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	4*10^68020+91	68021	Robert Price	11/2017
7252	156(10^(417000)-1)/101-1	68001	Robert Price	05/2014
7253	2^225878-1017	67997	Lelio R Paula	04/2012
7254	38^75289+5^75289-34^75289+3*2^75289	67994	Mike Oakes	11/2010
7255	3*2^225865+5	67993	Lelio R Paula	04/2014
7257	11^65284-5820	67987	Enzo Doria	01/2013
7256	19^53166+70	67987	Lelio R Paula	08/2013
7258	2^225837+75407	67984	Enzo Doria	04/2016
7259	3^142464-112654	67973	Enzo Doria	06/2014
7260	2^225777+95	67966	Lelio R Paula	02/2012
7261	(2^225641-1017)/138815	67920	Lelio R Paula	04/2012
7262	2^225609-18445	67916	Enzo Doria	05/2013
7263	2^225542-177	67895	Lelio R Paula	02/2012
7264	2^225536-29	67894	Henri Lifchitz	05/2005
7265	11^65190-3390	67889	Enzo Doria	12/2012
7266	3^142249-2^(142249-1)	67871	Robert Price	01/2016
7267	11^65168-4830	67866	Enzo Doria	01/2013
7268	10^67863+58627	67864	Patrick De Geest	01/2016
7269	10^67863-11	67863	Robert Price	05/2011
7270	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
7271	(19*2^225357-1)/11	67840	Lelio R Paula	01/2014
7272	9*6^87164-7	67828	Lelio R Paula	09/2014
7273	131^32034+130	67825	Norbert Schneider	03/2015
7274	(29*2^225314+1)/10881	67824	Lelio R Paula	08/2012
7275	(134*10^67816+7)/3	67818	Robert Price	02/2017
7276	2^225261+855	67811	Lelio R Paula	04/2012
7277	(29*2^225252-1)/2933	67806	Lelio R Paula	01/2014
7278	(4*10^67796+23)/9	67796	Robert Price	11/2014
7279	15477^16180-16180^15477	67790	Norbert Schneider	09/2018
7280	(23*2^225177+1)/31	67785	Lelio R Paula	08/2012
7281	(4*10^67784+149)/9	67784	Robert Price	03/2017
7282	2^225120+151	67768	Lelio R Paula	02/2012
7283	(44^41233+1)/45	67763	Robert Price	11/2013
7284	89933!6-16	67747	Robert Price	08/2018
7285	8*10^67742+9	67743	Dmitry Domanov	11/2010
7286	2^224977+1089	67725	Lelio R Paula	04/2012
7287	(2^224950+5)/19509	67713	Lelio R Paula	04/2012
7288	11^65011-5970	67702	Enzo Doria	01/2013
7289	88*10^67691+7	67693	Robert Price	11/2016
7290	11^65000-7140	67691	Enzo Doria	01/2013
7291	2^224841+59	67684	Lelio R Paula	02/2012
7292	33129!2+2^33129	67684	Robert Price	09/2015
7293	2^224827+8415	67680	Lelio R Paula	02/2013
7294	(9913*2^224821-1)/19825	67678	Lelio R Paula	04/2015
7295	2^224815-49789	67677	Henri Lifchitz	04/2005
7296	(43*10^67664+11)/9	67665	Robert Price	06/2015
7297	(292*10^67659-1)/3	67661	Robert Price	01/2017
7298	(17*2^224766+1)/29007	67659	Lelio R Paula	06/2012
7299	2^224744+577294575	67655	Lelio R Paula	02/2016
7300	((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
7301	(2^224721+78557)/1739	67645	Lelio R Paula	05/2012
7302	2^224700+1915	67642	Lelio R Paula	04/2012
7303	(29*2^224694-1)/198905	67636	Lelio R Paula	01/2014
7304	2^224658-93	67629	Lelio R Paula	02/2012
7305	2^224624-13077	67619	Enzo Doria	10/2012
7306	18^53860-3319	67609	Enzo Doria	03/2013
7307	(21181*2^224570+1)/5	67606	Lelio R Paula	06/2014
7308	89762!6-3	67606	Robert Price	08/2018
7309	2^224578-111041	67605	Enzo Doria	05/2014
7310	2^224569-113233	67603	Enzo Doria	07/2014
7311	2^224562-113171	67600	Enzo Doria	07/2014
7312	2^224556-113129	67599	Enzo Doria	07/2014
7313	6*7^79980-5	67592	Lelio R Paula	09/2014
7314	(6883*2^224523-1)/16031	67588	Lelio R Paula	04/2015
7315	10^67579+164779	67580	Patrick De Geest	07/2017
7317	(52*10^67578-61)/9	67579	Robert Price	09/2015
7316	10^67579-401	67579	Robert Price	06/2017
7318	(17^54919-1)/16	67574	Paul Bourdelais	03/2010
7319	(2^224363-9)/1951	67537	Lelio R Paula	04/2012
7320	(709*10^67517-7)/9	67519	Robert Price	09/2017
7321	47719!3-59049	67516	Robert Price	12/2015
7322	(22^50287+1)/23	67506	Robert Price	06/2013
7323	3*10^67499+67	67500	Robert Price	11/2017
7324	11^64811-5820	67494	Enzo Doria	01/2013
7325	131^31870+31870^131	67478	Serge Batalov	05/2014
7326	9*10^67468+7	67469	Dmitry Domanov	11/2010
7327	(31*2^224115-1)/47723	67463	Lelio R Paula	01/2014
7328	128^32001+32001^128	67433	Serge Batalov	05/2014
7329	(89*10^67431-17)/9	67432	Robert Price	11/2015
7330	2^223912-111059	67405	Enzo Doria	05/2014
7332	2^223913+73697	67405	Enzo Doria	04/2016
7331	(2*10^67405-23)/3	67405	Robert Price	09/2017
7334	(10^67404+179)/9	67404	Serge Batalov	12/2014
7333	18738^3955+3955^18738	67404	Hans Havermann	09/2016
7335	9*7^79728-2	67379	Lelio R Paula	09/2014
7336	(28*10^67378-43)/3	67379	Robert Price	04/2016
7337	(3^141234-7)/430241282	67378	Lelio R Paula	04/2012
7338	211^28988-2	67377	Lelio R Paula	09/2013
7339	4*10^67375+91	67376	Robert Price	11/2017
7340	2^223793-18069	67369	Enzo Doria	05/2013
7341	2^223777-2521	67364	Yves Minet	07/2014
7342	(15185*2^223775-1)/15183	67363	Lelio R Paula	04/2015
7343	(2^223759-lucasV(1,2,223759)+1)/2	67358	Mike Oakes	11/2016
7344	V(340138)	67336	Serge Batalov	03/2015
7345	43125^14528-106	67334	Enzo Doria	07/2012
7346	15275^16086-16086^15275	67304	Norbert Schneider	09/2018
7347	8*10^67302-51	67303	Robert Price	10/2017
7348	17458^7153+7153^17458	67292	Hans Havermann	08/2016
7349	16366^12925+12925^16366	67288	Hans Havermann	08/2016
7350	37^42906-2	67286	Lelio R Paula	08/2013
7351	18^53592-13	67273	Lelio R Paula	08/2013
7352	V(396221)	67256	Serge Batalov	03/2015
7353	(34*10^67245-7)/9/3^4/193/1381537	67236	Makoto Morimoto	04/2016
7354	(14*10^67235-101)/3	67236	Robert Price	04/2017
7355	53^38993-52^38993	67235	Robert Price	01/2013
7356	(2^223349-7)/6485	67231	Lelio R Paula	04/2012
7357	2^223333+315	67230	Lelio R Paula	04/2012
7358	2^223278-111041	67214	Enzo Doria	05/2014
7359	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
7360	2^223256-45	67207	Lelio R Paula	02/2012
7361	2^223253-112111	67206	Enzo Doria	06/2014
7362	18407^4474+4474^18407	67199	Hans Havermann	08/2016
7363	47^40182+40182^47	67189	Norbert Schneider	11/2014
7364	13^60309+94	67181	Lelio R Paula	07/2013
7365	11^64503-84	67173	Lelio R Paula	07/2013
7366	3^140781+236	67170	Lelio R Paula	06/2013
7367	2^223107-865057	67162	Paul Bourdelais	03/2013
7368	2^223100-59	67160	Lelio R Paula	02/2012
7369	2^223087+71963	67156	Enzo Doria	04/2016
7371	18^53481-3779	67134	Enzo Doria	03/2013
7370	(326^26713-1)/325	67134	Eric Chen	09/2017
7372	4^111473-62573	67114	Mike Oakes	02/2011
7373	2^222943+29	67113	Henri Lifchitz	08/2005
7374	(2^222939-9)/103	67110	Lelio R Paula	04/2012
7375	2^222862-459161	67089	Enzo Doria	05/2015
7376	2^222828+8193	67078	Lelio R Paula	04/2012
7377	3^140570+2660	67069	Lelio R Paula	06/2013
7378	2^222744+855	67053	Lelio R Paula	04/2012
7379	13^60189+84	67048	Lelio R Paula	07/2013
7380	2*10^67043-51	67044	Robert Price	11/2017
7381	2^222701+577294575	67040	Lelio R Paula	02/2016
7382	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
7383	(151*10^67027-7)/9	67029	Robert Price	07/2017
7384	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
7385	2^222614-111041	67014	Enzo Doria	05/2014
7386	118^32333-117	66991	Norbert Schneider	08/2018
7387	2^222520-1907	66986	Yves Minet	03/2013
7388	(4^111231+23)/3	66968	Robert Price	02/2017
7389	2^222408-111275	66952	Enzo Doria	05/2014
7390	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
7391	2^222378-1005	66943	Lelio R Paula	04/2012
7392	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
7393	7^79202-6^(79202+1)	66934	Robert Price	06/2016
7394	2^222325-112255	66927	Enzo Doria	06/2014
7395	20^51428+33	66910	Lelio R Paula	08/2013
7396	2^222224-18509	66897	Enzo Doria	05/2013
7397	(38*10^66896+187)/9	66897	Robert Price	11/2017
7398	2^222192-869688105	66887	Lelio R Paula	02/2016
7399	(19*10^66878-43)/3	66879	Robert Price	10/2017
7400	11^64219-64	66878	Lelio R Paula	07/2013
7401	2^222151-17295	66875	Lelio R Paula	04/2012
7402	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
7403	2^222085-111031	66855	Enzo Doria	05/2014
7404	8*10^66848-13	66849	Robert Price	05/2017
7405	(3^140087+4)/13	66838	Lelio R Paula	04/2012
7406	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
7407	19^52265+52	66835	Lelio R Paula	08/2013
7408	2*10^66826-27	66827	Robert Price	02/2017
7409	4*6^85867+5	66819	Lelio R Paula	09/2014
7410	11955^16384+2	66807	Matt Stath	12/2018
7411	15^56800+8	66802	Lelio R Paula	08/2013
7412	(2^221891-2^110946+1)/5	66796		11/2006
7413	10^66793+69441	66794	Patrick De Geest	05/2013
7414	10^66793-63	66793	Robert Price	05/2011
7415	35^43256-1704	66791	Enzo Doria	03/2013
7416	3^139976+2^(139976-1)	66786	Robert Price	05/2016
7417	88769!6-48	66786	Robert Price	08/2018
7418	7^79023-54	66783	Lelio R Paula	06/2013
7419	104^33109-103	66782	Norbert Schneider	11/2016
7420	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
7421	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
7422	2^221768+183	66759	Lelio R Paula	02/2012
7423	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
7424	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
7425	11^64097+48	66751	Lelio R Paula	07/2013
7426	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
7427	(19*10^66748+413)/9	66749	Robert Price	10/2017
7428	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
7429	8*6^85758-7	66734	Lelio R Paula	09/2014
7430	135^31325+2	66733	Lelio R Paula	05/2013
7431	(49*10^66729+41)/9	66730	Robert Price	07/2015
7432	(349*10^66720-7)/9	66722	Robert Price	03/2017
7433	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
7434	(25*10^66714+71)/3	66715	Robert Price	01/2017
7435	11^64061-780	66713	Enzo Doria	11/2012
7436	7^78929+4	66703	Lelio R Paula	06/2013
7437	11^64048-930	66700	Enzo Doria	11/2012
7438	120^32079-119	66699	Norbert Schneider	09/2018
7439	2*7^78921+5	66697	Lelio R Paula	09/2014
7440	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
7441	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
7442	2^221479+72953	66672	Enzo Doria	04/2016
7443	10^66666+275403	66667	Patrick De Geest	03/2010
7444	10^66666-115521	66666	Patrick De Geest	03/2010
7445	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
7446	4*10^66653+21	66654	Robert Price	08/2016
7447	(10^66650+149)/3	66650	Serge Batalov	12/2014
7448	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
7449	2^221391-2145	66646	Lelio R Paula	04/2012
7450	(5*10^66613-119)/3	66614	Robert Price	04/2016
7451	2^221273-113233	66610	Enzo Doria	07/2014
7452	3^139571-46	66593	Lelio R Paula	06/2013
7453	(410^(233295)-2*(10^33295)+1)/3	66591	Robert Price	04/2018
7454	2^221181-869688105	66583	Lelio R Paula	02/2016
7455	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
7456	2^221126+133	66566	Lelio R Paula	02/2012
7458	12^61680+91	66564	Lelio R Paula	07/2013
7457	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
7459	(13*10^66551-73)/3	66552	Robert Price	12/2016
7460	11^63901-1590	66547	Enzo Doria	12/2012
7461	11^63901-1500	66547	Enzo Doria	12/2012
7462	6^85517+23	66546	Lelio R Paula	07/2013
7463	17^54069-40	66530	Lelio R Paula	08/2013
7464	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
7465	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
7466	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
7467	3^139432+26	66526	Lelio R Paula	06/2013
7468	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
7469	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
7470	6^85481+85481	66518	Henri Lifchitz	08/2014
7471	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
7472	13^59687+66	66488	Lelio R Paula	07/2013
7473	(49*10^66485-31)/9	66486	Robert Price	07/2015
7474	(46*10^66469+17)/9	66470	Robert Price	06/2015
7475	2^220790+97	66465	Lelio R Paula	02/2012
7476	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
7477	40009^14441-102	66460	Enzo Doria	07/2012
7478	2^220736-143	66449	Lelio R Paula	02/2012
7479	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
7480	2^220675+69	66430	Lelio R Paula	02/2012
7481	88323!6-16	66419	Robert Price	08/2018
7482	2^220633-111381	66418	Enzo Doria	05/2014
7483	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
7484	2^220596-15813	66407	Enzo Doria	04/2013
7485	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
7486	2^220549-1859173	66392	Enzo Doria	04/2016
7487	2^220478-161	66371	Lelio R Paula	02/2012
7488	5^94938-14636	66359	Enzo Doria	02/2013
7489	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
7490	15444^15839-15839^15444	66346	Norbert Schneider	08/2018
7491	2^220253-114871	66303	Enzo Doria	05/2015
7492	12^61432+95	66297	Lelio R Paula	07/2013
7493	2^220192-111563	66285	Enzo Doria	05/2014
7494	2^220188-111449	66284	Enzo Doria	05/2014
7495	(4*10^66284+23)/9	66284	Robert Price	11/2014
7496	32501!2+2	66266	Robert Price	01/2015
7497	(8*10^66261-101)/3	66262	Robert Price	10/2017
7498	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
7499	(47^39623-1)/46	66252	Robert Price	06/2014
7500	2^220044-97305	66240	Lelio R Paula	04/2012

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Probable Primes Top 10000

(252538 PRPs in the top)