378	2^227314-1965	68429	Lelio R Paula	04/2012
7379	2^227303-110617	68426	Enzo Doria	05/2014
7380	7^80963+66	68422	Lelio R Paula	07/2013
7381	2^227290+73849	68422	Enzo Doria	04/2016
7382	(14^59693-1)/13	68415	Paul Bourdelais	06/2008
7383	2^227256-2786249	68411	Enzo Doria	03/2016
7384	8*10^68400-7	68401	Dmitry Domanov	11/2010
7385	(15*2^227228-1)/583	68401	Lelio R Paula	01/2014
7386	2^227210+1869169	68398	Enzo Doria	05/2016
7387	2^227159-1838635	68382	Enzo Doria	05/2015
7388	44*10^68368+3	68370	Robert Price	08/2017
7389	2^227115-7807	68369	Lelio R Paula	10/2009
7390	2^227078-47355	68358	Lelio R Paula	04/2012
7391	(2^227063-1017)/349	68351	Lelio R Paula	04/2012
7392	2^227057+148091	68351	Lelio R Paula	04/2012
7393	2^227046+187	68348	Lelio R Paula	02/2012
7394	2^227009-4693	68337	Yves Minet	05/2019
7395	9*10^68331+59	68332	Robert Price	10/2017
7396	11^65608-720	68324	Enzo Doria	11/2012
7397	(32*10^68320+319)/9	68321	Robert Price	10/2017
7398	33408!2-2^33408-1	68315	Joe McLean	05/2017
7399	2^226894-123	68302	Lelio R Paula	02/2012
7400	10^68297+141559	68298	Patrick De Geest	05/2013
7401	10^68297-93	68297	Robert Price	05/2011
7402	680^24107-679^24107	68284	Jean-Louis Charton	07/2010
7403	12^63267+59	68277	Lelio R Paula	07/2013
7404	2^226785-1159	68270	Yves Minet	11/2012
7405	7^80769+90	68258	Lelio R Paula	07/2013
7406	(88*10^68256-1)/3	68258	Robert Price	10/2017
7407	2^226741+66587	68256	Yves Minet	10/2010
7408	2^226720-112403	68250	Enzo Doria	06/2014
7409	(78557*2^226694+1)/3	68247	Lelio R Paula	06/2014
7410	(83*10^68231+7)/9	68232	Robert Price	10/2015
7411	65^37636+16	68231	Lelio R Paula	01/2016
7412	5^97615-4^(97615+1)	68230	Robert Price	04/2016
7413	12^63200-43	68205	Lelio R Paula	07/2013
7414	-330*Bern(21940)/223790620733	68201	Serge Batalov	04/2015
7415	3^142925+8680	68193	Lelio R Paula	06/2013
7416	3*2^226512-7	68188	Lelio R Paula	04/2014
7417	14^59484+57	68177	Lelio R Paula	08/2013
7418	11^65438-2190	68147	Enzo Doria	12/2012
7419	91^34784-2	68144	Lelio R Paula	09/2013
7420	(2^226336-3)*6-7	68135	Gilbert Mozzo	06/2016
7421	(22*10^68133-37)/3	68134	Robert Price	05/2017
7422	5^97476+36	68133	Lelio R Paula	06/2013
7423	3*5^97474-2	68132	Lelio R Paula	09/2014
7424	12^63130+49	68129	Lelio R Paula	07/2013
7425	2^226281+5385	68118	Lelio R Paula	04/2012
7426	2^226257-3049	68111	Yves Minet	10/2014
7427	(28*10^68107-43)/3	68108	Robert Price	04/2016
7428	2^226243-2587	68106	Yves Minet	07/2014
7429	20^52346-11	68104	Lelio R Paula	09/2013
7430	2^226205-99	68095	Lelio R Paula	02/2012
7431	2^226187-49	68090	Lelio R Paula	02/2012
7432	3^142708+76	68090	Lelio R Paula	06/2013
7433	7*10^68088-89	68089	Robert Price	01/2017
7434	2^226154+71839	68080	Enzo Doria	04/2016
7435	(10^68078+59)/3	68078	Serge Batalov	12/2014
7437	14^59387+69	68066	Lelio R Paula	08/2013
7436	2^226108-113429	68066	Enzo Doria	07/2014
7438	(62*10^68059-197)/9	68060	Robert Price	10/2017
7439	(24^49307-1)/23	68053	Robert Price	04/2012
7440	15^57859-28	68048	Lelio R Paula	08/2013
7441	(509203*2^226003-1)/13	68039	Lelio R Paula	04/2015
7442	2^226015-111361	68038	Enzo Doria	05/2014
7443	(10^(234016+1)+7210^34016-1)/9	68033	Robert Price	09/2017
7444	4*10^68020+91	68021	Robert Price	11/2017
7445	156(10^(417000)-1)/101-1	68001	Robert Price	05/2014
7446	2^225878-1017	67997	Lelio R Paula	04/2012
7447	38^75289+5^75289-34^75289+3*2^75289	67994	Mike Oakes	11/2010
7448	3*2^225865+5	67993	Lelio R Paula	04/2014
7450	11^65284-5820	67987	Enzo Doria	01/2013
7449	19^53166+70	67987	Lelio R Paula	08/2013
7451	2^225837+75407	67984	Enzo Doria	04/2016
7452	3^142464-112654	67973	Enzo Doria	06/2014
7453	2^225777+95	67966	Lelio R Paula	02/2012
7454	(2^225641-1017)/138815	67920	Lelio R Paula	04/2012
7455	2^225609-18445	67916	Enzo Doria	05/2013
7456	2^225542-177	67895	Lelio R Paula	02/2012
7457	2^225536-29	67894	Henri Lifchitz	05/2005
7458	11^65190-3390	67889	Enzo Doria	12/2012
7459	3^142249-2^(142249-1)	67871	Robert Price	01/2016
7460	11^65168-4830	67866	Enzo Doria	01/2013
7461	10^67863+58627	67864	Patrick De Geest	01/2016
7462	10^67863-11	67863	Robert Price	05/2011
7463	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
7464	(19*2^225357-1)/11	67840	Lelio R Paula	01/2014
7465	9*6^87164-7	67828	Lelio R Paula	09/2014
7466	131^32034+130	67825	Norbert Schneider	03/2015
7467	(29*2^225314+1)/10881	67824	Lelio R Paula	08/2012
7468	(134*10^67816+7)/3	67818	Robert Price	02/2017
7469	2^225261+855	67811	Lelio R Paula	04/2012
7470	(29*2^225252-1)/2933	67806	Lelio R Paula	01/2014
7471	(4*10^67796+23)/9	67796	Robert Price	11/2014
7472	15477^16180-16180^15477	67790	Norbert Schneider	09/2018
7473	(23*2^225177+1)/31	67785	Lelio R Paula	08/2012
7474	(4*10^67784+149)/9	67784	Robert Price	03/2017
7475	8177^17322+17322^8177	67774	Norbert Schneider	03/2019
7476	2^225120+151	67768	Lelio R Paula	02/2012
7477	(44^41233+1)/45	67763	Robert Price	11/2013
7478	89933!6-16	67747	Robert Price	08/2018
7479	8*10^67742+9	67743	Dmitry Domanov	11/2010
7480	2^224977+1089	67725	Lelio R Paula	04/2012
7481	(2^224950+5)/19509	67713	Lelio R Paula	04/2012
7482	11^65011-5970	67702	Enzo Doria	01/2013
7483	88*10^67691+7	67693	Robert Price	11/2016
7484	11^65000-7140	67691	Enzo Doria	01/2013
7486	2^224841+59	67684	Lelio R Paula	02/2012
7485	33129!2+2^33129	67684	Robert Price	09/2015
7487	2^224827+8415	67680	Lelio R Paula	02/2013
7488	(9913*2^224821-1)/19825	67678	Lelio R Paula	04/2015
7489	2^224815-49789	67677	Henri Lifchitz	04/2005
7490	(43*10^67664+11)/9	67665	Robert Price	06/2015
7491	(292*10^67659-1)/3	67661	Robert Price	01/2017
7492	(17*2^224766+1)/29007	67659	Lelio R Paula	06/2012
7493	2^224744+577294575	67655	Lelio R Paula	02/2016
7494	((1+sqrt(7)+sqrt(6))^45863-1)((1+sqrt(7)-sqrt(6))^45863-1)((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(7	67653	Mike Oakes	05/2009
7495	(2^224721+78557)/1739	67645	Lelio R Paula	05/2012
7496	2^224700+1915	67642	Lelio R Paula	04/2012
7497	(29*2^224694-1)/198905	67636	Lelio R Paula	01/2014
7498	2^224658-93	67629	Lelio R Paula	02/2012
7499	2^224624-13077	67619	Enzo Doria	10/2012
7500	18^53860-3319	67609	Enzo Doria	03/2013

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)