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 (> 50000)	Who ?	When ?
7251	2^222862-459161	67089	Enzo Doria	05/2015
7252	2^222828+8193	67078	Lelio R Paula	04/2012
7253	3^140570+2660	67069	Lelio R Paula	06/2013
7254	2^222744+855	67053	Lelio R Paula	04/2012
7255	13^60189+84	67048	Lelio R Paula	07/2013
7256	2*10^67043-51	67044	Robert Price	11/2017
7257	2^222701+577294575	67040	Lelio R Paula	02/2016
7258	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
7259	(151*10^67027-7)/9	67029	Robert Price	07/2017
7260	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
7261	2^222614-111041	67014	Enzo Doria	05/2014
7262	118^32333-117	66991	Norbert Schneider	08/2018
7263	2^222520-1907	66986	Yves Minet	03/2013
7264	(4^111231+23)/3	66968	Robert Price	02/2017
7265	2^222408-111275	66952	Enzo Doria	05/2014
7266	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
7267	2^222378-1005	66943	Lelio R Paula	04/2012
7268	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
7269	7^79202-6^(79202+1)	66934	Robert Price	06/2016
7270	2^222325-112255	66927	Enzo Doria	06/2014
7271	20^51428+33	66910	Lelio R Paula	08/2013
7272	2^222224-18509	66897	Enzo Doria	05/2013
7273	(38*10^66896+187)/9	66897	Robert Price	11/2017
7274	2^222192-869688105	66887	Lelio R Paula	02/2016
7275	(19*10^66878-43)/3	66879	Robert Price	10/2017
7276	11^64219-64	66878	Lelio R Paula	07/2013
7277	2^222151-17295	66875	Lelio R Paula	04/2012
7278	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
7279	2^222085-111031	66855	Enzo Doria	05/2014
7280	8*10^66848-13	66849	Robert Price	05/2017
7281	(3^140087+4)/13	66838	Lelio R Paula	04/2012
7282	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
7283	19^52265+52	66835	Lelio R Paula	08/2013
7284	2*10^66826-27	66827	Robert Price	02/2017
7285	4*6^85867+5	66819	Lelio R Paula	09/2014
7286	15^56800+8	66802	Lelio R Paula	08/2013
7287	(2^221891-2^110946+1)/5	66796		11/2006
7288	10^66793+69441	66794	Patrick De Geest	05/2013
7289	10^66793-63	66793	Robert Price	05/2011
7290	35^43256-1704	66791	Enzo Doria	03/2013
7291	3^139976+2^(139976-1)	66786	Robert Price	05/2016
7292	88769!6-48	66786	Robert Price	08/2018
7293	7^79023-54	66783	Lelio R Paula	06/2013
7294	104^33109-103	66782	Norbert Schneider	11/2016
7295	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
7296	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
7297	2^221768+183	66759	Lelio R Paula	02/2012
7298	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
7299	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
7300	11^64097+48	66751	Lelio R Paula	07/2013
7301	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
7302	(19*10^66748+413)/9	66749	Robert Price	10/2017
7303	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
7304	8*6^85758-7	66734	Lelio R Paula	09/2014
7305	135^31325+2	66733	Lelio R Paula	05/2013
7306	(49*10^66729+41)/9	66730	Robert Price	07/2015
7307	(349*10^66720-7)/9	66722	Robert Price	03/2017
7308	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
7309	(25*10^66714+71)/3	66715	Robert Price	01/2017
7310	11^64061-780	66713	Enzo Doria	11/2012
7311	7^78929+4	66703	Lelio R Paula	06/2013
7312	11^64048-930	66700	Enzo Doria	11/2012
7313	120^32079-119	66699	Norbert Schneider	09/2018
7314	2*7^78921+5	66697	Lelio R Paula	09/2014
7315	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
7316	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
7317	2^221479+72953	66672	Enzo Doria	04/2016
7318	10^66666+275403	66667	Patrick De Geest	03/2010
7319	10^66666-115521	66666	Patrick De Geest	03/2010
7320	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
7321	4*10^66653+21	66654	Robert Price	08/2016
7322	(10^66650+149)/3	66650	Serge Batalov	12/2014
7323	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
7324	2^221391-2145	66646	Lelio R Paula	04/2012
7325	(5*10^66613-119)/3	66614	Robert Price	04/2016
7326	2^221273-113233	66610	Enzo Doria	07/2014
7327	3^139571-46	66593	Lelio R Paula	06/2013
7328	(410^(233295)-2*(10^33295)+1)/3	66591	Robert Price	04/2018
7329	2^221181-869688105	66583	Lelio R Paula	02/2016
7330	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
7331	2^221126+133	66566	Lelio R Paula	02/2012
7332	12^61680+91	66564	Lelio R Paula	07/2013
7333	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
7334	(13*10^66551-73)/3	66552	Robert Price	12/2016
7335	11^63901-1590	66547	Enzo Doria	12/2012
7336	11^63901-1500	66547	Enzo Doria	12/2012
7337	6^85517+23	66546	Lelio R Paula	07/2013
7338	17^54069-40	66530	Lelio R Paula	08/2013
7339	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
7340	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
7341	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
7342	3^139432+26	66526	Lelio R Paula	06/2013
7343	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
7344	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
7345	6^85481+85481	66518	Henri Lifchitz	08/2014
7346	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
7347	13^59687+66	66488	Lelio R Paula	07/2013
7348	(49*10^66485-31)/9	66486	Robert Price	07/2015
7349	(46*10^66469+17)/9	66470	Robert Price	06/2015
7350	2^220790+97	66465	Lelio R Paula	02/2012
7351	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
7352	40009^14441-102	66460	Enzo Doria	07/2012
7353	2^220736-143	66449	Lelio R Paula	02/2012
7354	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
7355	2^220675+69	66430	Lelio R Paula	02/2012
7356	88323!6-16	66419	Robert Price	08/2018
7357	2^220633-111381	66418	Enzo Doria	05/2014
7358	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
7359	2^220596-15813	66407	Enzo Doria	04/2013
7360	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
7361	2^220549-1859173	66392	Enzo Doria	04/2016
7362	2^220478-161	66371	Lelio R Paula	02/2012
7363	5^94938-14636	66359	Enzo Doria	02/2013
7364	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
7365	15444^15839-15839^15444	66346	Norbert Schneider	08/2018
7366	2^220253-114871	66303	Enzo Doria	05/2015
7367	12^61432+95	66297	Lelio R Paula	07/2013
7368	2^220192-111563	66285	Enzo Doria	05/2014
7369	2^220188-111449	66284	Enzo Doria	05/2014
7370	(4*10^66284+23)/9	66284	Robert Price	11/2014
7371	32501!2+2	66266	Robert Price	01/2015
7372	(8*10^66261-101)/3	66262	Robert Price	10/2017
7373	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
7374	(47^39623-1)/46	66252	Robert Price	06/2014
7375	2^220044-97305	66240	Lelio R Paula	04/2012
7376	(77*10^66237-257)/9	66238	Robert Price	10/2017
7377	29^45285+2	66225	Ray Chandler	08/2011
7378	15^56289+38	66202	Lelio R Paula	08/2013
7379	3^138749+98	66201	Lelio R Paula	06/2013
7380	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
7381	2^219904-16995	66198	Lelio R Paula	10/2011
7382	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
7383	Phi(198552,10)	66177	Ray Chandler	07/2010
7384	4*6^85041+7	66176	Lelio R Paula	09/2014
7385	2^219812-3149	66171	Yves Minet	10/2009
7386	2^219795-611167	66165	Paul Bourdelais	03/2013
7387	32455!2+512	66162	Robert Price	02/2015
7388	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
7390	(11^63521-4^63521)/7	66150	Robert Price	03/2013
7389	5*7^78274-6	66150	Lelio R Paula	09/2014
7391	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
7392	2^219679-112015	66130	Enzo Doria	05/2014
7393	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
7394	15445^15782-15782^15445	66108	Norbert Schneider	08/2018
7395	2^219600+76561	66107	Enzo Doria	05/2016
7396	2^219594+255255	66105	Lelio R Paula	10/2011
7397	4*7^78210-3	66096	Lelio R Paula	09/2014
7398	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
7399	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
7400	2^219496+66615	66075	Lelio R Paula	10/2011
7401	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
7402	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
7403	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
7404	10^66033+19	66034	Robert Price	01/2011
7405	10^66033-78309	66033	Patrick De Geest	05/2013
7406	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
7407	2^219304+454245	66018	Henri Lifchitz	03/2007
7408	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
7409	2^219273-112635	66008	Enzo Doria	06/2014
7410	2^219250+25	66001	Lelio R Paula	08/2011
7411	132^31123+131	65999	Norbert Schneider	03/2015
7412	V(319871)	65987	Serge Batalov	03/2015
7413	2^219189-195	65983	Lelio R Paula	08/2011
7414	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
7415	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
7416	2^219112-17009	65960	Enzo Doria	05/2013
7417	2^219093-111201	65954	Enzo Doria	05/2014
7418	2^219089-112099	65953	Enzo Doria	06/2014
7419	46714!3+81	65950	Robert Price	09/2014
7420	(11*10^65944-131)/3	65945	Robert Price	02/2017
7421	2^219021-3553	65932	Yves Minet	03/2017
7422	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
7423	2^218990+73519	65923	Enzo Doria	04/2016
7424	58^37378-57	65914	Norbert Schneider	09/2014
7426	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
7425	5*10^65905+81	65906	Robert Price	08/2017
7427	3*10^65899-13	65900	Robert Price	11/2017
7428	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
7429	127^31322-2	65896	Lelio R Paula	10/2017
7431	2^218897-111889	65895	Enzo Doria	05/2014
7430	2^218896+1869451	65895	Enzo Doria	05/2016
7432	63^36616+2	65885	Lelio R Paula	05/2013
7433	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
7434	2^218796-113297	65865	Enzo Doria	07/2014
7435	2^218797+73727	65865	Enzo Doria	04/2016
7436	3^138040-110	65862	Lelio R Paula	06/2013
7437	11^63240-1950	65858	Enzo Doria	12/2012
7438	2^218764-111873	65855	Enzo Doria	05/2014
7439	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
7440	3^137988+26	65838	Lelio R Paula	06/2013
7441	2^218680-719	65830	Yves Minet	05/2012
7442	18^52424+17	65807	Lelio R Paula	08/2013
7443	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
7444	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
7445	(5*10^65773+1)/3	65774	Erik Branger	12/2013
7446	2^218457-17329	65763	Enzo Doria	05/2013
7447	151703#+223381	65759	Nicolas PALAU	10/2016
7448	2^218436+40755	65756	Lelio R Paula	10/2011
7449	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
7450	157^29934+29934^157	65733	Serge Batalov	05/2014
7451	211^28273-2	65715	Lelio R Paula	09/2013
7452	(59*10^65712+31)/9	65713	Robert Price	09/2015
7453	611^23586+23586^611	65712	Norbert Schneider	08/2016
7454	p(13991)#/2+32	65712	Robert Price	12/2016
7455	2^218282-18485	65710	Enzo Doria	05/2013
7456	2^218274-111251	65708	Enzo Doria	05/2014
7457	2*F(314335)-1	65693	Henri Lifchitz	12/2009
7458	2^218200+427	65685	Henri Lifchitz	01/2005
7459	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
7460	(10199^(2^14)+(10197)^(2^14))/2	65676	Robert Price	05/2018
7461	46532!3+3	65667	Robert Price	10/2014
7462	2^218120-147	65661	Lelio R Paula	08/2011
7463	452^24729+24729^452	65659	Norbert Schneider	09/2016
7464	2^218102-114893	65656	Enzo Doria	05/2015
7465	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
7466	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
7467	(306^26407-1)/305	65638	Eric Chen	09/2017
7468	19^51326+36	65634	Lelio R Paula	08/2013
7469	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
7470	2^217989-33	65622	Lelio R Paula	08/2011
7471	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
7472	4*6^84315-5	65611	Lelio R Paula	09/2014
7473	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
7474	6^84303+55	65601	Lelio R Paula	07/2013
7475	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
7476	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
7477	5*2^217858+3	65583	Lelio R Paula	04/2014
7478	(19*10^65572+119)/3	65573	Robert Price	02/2017
7480	20^50399+51	65571	Lelio R Paula	08/2013
7479	7162^17009+17009^7162	65571	Norbert Schneider	07/2018
7481	11^62946-5670	65552	Enzo Doria	01/2013
7482	2^217742-3911	65547	Yves Minet	08/2009
7483	(19*10^65545+77)/3	65546	Robert Price	08/2016
7484	2^217731+131	65544	Lelio R Paula	08/2011
7485	2^217720-111287	65541	Enzo Doria	05/2014
7486	(365^25579+1)/366	65539	Eric Chen	10/2017
7487	10^65537+27	65538	Robert Price	01/2011
7488	10^65537-76859	65537	Patrick De Geest	05/2013
7489	(28*10^65532+359)/9	65533	Robert Price	11/2017
7490	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
7491	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
7492	5*10^65509+23	65510	Robert Price	11/2017
7493	(8*10^65507-83)/3	65508	Robert Price	10/2017
7494	7*10^65492-47	65493	Robert Price	02/2017
7495	2^217547-1868407	65489	Enzo Doria	04/2016
7496	2^217531-111769	65484	Enzo Doria	05/2014
7497	7^77484-18	65482	Lelio R Paula	06/2013
7498	2^217488-113285	65471	Enzo Doria	07/2014
7499	151153#/30-30	65468	Henri Lifchitz	12/2011
7500	2^217466+4257	65464	Lelio R Paula	10/2011

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Probable Primes Top 10000

(252402 PRPs in the top)