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	2^219904-16995	66198	Lelio R Paula	10/2011
7252	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
7253	Phi(198552,10)	66177	Ray Chandler	07/2010
7254	4*6^85041+7	66176	Lelio R Paula	09/2014
7255	2^219812-3149	66171	Yves Minet	10/2009
7256	2^219795-611167	66165	Paul Bourdelais	03/2013
7257	32455!2+512	66162	Robert Price	02/2015
7258	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
7260	(11^63521-4^63521)/7	66150	Robert Price	03/2013
7259	5*7^78274-6	66150	Lelio R Paula	09/2014
7261	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
7262	2^219679-112015	66130	Enzo Doria	05/2014
7263	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
7264	15445^15782-15782^15445	66108	Norbert Schneider	08/2018
7265	2^219600+76561	66107	Enzo Doria	05/2016
7266	2^219594+255255	66105	Lelio R Paula	10/2011
7267	4*7^78210-3	66096	Lelio R Paula	09/2014
7268	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
7269	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
7270	2^219496+66615	66075	Lelio R Paula	10/2011
7271	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
7272	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
7273	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
7274	10^66033+19	66034	Robert Price	01/2011
7275	10^66033-78309	66033	Patrick De Geest	05/2013
7276	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
7277	2^219304+454245	66018	Henri Lifchitz	03/2007
7278	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
7279	2^219273-112635	66008	Enzo Doria	06/2014
7280	2^219250+25	66001	Lelio R Paula	08/2011
7281	132^31123+131	65999	Norbert Schneider	03/2015
7282	V(319871)	65987	Serge Batalov	03/2015
7283	2^219189-195	65983	Lelio R Paula	08/2011
7284	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
7285	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
7286	2^219112-17009	65960	Enzo Doria	05/2013
7287	2^219093-111201	65954	Enzo Doria	05/2014
7288	2^219089-112099	65953	Enzo Doria	06/2014
7289	46714!3+81	65950	Robert Price	09/2014
7290	(11*10^65944-131)/3	65945	Robert Price	02/2017
7291	2^219021-3553	65932	Yves Minet	03/2017
7292	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
7293	2^218990+73519	65923	Enzo Doria	04/2016
7294	58^37378-57	65914	Norbert Schneider	09/2014
7296	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
7295	5*10^65905+81	65906	Robert Price	08/2017
7297	3*10^65899-13	65900	Robert Price	11/2017
7298	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
7299	127^31322-2	65896	Lelio R Paula	10/2017
7300	2^218897-111889	65895	Enzo Doria	05/2014
7301	2^218896+1869451	65895	Enzo Doria	05/2016
7302	63^36616+2	65885	Lelio R Paula	05/2013
7303	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
7304	2^218796-113297	65865	Enzo Doria	07/2014
7305	2^218797+73727	65865	Enzo Doria	04/2016
7306	3^138040-110	65862	Lelio R Paula	06/2013
7307	11^63240-1950	65858	Enzo Doria	12/2012
7308	2^218764-111873	65855	Enzo Doria	05/2014
7309	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
7310	3^137988+26	65838	Lelio R Paula	06/2013
7311	2^218680-719	65830	Yves Minet	05/2012
7312	18^52424+17	65807	Lelio R Paula	08/2013
7313	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
7314	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
7315	(5*10^65773+1)/3	65774	Erik Branger	12/2013
7316	2^218457-17329	65763	Enzo Doria	05/2013
7317	151703#+223381	65759	Nicolas PALAU	10/2016
7318	2^218436+40755	65756	Lelio R Paula	10/2011
7319	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
7320	157^29934+29934^157	65733	Serge Batalov	05/2014
7321	211^28273-2	65715	Lelio R Paula	09/2013
7322	(59*10^65712+31)/9	65713	Robert Price	09/2015
7324	611^23586+23586^611	65712	Norbert Schneider	08/2016
7323	p(13991)#/2+32	65712	Robert Price	12/2016
7325	2^218282-18485	65710	Enzo Doria	05/2013
7326	2^218274-111251	65708	Enzo Doria	05/2014
7327	2*F(314335)-1	65693	Henri Lifchitz	12/2009
7328	2^218200+427	65685	Henri Lifchitz	01/2005
7329	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
7330	(10199^(2^14)+(10197)^(2^14))/2	65676	Robert Price	05/2018
7331	46532!3+3	65667	Robert Price	10/2014
7332	2^218120-147	65661	Lelio R Paula	08/2011
7333	452^24729+24729^452	65659	Norbert Schneider	09/2016
7334	2^218102-114893	65656	Enzo Doria	05/2015
7335	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
7336	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
7337	(306^26407-1)/305	65638	Eric Chen	09/2017
7338	19^51326+36	65634	Lelio R Paula	08/2013
7339	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
7340	2^217989-33	65622	Lelio R Paula	08/2011
7341	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
7342	4*6^84315-5	65611	Lelio R Paula	09/2014
7343	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
7344	6^84303+55	65601	Lelio R Paula	07/2013
7345	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
7346	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
7347	5*2^217858+3	65583	Lelio R Paula	04/2014
7348	(19*10^65572+119)/3	65573	Robert Price	02/2017
7350	20^50399+51	65571	Lelio R Paula	08/2013
7349	7162^17009+17009^7162	65571	Norbert Schneider	07/2018
7351	11^62946-5670	65552	Enzo Doria	01/2013
7352	2^217742-3911	65547	Yves Minet	08/2009
7353	(19*10^65545+77)/3	65546	Robert Price	08/2016
7354	2^217731+131	65544	Lelio R Paula	08/2011
7355	2^217720-111287	65541	Enzo Doria	05/2014
7356	(365^25579+1)/366	65539	Eric Chen	10/2017
7357	10^65537+27	65538	Robert Price	01/2011
7358	10^65537-76859	65537	Patrick De Geest	05/2013
7359	(28*10^65532+359)/9	65533	Robert Price	11/2017
7360	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
7361	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
7362	5*10^65509+23	65510	Robert Price	11/2017
7363	(8*10^65507-83)/3	65508	Robert Price	10/2017
7364	7*10^65492-47	65493	Robert Price	02/2017
7365	2^217547-1868407	65489	Enzo Doria	04/2016
7366	2^217531-111769	65484	Enzo Doria	05/2014
7367	7^77484-18	65482	Lelio R Paula	06/2013
7368	2^217488-113285	65471	Enzo Doria	07/2014
7369	151153#/30-30	65468	Henri Lifchitz	12/2011
7370	2^217466+4257	65464	Lelio R Paula	10/2011
7371	46396!3-81	65455	Robert Price	09/2014
7372	2^217421-113185	65451	Enzo Doria	07/2014
7373	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
7374	2^217408-2145	65447	Lelio R Paula	10/2011
7375	2^217398-16947	65444	Enzo Doria	05/2013
7376	8*5^93613+3	65434	Lelio R Paula	09/2014
7377	11^62828-5310	65429	Enzo Doria	01/2013
7378	10^65426+13	65427	Robert Price	01/2011
7379	2^217341-6555	65427	Lelio R Paula	10/2011
7380	10^65426-54849	65426	Patrick De Geest	05/2013
7381	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
7382	30011^14608-108	65405	Enzo Doria	07/2012
7383	119^31504-2	65389	Lelio R Paula	10/2017
7384	(43^40031-1)/42	65388	Robert Price	04/2014
7385	2^217190+94395	65381	Henri Lifchitz	02/2005
7386	15^55587+46	65376	Lelio R Paula	08/2013
7387	2^217088-111833	65350	Enzo Doria	05/2014
7388	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
7389	(10^65340+47)/3	65340	Robert Price	11/2017
7390	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
7391	2^216947-111351	65308	Enzo Doria	05/2014
7392	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
7393	(13*10^65297+83)/3	65298	Robert Price	09/2016
7394	5^93400-8	65284	Lelio R Paula	06/2013
7395	2^216802-165	65264	Lelio R Paula	08/2011
7396	2^216799-28635	65264	Lelio R Paula	10/2011
7397	5*10^65255+51	65256	Robert Price	01/2017
7398	2^216762-167	65252	Lelio R Paula	08/2011
7399	11^62657-5790	65251	Enzo Doria	01/2013
7400	3^136756-112880	65250	Enzo Doria	06/2014
7401	2^216752+21	65249	Lelio R Paula	08/2011
7402	3*10^65247+11	65248	Robert Price	11/2017
7403	11^62651-2700	65245	Enzo Doria	12/2012
7404	15130^15609-15609^15130	65244	Norbert Schneider	07/2018
7405	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
7406	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
7407	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
7408	2^216652-2327	65219	Yves Minet	10/2013
7409	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
7410	(5*10^65203-119)/3	65204	Robert Price	04/2016
7411	2^216555-113269	65190	Enzo Doria	07/2014
7412	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
7413	2^216474+12915	65166	Lelio R Paula	02/2013
7414	19^50958-32	65163	Lelio R Paula	08/2013
7415	2^216442-112133	65156	Enzo Doria	06/2014
7416	2^216437-112213	65155	Enzo Doria	06/2014
7417	2^216435-112767	65154	Enzo Doria	06/2014
7418	2^216420+12705	65149	Lelio R Paula	02/2013
7419	8*3^136507-7	65132	Lelio R Paula	04/2014
7420	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
7421	15132^15575-15575^15132	65102	Norbert Schneider	07/2018
7422	5*10^65086-51	65087	Robert Price	10/2017
7423	2^216197-111769	65082	Enzo Doria	05/2014
7425	6^83631-79	65078	Lelio R Paula	07/2013
7424	572^23601+23601^572	65078	Norbert Schneider	08/2016
7426	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
7427	2^216154-1421	65069	Yves Minet	01/2013
7428	2^216145-112663	65067	Enzo Doria	06/2014
7429	(7*10^65064+53)/3	65065	Robert Price	10/2017
7430	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7431	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7432	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7433	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7434	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
7436	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
7437	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7435	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7438	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
7439	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
7440	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
7441	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
7442	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
7443	p(13861)#/2+256	65039	Robert Price	05/2017
7444	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
7445	11^62439-4380	65024	Enzo Doria	01/2013
7446	3^136244+2	65005	Mike Oakes	11/2009
7447	13^58343-50	64991	Lelio R Paula	07/2013
7448	331^25791-10002	64989	Enzo Doria	07/2012
7449	2^215877+131	64986	Lelio R Paula	08/2011
7450	4*5^92959+9	64977	Lelio R Paula	09/2014
7451	2^215789-18825	64959	Lelio R Paula	09/2011
7452	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
7453	U(315311)	64954	Serge Batalov	03/2015
7454	46072!3-59049	64951	Robert Price	12/2015
7455	2^215750-5955	64948	Lelio R Paula	09/2011
7456	13^58281+46	64922	Lelio R Paula	07/2013
7457	2^215623+183	64909	Lelio R Paula	08/2011
7458	(46*10^64904+521)/9	64905	Robert Price	08/2017
7459	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
7460	5*2^215554+3	64889	Lelio R Paula	04/2014
7461	2^215541-112075	64885	Enzo Doria	06/2014
7462	2*10^64882-3	64883	Dmitry Domanov	11/2010
7463	10^64862+342339	64863	Patrick De Geest	05/2013
7464	10^64862-47	64862	Robert Price	05/2011
7465	19^50718-84	64856	Lelio R Paula	08/2013
7466	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
7467	86413!6-12	64846	Robert Price	08/2018
7469	10^64843+4278697839	64844	Robert Price	05/2015
7468	10^64843+21967	64844	Patrick De Geest	03/2016
7470	10^64843-340073	64843	Patrick De Geest	03/2016
7471	11^62254+70	64831	Lelio R Paula	07/2013
7472	2^215351-111925	64828	Enzo Doria	05/2014
7473	2^215310-117	64815	Lelio R Paula	08/2011
7474	124^30958-123	64809	Norbert Schneider	02/2015
7475	(7*10^64807+17)/3	64808	Erik Branger	03/2014
7476	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
7477	2^215243-15949	64795	Enzo Doria	04/2013
7478	23^47581-22^47581	64793	Robert Price	08/2012
7479	(62*10^64783-17)/9	64784	Robert Price	09/2015
7480	5*3^135747-4	64769	Lelio R Paula	04/2014
7481	(59*10^64767-41)/9	64768	Robert Price	09/2015
7483	(2^215140+3)/19	64763	Lelio R Paula	04/2012
7482	2^215135-17169	64763	Enzo Doria	05/2013
7484	2^215115-111277	64757	Enzo Doria	05/2014
7485	9*5^92641+2	64755	Lelio R Paula	09/2014
7486	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
7487	(5*10^64715-23)/9	64715	Robert Price	11/2014
7488	2^214938-1781	64703	Yves Minet	03/2013
7489	11^62111-420	64682	Enzo Doria	08/2012
7490	5^92525+42	64673	Lelio R Paula	06/2013
7491	2^214824+71893	64669	Enzo Doria	04/2016
7492	2^214799-2221	64661	Yves Minet	08/2013
7493	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
7494	92^32907+32907^92	64623	Serge Batalov	05/2014
7495	(89*10^64608-539)/9	64609	Robert Price	11/2017
7496	6^83013+101	64597	Lelio R Paula	07/2013
7497	p(13775)#/2+8	64594	Robert Price	01/2017
7498	(7*10^64568-43)/9	64568	Robert Price	10/2014
7499	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
7500	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014

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Probable Primes Top 10000

(225451 PRPs in the top)