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) !!!

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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 (> 30000)	Who ?	When ?
7251	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
7253	(11^63521-4^63521)/7	66150	Robert Price	03/2013
7252	5*7^78274-6	66150	Lelio R Paula	09/2014
7254	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
7255	2^219679-112015	66130	Enzo Doria	05/2014
7256	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
7257	15445^15782-15782^15445	66108	Norbert Schneider	08/2018
7258	2^219600+76561	66107	Enzo Doria	05/2016
7259	2^219594+255255	66105	Lelio R Paula	10/2011
7260	4*7^78210-3	66096	Lelio R Paula	09/2014
7261	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
7262	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
7263	2^219496+66615	66075	Lelio R Paula	10/2011
7264	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
7265	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
7266	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
7267	10^66033+19	66034	Robert Price	01/2011
7268	10^66033-78309	66033	Patrick De Geest	05/2013
7269	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
7270	2^219304+454245	66018	Henri Lifchitz	03/2007
7271	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
7272	2^219273-112635	66008	Enzo Doria	06/2014
7273	2^219250+25	66001	Lelio R Paula	08/2011
7274	132^31123+131	65999	Norbert Schneider	03/2015
7275	V(319871)	65987	Serge Batalov	03/2015
7276	2^219189-195	65983	Lelio R Paula	08/2011
7277	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
7278	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
7279	2^219112-17009	65960	Enzo Doria	05/2013
7280	2^219093-111201	65954	Enzo Doria	05/2014
7281	2^219089-112099	65953	Enzo Doria	06/2014
7282	46714!3+81	65950	Robert Price	09/2014
7283	(11*10^65944-131)/3	65945	Robert Price	02/2017
7284	2^219021-3553	65932	Yves Minet	03/2017
7285	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
7286	2^218990+73519	65923	Enzo Doria	04/2016
7287	58^37378-57	65914	Norbert Schneider	09/2014
7289	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
7288	5*10^65905+81	65906	Robert Price	08/2017
7290	3*10^65899-13	65900	Robert Price	11/2017
7291	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
7292	127^31322-2	65896	Lelio R Paula	10/2017
7293	2^218897-111889	65895	Enzo Doria	05/2014
7294	2^218896+1869451	65895	Enzo Doria	05/2016
7295	63^36616+2	65885	Lelio R Paula	05/2013
7296	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
7297	2^218796-113297	65865	Enzo Doria	07/2014
7298	2^218797+73727	65865	Enzo Doria	04/2016
7299	3^138040-110	65862	Lelio R Paula	06/2013
7300	11^63240-1950	65858	Enzo Doria	12/2012
7301	2^218764-111873	65855	Enzo Doria	05/2014
7302	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
7303	3^137988+26	65838	Lelio R Paula	06/2013
7304	2^218680-719	65830	Yves Minet	05/2012
7305	18^52424+17	65807	Lelio R Paula	08/2013
7306	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
7307	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
7308	(5*10^65773+1)/3	65774	Erik Branger	12/2013
7309	2^218457-17329	65763	Enzo Doria	05/2013
7310	151703#+223381	65759	Nicolas PALAU	10/2016
7311	2^218436+40755	65756	Lelio R Paula	10/2011
7312	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
7313	157^29934+29934^157	65733	Serge Batalov	05/2014
7314	211^28273-2	65715	Lelio R Paula	09/2013
7315	(59*10^65712+31)/9	65713	Robert Price	09/2015
7316	611^23586+23586^611	65712	Norbert Schneider	08/2016
7317	p(13991)#/2+32	65712	Robert Price	12/2016
7318	2^218282-18485	65710	Enzo Doria	05/2013
7319	2^218274-111251	65708	Enzo Doria	05/2014
7320	2*F(314335)-1	65693	Henri Lifchitz	12/2009
7321	2^218200+427	65685	Henri Lifchitz	01/2005
7322	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
7323	(10199^(2^14)+(10197)^(2^14))/2	65676	Robert Price	05/2018
7324	46532!3+3	65667	Robert Price	10/2014
7325	2^218120-147	65661	Lelio R Paula	08/2011
7326	452^24729+24729^452	65659	Norbert Schneider	09/2016
7327	2^218102-114893	65656	Enzo Doria	05/2015
7328	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
7329	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
7330	(306^26407-1)/305	65638	Eric Chen	09/2017
7331	19^51326+36	65634	Lelio R Paula	08/2013
7332	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
7333	2^217989-33	65622	Lelio R Paula	08/2011
7334	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
7335	4*6^84315-5	65611	Lelio R Paula	09/2014
7336	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
7337	6^84303+55	65601	Lelio R Paula	07/2013
7338	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
7339	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
7340	5*2^217858+3	65583	Lelio R Paula	04/2014
7341	(19*10^65572+119)/3	65573	Robert Price	02/2017
7342	20^50399+51	65571	Lelio R Paula	08/2013
7343	7162^17009+17009^7162	65571	Norbert Schneider	07/2018
7344	11^62946-5670	65552	Enzo Doria	01/2013
7345	2^217742-3911	65547	Yves Minet	08/2009
7346	(19*10^65545+77)/3	65546	Robert Price	08/2016
7347	2^217731+131	65544	Lelio R Paula	08/2011
7348	2^217720-111287	65541	Enzo Doria	05/2014
7349	(365^25579+1)/366	65539	Eric Chen	10/2017
7350	10^65537+27	65538	Robert Price	01/2011
7351	10^65537-76859	65537	Patrick De Geest	05/2013
7352	(28*10^65532+359)/9	65533	Robert Price	11/2017
7353	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
7354	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
7355	5*10^65509+23	65510	Robert Price	11/2017
7356	(8*10^65507-83)/3	65508	Robert Price	10/2017
7357	7*10^65492-47	65493	Robert Price	02/2017
7358	2^217547-1868407	65489	Enzo Doria	04/2016
7359	2^217531-111769	65484	Enzo Doria	05/2014
7360	7^77484-18	65482	Lelio R Paula	06/2013
7361	2^217488-113285	65471	Enzo Doria	07/2014
7362	151153#/30-30	65468	Henri Lifchitz	12/2011
7363	2^217466+4257	65464	Lelio R Paula	10/2011
7364	46396!3-81	65455	Robert Price	09/2014
7365	2^217421-113185	65451	Enzo Doria	07/2014
7366	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
7367	2^217408-2145	65447	Lelio R Paula	10/2011
7368	2^217398-16947	65444	Enzo Doria	05/2013
7369	8*5^93613+3	65434	Lelio R Paula	09/2014
7370	11^62828-5310	65429	Enzo Doria	01/2013
7371	10^65426+13	65427	Robert Price	01/2011
7372	2^217341-6555	65427	Lelio R Paula	10/2011
7373	10^65426-54849	65426	Patrick De Geest	05/2013
7374	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
7375	30011^14608-108	65405	Enzo Doria	07/2012
7376	119^31504-2	65389	Lelio R Paula	10/2017
7377	(43^40031-1)/42	65388	Robert Price	04/2014
7378	2^217190+94395	65381	Henri Lifchitz	02/2005
7379	15^55587+46	65376	Lelio R Paula	08/2013
7380	2^217088-111833	65350	Enzo Doria	05/2014
7381	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
7382	(10^65340+47)/3	65340	Robert Price	11/2017
7383	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
7384	2^216947-111351	65308	Enzo Doria	05/2014
7385	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
7386	(13*10^65297+83)/3	65298	Robert Price	09/2016
7387	5^93400-8	65284	Lelio R Paula	06/2013
7388	2^216802-165	65264	Lelio R Paula	08/2011
7389	2^216799-28635	65264	Lelio R Paula	10/2011
7390	5*10^65255+51	65256	Robert Price	01/2017
7391	2^216762-167	65252	Lelio R Paula	08/2011
7392	11^62657-5790	65251	Enzo Doria	01/2013
7393	3^136756-112880	65250	Enzo Doria	06/2014
7394	2^216752+21	65249	Lelio R Paula	08/2011
7395	3*10^65247+11	65248	Robert Price	11/2017
7396	11^62651-2700	65245	Enzo Doria	12/2012
7397	15130^15609-15609^15130	65244	Norbert Schneider	07/2018
7399	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
7398	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
7400	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
7401	2^216652-2327	65219	Yves Minet	10/2013
7402	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
7403	(5*10^65203-119)/3	65204	Robert Price	04/2016
7404	2^216555-113269	65190	Enzo Doria	07/2014
7405	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
7406	2^216474+12915	65166	Lelio R Paula	02/2013
7407	19^50958-32	65163	Lelio R Paula	08/2013
7408	2^216442-112133	65156	Enzo Doria	06/2014
7409	2^216437-112213	65155	Enzo Doria	06/2014
7410	2^216435-112767	65154	Enzo Doria	06/2014
7411	2^216420+12705	65149	Lelio R Paula	02/2013
7412	8*3^136507-7	65132	Lelio R Paula	04/2014
7413	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
7414	15132^15575-15575^15132	65102	Norbert Schneider	07/2018
7415	5*10^65086-51	65087	Robert Price	10/2017
7416	2^216197-111769	65082	Enzo Doria	05/2014
7418	6^83631-79	65078	Lelio R Paula	07/2013
7417	572^23601+23601^572	65078	Norbert Schneider	08/2016
7419	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
7420	2^216154-1421	65069	Yves Minet	01/2013
7421	2^216145-112663	65067	Enzo Doria	06/2014
7422	(7*10^65064+53)/3	65065	Robert Price	10/2017
7423	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7424	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7425	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7426	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7427	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
7430	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
7429	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7428	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7431	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
7432	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
7433	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
7434	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
7435	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
7436	p(13861)#/2+256	65039	Robert Price	05/2017
7437	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
7438	11^62439-4380	65024	Enzo Doria	01/2013
7439	3^136244+2	65005	Mike Oakes	11/2009
7440	13^58343-50	64991	Lelio R Paula	07/2013
7441	331^25791-10002	64989	Enzo Doria	07/2012
7442	2^215877+131	64986	Lelio R Paula	08/2011
7443	4*5^92959+9	64977	Lelio R Paula	09/2014
7444	2^215789-18825	64959	Lelio R Paula	09/2011
7445	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
7446	U(315311)	64954	Serge Batalov	03/2015
7447	46072!3-59049	64951	Robert Price	12/2015
7448	2^215750-5955	64948	Lelio R Paula	09/2011
7449	13^58281+46	64922	Lelio R Paula	07/2013
7450	2^215623+183	64909	Lelio R Paula	08/2011
7451	(46*10^64904+521)/9	64905	Robert Price	08/2017
7452	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
7453	5*2^215554+3	64889	Lelio R Paula	04/2014
7454	2^215541-112075	64885	Enzo Doria	06/2014
7455	2*10^64882-3	64883	Dmitry Domanov	11/2010
7456	10^64862+342339	64863	Patrick De Geest	05/2013
7457	10^64862-47	64862	Robert Price	05/2011
7458	19^50718-84	64856	Lelio R Paula	08/2013
7459	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
7460	86413!6-12	64846	Robert Price	08/2018
7461	10^64843+4278697839	64844	Robert Price	05/2015
7462	10^64843+21967	64844	Patrick De Geest	03/2016
7463	10^64843-340073	64843	Patrick De Geest	03/2016
7464	11^62254+70	64831	Lelio R Paula	07/2013
7465	2^215351-111925	64828	Enzo Doria	05/2014
7466	2^215310-117	64815	Lelio R Paula	08/2011
7467	124^30958-123	64809	Norbert Schneider	02/2015
7468	(7*10^64807+17)/3	64808	Erik Branger	03/2014
7469	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
7470	2^215243-15949	64795	Enzo Doria	04/2013
7471	23^47581-22^47581	64793	Robert Price	08/2012
7472	(62*10^64783-17)/9	64784	Robert Price	09/2015
7473	5*3^135747-4	64769	Lelio R Paula	04/2014
7474	(59*10^64767-41)/9	64768	Robert Price	09/2015
7476	(2^215140+3)/19	64763	Lelio R Paula	04/2012
7475	2^215135-17169	64763	Enzo Doria	05/2013
7477	2^215115-111277	64757	Enzo Doria	05/2014
7478	9*5^92641+2	64755	Lelio R Paula	09/2014
7479	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
7480	(5*10^64715-23)/9	64715	Robert Price	11/2014
7481	2^214938-1781	64703	Yves Minet	03/2013
7482	11^62111-420	64682	Enzo Doria	08/2012
7483	5^92525+42	64673	Lelio R Paula	06/2013
7484	2^214824+71893	64669	Enzo Doria	04/2016
7485	2^214799-2221	64661	Yves Minet	08/2013
7486	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
7487	92^32907+32907^92	64623	Serge Batalov	05/2014
7488	(89*10^64608-539)/9	64609	Robert Price	11/2017
7489	6^83013+101	64597	Lelio R Paula	07/2013
7490	p(13775)#/2+8	64594	Robert Price	01/2017
7491	(7*10^64568-43)/9	64568	Robert Price	10/2014
7492	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
7493	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
7494	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
7495	2^214458+54615	64559	Lelio R Paula	10/2011
7496	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
7497	2^214389-683113	64538	Paul Bourdelais	03/2013
7498	(76*10^64534+113)/9	64535	Robert Price	11/2017
7499	2^214369-111241	64532	Enzo Doria	05/2014
7500	(19^50461+3^50461)/22	64526	Robert Price	07/2013

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Probable Primes Top 10000

(224660 PRPs in the top)