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 ?
7001	2^222744+855	67053	Lelio R Paula	04/2012
7002	13^60189+84	67048	Lelio R Paula	07/2013
7003	2*10^67043-51	67044	Robert Price	11/2017
7004	2^222701+577294575	67040	Lelio R Paula	02/2016
7005	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
7006	(151*10^67027-7)/9	67029	Robert Price	07/2017
7007	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
7008	2^222614-111041	67014	Enzo Doria	05/2014
7009	2^222520-1907	66986	Yves Minet	03/2013
7010	(4^111231+23)/3	66968	Robert Price	02/2017
7011	2^222408-111275	66952	Enzo Doria	05/2014
7012	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
7013	2^222378-1005	66943	Lelio R Paula	04/2012
7014	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
7015	7^79202-6^(79202+1)	66934	Robert Price	06/2016
7016	2^222325-112255	66927	Enzo Doria	06/2014
7017	20^51428+33	66910	Lelio R Paula	08/2013
7018	2^222224-18509	66897	Enzo Doria	05/2013
7019	(38*10^66896+187)/9	66897	Robert Price	11/2017
7020	2^222192-869688105	66887	Lelio R Paula	02/2016
7021	(19*10^66878-43)/3	66879	Robert Price	10/2017
7022	11^64219-64	66878	Lelio R Paula	07/2013
7023	2^222151-17295	66875	Lelio R Paula	04/2012
7024	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
7025	2^222085-111031	66855	Enzo Doria	05/2014
7026	8*10^66848-13	66849	Robert Price	05/2017
7027	(3^140087+4)/13	66838	Lelio R Paula	04/2012
7028	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
7029	19^52265+52	66835	Lelio R Paula	08/2013
7030	2*10^66826-27	66827	Robert Price	02/2017
7031	4*6^85867+5	66819	Lelio R Paula	09/2014
7032	15^56800+8	66802	Lelio R Paula	08/2013
7033	(2^221891-2^110946+1)/5	66796		11/2006
7034	10^66793+69441	66794	Patrick De Geest	05/2013
7035	10^66793-63	66793	Robert Price	05/2011
7036	35^43256-1704	66791	Enzo Doria	03/2013
7037	3^139976+2^(139976-1)	66786	Robert Price	05/2016
7038	88769!6-48	66786	Robert Price	08/2018
7039	7^79023-54	66783	Lelio R Paula	06/2013
7040	104^33109-103	66782	Norbert Schneider	11/2016
7041	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
7042	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
7044	2^221768+183	66759	Lelio R Paula	02/2012
7043	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
7045	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
7046	11^64097+48	66751	Lelio R Paula	07/2013
7047	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
7048	(19*10^66748+413)/9	66749	Robert Price	10/2017
7049	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
7050	8*6^85758-7	66734	Lelio R Paula	09/2014
7051	135^31325+2	66733	Lelio R Paula	05/2013
7052	(49*10^66729+41)/9	66730	Robert Price	07/2015
7053	(349*10^66720-7)/9	66722	Robert Price	03/2017
7054	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
7055	(25*10^66714+71)/3	66715	Robert Price	01/2017
7056	11^64061-780	66713	Enzo Doria	11/2012
7057	7^78929+4	66703	Lelio R Paula	06/2013
7058	11^64048-930	66700	Enzo Doria	11/2012
7059	2*7^78921+5	66697	Lelio R Paula	09/2014
7060	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
7061	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
7062	2^221479+72953	66672	Enzo Doria	04/2016
7063	10^66666+275403	66667	Patrick De Geest	03/2010
7064	10^66666-115521	66666	Patrick De Geest	03/2010
7065	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
7066	4*10^66653+21	66654	Robert Price	08/2016
7067	(10^66650+149)/3	66650	Serge Batalov	12/2014
7068	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
7069	2^221391-2145	66646	Lelio R Paula	04/2012
7070	(5*10^66613-119)/3	66614	Robert Price	04/2016
7071	2^221273-113233	66610	Enzo Doria	07/2014
7072	3^139571-46	66593	Lelio R Paula	06/2013
7073	(410^(233295)-2*(10^33295)+1)/3	66591	Robert Price	04/2018
7074	2^221181-869688105	66583	Lelio R Paula	02/2016
7075	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
7076	2^221126+133	66566	Lelio R Paula	02/2012
7077	12^61680+91	66564	Lelio R Paula	07/2013
7078	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
7079	(13*10^66551-73)/3	66552	Robert Price	12/2016
7080	11^63901-1590	66547	Enzo Doria	12/2012
7081	11^63901-1500	66547	Enzo Doria	12/2012
7082	6^85517+23	66546	Lelio R Paula	07/2013
7083	17^54069-40	66530	Lelio R Paula	08/2013
7084	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
7085	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
7087	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
7086	3^139432+26	66526	Lelio R Paula	06/2013
7088	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
7089	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
7090	6^85481+85481	66518	Henri Lifchitz	08/2014
7091	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
7092	13^59687+66	66488	Lelio R Paula	07/2013
7093	(49*10^66485-31)/9	66486	Robert Price	07/2015
7094	(46*10^66469+17)/9	66470	Robert Price	06/2015
7095	2^220790+97	66465	Lelio R Paula	02/2012
7096	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
7097	40009^14441-102	66460	Enzo Doria	07/2012
7098	2^220736-143	66449	Lelio R Paula	02/2012
7099	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
7100	2^220675+69	66430	Lelio R Paula	02/2012
7101	88323!6-16	66419	Robert Price	08/2018
7102	2^220633-111381	66418	Enzo Doria	05/2014
7103	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
7104	2^220596-15813	66407	Enzo Doria	04/2013
7105	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
7106	2^220549-1859173	66392	Enzo Doria	04/2016
7107	2^220478-161	66371	Lelio R Paula	02/2012
7108	5^94938-14636	66359	Enzo Doria	02/2013
7109	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
7110	2^220253-114871	66303	Enzo Doria	05/2015
7111	12^61432+95	66297	Lelio R Paula	07/2013
7112	2^220192-111563	66285	Enzo Doria	05/2014
7113	2^220188-111449	66284	Enzo Doria	05/2014
7114	(4*10^66284+23)/9	66284	Robert Price	11/2014
7115	32501!2+2	66266	Robert Price	01/2015
7116	(8*10^66261-101)/3	66262	Robert Price	10/2017
7117	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
7118	(47^39623-1)/46	66252	Robert Price	06/2014
7119	2^220044-97305	66240	Lelio R Paula	04/2012
7120	(77*10^66237-257)/9	66238	Robert Price	10/2017
7121	29^45285+2	66225	Ray Chandler	08/2011
7122	15^56289+38	66202	Lelio R Paula	08/2013
7123	3^138749+98	66201	Lelio R Paula	06/2013
7124	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
7125	2^219904-16995	66198	Lelio R Paula	10/2011
7126	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
7127	Phi(198552,10)	66177	Ray Chandler	07/2010
7128	4*6^85041+7	66176	Lelio R Paula	09/2014
7129	2^219812-3149	66171	Yves Minet	10/2009
7130	2^219795-611167	66165	Paul Bourdelais	03/2013
7131	32455!2+512	66162	Robert Price	02/2015
7132	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
7134	(11^63521-4^63521)/7	66150	Robert Price	03/2013
7133	5*7^78274-6	66150	Lelio R Paula	09/2014
7135	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
7136	2^219679-112015	66130	Enzo Doria	05/2014
7137	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
7138	2^219600+76561	66107	Enzo Doria	05/2016
7139	2^219594+255255	66105	Lelio R Paula	10/2011
7140	4*7^78210-3	66096	Lelio R Paula	09/2014
7141	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
7142	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
7143	2^219496+66615	66075	Lelio R Paula	10/2011
7144	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
7145	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
7146	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
7147	10^66033+19	66034	Robert Price	01/2011
7148	10^66033-78309	66033	Patrick De Geest	05/2013
7149	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
7150	2^219304+454245	66018	Henri Lifchitz	03/2007
7151	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
7152	2^219273-112635	66008	Enzo Doria	06/2014
7153	2^219250+25	66001	Lelio R Paula	08/2011
7154	132^31123+131	65999	Norbert Schneider	03/2015
7155	V(319871)	65987	Serge Batalov	03/2015
7156	2^219189-195	65983	Lelio R Paula	08/2011
7157	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
7158	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
7159	2^219112-17009	65960	Enzo Doria	05/2013
7160	2^219093-111201	65954	Enzo Doria	05/2014
7161	2^219089-112099	65953	Enzo Doria	06/2014
7162	46714!3+81	65950	Robert Price	09/2014
7163	(11*10^65944-131)/3	65945	Robert Price	02/2017
7164	2^219021-3553	65932	Yves Minet	03/2017
7165	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
7166	2^218990+73519	65923	Enzo Doria	04/2016
7167	58^37378-57	65914	Norbert Schneider	09/2014
7169	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
7168	5*10^65905+81	65906	Robert Price	08/2017
7170	3*10^65899-13	65900	Robert Price	11/2017
7171	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
7172	127^31322-2	65896	Lelio R Paula	10/2017
7174	2^218897-111889	65895	Enzo Doria	05/2014
7173	2^218896+1869451	65895	Enzo Doria	05/2016
7175	63^36616+2	65885	Lelio R Paula	05/2013
7176	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
7177	2^218796-113297	65865	Enzo Doria	07/2014
7178	2^218797+73727	65865	Enzo Doria	04/2016
7179	3^138040-110	65862	Lelio R Paula	06/2013
7180	11^63240-1950	65858	Enzo Doria	12/2012
7181	2^218764-111873	65855	Enzo Doria	05/2014
7182	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
7183	3^137988+26	65838	Lelio R Paula	06/2013
7184	2^218680-719	65830	Yves Minet	05/2012
7185	18^52424+17	65807	Lelio R Paula	08/2013
7186	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
7187	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
7188	(5*10^65773+1)/3	65774	Erik Branger	12/2013
7189	2^218457-17329	65763	Enzo Doria	05/2013
7190	151703#+223381	65759	Nicolas PALAU	10/2016
7191	2^218436+40755	65756	Lelio R Paula	10/2011
7192	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
7193	157^29934+29934^157	65733	Serge Batalov	05/2014
7194	211^28273-2	65715	Lelio R Paula	09/2013
7195	(59*10^65712+31)/9	65713	Robert Price	09/2015
7196	611^23586+23586^611	65712	Norbert Schneider	08/2016
7197	p(13991)#/2+32	65712	Robert Price	12/2016
7198	2^218282-18485	65710	Enzo Doria	05/2013
7199	2^218274-111251	65708	Enzo Doria	05/2014
7200	2*F(314335)-1	65693	Henri Lifchitz	12/2009
7201	2^218200+427	65685	Henri Lifchitz	01/2005
7202	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
7203	(10199^(2^14)+(10197)^(2^14))/2	65676	Robert Price	05/2018
7204	46532!3+3	65667	Robert Price	10/2014
7205	2^218120-147	65661	Lelio R Paula	08/2011
7206	452^24729+24729^452	65659	Norbert Schneider	09/2016
7207	2^218102-114893	65656	Enzo Doria	05/2015
7208	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
7209	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
7210	(306^26407-1)/305	65638	Eric Chen	09/2017
7211	19^51326+36	65634	Lelio R Paula	08/2013
7212	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
7213	2^217989-33	65622	Lelio R Paula	08/2011
7214	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
7215	4*6^84315-5	65611	Lelio R Paula	09/2014
7216	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
7217	6^84303+55	65601	Lelio R Paula	07/2013
7218	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
7219	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
7220	5*2^217858+3	65583	Lelio R Paula	04/2014
7221	(19*10^65572+119)/3	65573	Robert Price	02/2017
7223	20^50399+51	65571	Lelio R Paula	08/2013
7222	7162^17009+17009^7162	65571	Norbert Schneider	07/2018
7224	11^62946-5670	65552	Enzo Doria	01/2013
7225	2^217742-3911	65547	Yves Minet	08/2009
7226	(19*10^65545+77)/3	65546	Robert Price	08/2016
7227	2^217731+131	65544	Lelio R Paula	08/2011
7228	2^217720-111287	65541	Enzo Doria	05/2014
7229	(365^25579+1)/366	65539	Eric Chen	10/2017
7230	10^65537+27	65538	Robert Price	01/2011
7231	10^65537-76859	65537	Patrick De Geest	05/2013
7232	(28*10^65532+359)/9	65533	Robert Price	11/2017
7233	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
7234	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
7235	5*10^65509+23	65510	Robert Price	11/2017
7236	(8*10^65507-83)/3	65508	Robert Price	10/2017
7237	7*10^65492-47	65493	Robert Price	02/2017
7238	2^217547-1868407	65489	Enzo Doria	04/2016
7239	2^217531-111769	65484	Enzo Doria	05/2014
7240	7^77484-18	65482	Lelio R Paula	06/2013
7241	2^217488-113285	65471	Enzo Doria	07/2014
7242	151153#/30-30	65468	Henri Lifchitz	12/2011
7243	2^217466+4257	65464	Lelio R Paula	10/2011
7244	46396!3-81	65455	Robert Price	09/2014
7245	2^217421-113185	65451	Enzo Doria	07/2014
7246	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
7247	2^217408-2145	65447	Lelio R Paula	10/2011
7248	2^217398-16947	65444	Enzo Doria	05/2013
7249	8*5^93613+3	65434	Lelio R Paula	09/2014
7250	11^62828-5310	65429	Enzo Doria	01/2013

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Probable Primes Top 10000

(218736 PRPs in the top)