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 ?
6251	-330*Bern(21940)/223790620733	68201	Serge Batalov	04/2015
6252	3^142925+8680	68193	Lelio R Paula	06/2013
6253	3*2^226512-7	68188	Lelio R Paula	04/2014
6254	14^59484+57	68177	Lelio R Paula	08/2013
6255	11^65438-2190	68147	Enzo Doria	12/2012
6256	91^34784-2	68144	Lelio R Paula	09/2013
6257	(2^226336-3)*6-7	68135	Gilbert Mozzo	06/2016
6258	(22*10^68133-37)/3	68134	Robert Price	05/2017
6259	5^97476+36	68133	Lelio R Paula	06/2013
6260	3*5^97474-2	68132	Lelio R Paula	09/2014
6261	12^63130+49	68129	Lelio R Paula	07/2013
6262	2^226281+5385	68118	Lelio R Paula	04/2012
6263	2^226257-3049	68111	Yves Minet	10/2014
6264	(28*10^68107-43)/3	68108	Robert Price	04/2016
6265	2^226243-2587	68106	Yves Minet	07/2014
6266	20^52346-11	68104	Lelio R Paula	09/2013
6267	2^226205-99	68095	Lelio R Paula	02/2012
6268	2^226187-49	68090	Lelio R Paula	02/2012
6269	3^142708+76	68090	Lelio R Paula	06/2013
6270	7*10^68088-89	68089	Robert Price	01/2017
6271	2^226154+71839	68080	Enzo Doria	04/2016
6272	(10^68078+59)/3	68078	Serge Batalov	12/2014
6274	14^59387+69	68066	Lelio R Paula	08/2013
6273	2^226108-113429	68066	Enzo Doria	07/2014
6275	(24^49307-1)/23	68053	Robert Price	04/2012
6276	15^57859-28	68048	Lelio R Paula	08/2013
6277	(509203*2^226003-1)/13	68039	Lelio R Paula	04/2015
6278	2^226015-111361	68038	Enzo Doria	05/2014
6279	156(10^(417000)-1)/101-1	68001	Robert Price	05/2014
6280	2^225878-1017	67997	Lelio R Paula	04/2012
6281	38^75289+5^75289-34^75289+3*2^75289	67994	Mike Oakes	11/2010
6282	3*2^225865+5	67993	Lelio R Paula	04/2014
6283	11^65284-5820	67987	Enzo Doria	01/2013
6284	19^53166+70	67987	Lelio R Paula	08/2013
6285	2^225837+75407	67984	Enzo Doria	04/2016
6286	3^142464-112654	67973	Enzo Doria	06/2014
6287	2^225777+95	67966	Lelio R Paula	02/2012
6288	(2^225641-1017)/138815	67920	Lelio R Paula	04/2012
6289	2^225609-18445	67916	Enzo Doria	05/2013
6290	2^225542-177	67895	Lelio R Paula	02/2012
6291	2^225536-29	67894	Henri Lifchitz	05/2005
6292	11^65190-3390	67889	Enzo Doria	12/2012
6293	3^142249-2^(142249-1)	67871	Robert Price	01/2016
6294	11^65168-4830	67866	Enzo Doria	01/2013
6295	10^67863+58627	67864	Patrick De Geest	01/2016
6296	10^67863-11	67863	Robert Price	05/2011
6297	(1!)^2+(2!)^2+(3!)^2+...+(9566!)^2	67856	T. D. Noe	02/2006
6298	(19*2^225357-1)/11	67840	Lelio R Paula	01/2014
6299	9*6^87164-7	67828	Lelio R Paula	09/2014
6300	131^32034+130	67825	Norbert Schneider	03/2015
6301	(29*2^225314+1)/10881	67824	Lelio R Paula	08/2012
6302	(134*10^67816+7)/3	67818	Robert Price	02/2017
6303	2^225261+855	67811	Lelio R Paula	04/2012
6304	(29*2^225252-1)/2933	67806	Lelio R Paula	01/2014
6305	(4*10^67796+23)/9	67796	Robert Price	11/2014
6306	(23*2^225177+1)/31	67785	Lelio R Paula	08/2012
6307	(4*10^67784+149)/9	67784	Robert Price	03/2017
6308	2^225120+151	67768	Lelio R Paula	02/2012
6309	(44^41233+1)/45	67763	Robert Price	11/2013
6310	8*10^67742+9	67743	Dmitry Domanov	11/2010
6311	2^224977+1089	67725	Lelio R Paula	04/2012
6312	(2^224950+5)/19509	67713	Lelio R Paula	04/2012
6313	11^65011-5970	67702	Enzo Doria	01/2013
6314	88*10^67691+7	67693	Robert Price	11/2016
6315	11^65000-7140	67691	Enzo Doria	01/2013
6316	2^224841+59	67684	Lelio R Paula	02/2012
6317	33129!2+2^33129	67684	Robert Price	09/2015
6318	2^224827+8415	67680	Lelio R Paula	02/2013
6319	(9913*2^224821-1)/19825	67678	Lelio R Paula	04/2015
6320	2^224815-49789	67677	Henri Lifchitz	04/2005
6321	(43*10^67664+11)/9	67665	Robert Price	06/2015
6322	(292*10^67659-1)/3	67661	Robert Price	01/2017
6323	(17*2^224766+1)/29007	67659	Lelio R Paula	06/2012
6324	2^224744+577294575	67655	Lelio R Paula	02/2016
6325	((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
6326	(2^224721+78557)/1739	67645	Lelio R Paula	05/2012
6327	2^224700+1915	67642	Lelio R Paula	04/2012
6328	(29*2^224694-1)/198905	67636	Lelio R Paula	01/2014
6329	2^224658-93	67629	Lelio R Paula	02/2012
6330	2^224624-13077	67619	Enzo Doria	10/2012
6331	18^53860-3319	67609	Enzo Doria	03/2013
6332	(21181*2^224570+1)/5	67606	Lelio R Paula	06/2014
6333	2^224578-111041	67605	Enzo Doria	05/2014
6334	2^224569-113233	67603	Enzo Doria	07/2014
6335	2^224562-113171	67600	Enzo Doria	07/2014
6336	2^224556-113129	67599	Enzo Doria	07/2014
6337	6*7^79980-5	67592	Lelio R Paula	09/2014
6338	(6883*2^224523-1)/16031	67588	Lelio R Paula	04/2015
6339	10^67579+164779	67580	Patrick De Geest	07/2017
6341	(52*10^67578-61)/9	67579	Robert Price	09/2015
6340	10^67579-401	67579	Robert Price	06/2017
6342	(17^54919-1)/16	67574	Paul Bourdelais	03/2010
6343	(2^224363-9)/1951	67537	Lelio R Paula	04/2012
6344	47719!3-59049	67516	Robert Price	12/2015
6345	(22^50287+1)/23	67506	Robert Price	06/2013
6346	11^64811-5820	67494	Enzo Doria	01/2013
6347	131^31870+31870^131	67478	Serge Batalov	05/2014
6348	9*10^67468+7	67469	Dmitry Domanov	11/2010
6349	(31*2^224115-1)/47723	67463	Lelio R Paula	01/2014
6350	128^32001+32001^128	67433	Serge Batalov	05/2014
6351	(89*10^67431-17)/9	67432	Robert Price	11/2015
6352	2^223912-111059	67405	Enzo Doria	05/2014
6353	2^223913+73697	67405	Enzo Doria	04/2016
6354	(10^67404+179)/9	67404	Serge Batalov	12/2014
6355	18738^3955+3955^18738	67404	Hans Havermann	09/2016
6356	9*7^79728-2	67379	Lelio R Paula	09/2014
6357	(28*10^67378-43)/3	67379	Robert Price	04/2016
6358	(3^141234-7)/430241282	67378	Lelio R Paula	04/2012
6359	211^28988-2	67377	Lelio R Paula	09/2013
6360	2^223793-18069	67369	Enzo Doria	05/2013
6361	2^223777-2521	67364	Yves Minet	07/2014
6362	(15185*2^223775-1)/15183	67363	Lelio R Paula	04/2015
6363	(2^223759-lucasV(1,2,223759)+1)/2	67358	Mike Oakes	11/2016
6364	V(340138)	67336	Serge Batalov	03/2015
6365	43125^14528-106	67334	Enzo Doria	07/2012
6366	17458^7153+7153^17458	67292	Hans Havermann	08/2016
6367	16366^12925+12925^16366	67288	Hans Havermann	08/2016
6368	37^42906-2	67286	Lelio R Paula	08/2013
6369	18^53592-13	67273	Lelio R Paula	08/2013
6370	V(396221)	67256	Serge Batalov	03/2015
6372	(34*10^67245-7)/9/3^4/193/1381537	67236	Makoto Morimoto	04/2016
6371	(14*10^67235-101)/3	67236	Robert Price	04/2017
6373	53^38993-52^38993	67235	Robert Price	01/2013
6374	(2^223349-7)/6485	67231	Lelio R Paula	04/2012
6375	2^223333+315	67230	Lelio R Paula	04/2012
6376	2^223278-111041	67214	Enzo Doria	05/2014
6377	(23472^223281+1)/(351971213*1783)	67208	Jens K. Andersen	09/2007
6378	2^223256-45	67207	Lelio R Paula	02/2012
6379	2^223253-112111	67206	Enzo Doria	06/2014
6380	18407^4474+4474^18407	67199	Hans Havermann	08/2016
6381	47^40182+40182^47	67189	Norbert Schneider	11/2014
6382	13^60309+94	67181	Lelio R Paula	07/2013
6383	11^64503-84	67173	Lelio R Paula	07/2013
6384	3^140781+236	67170	Lelio R Paula	06/2013
6385	2^223107-865057	67162	Paul Bourdelais	03/2013
6386	2^223100-59	67160	Lelio R Paula	02/2012
6387	2^223087+71963	67156	Enzo Doria	04/2016
6388	18^53481-3779	67134	Enzo Doria	03/2013
6389	4^111473-62573	67114	Mike Oakes	02/2011
6390	2^222943+29	67113	Henri Lifchitz	08/2005
6391	(2^222939-9)/103	67110	Lelio R Paula	04/2012
6392	2^222862-459161	67089	Enzo Doria	05/2015
6393	2^222828+8193	67078	Lelio R Paula	04/2012
6394	3^140570+2660	67069	Lelio R Paula	06/2013
6395	2^222744+855	67053	Lelio R Paula	04/2012
6396	13^60189+84	67048	Lelio R Paula	07/2013
6397	2^222701+577294575	67040	Lelio R Paula	02/2016
6398	(13*10^67038-31)/9	67039	Serge Batalov	11/2008
6399	(151*10^67027-7)/9	67029	Robert Price	07/2017
6400	(58695*2^222620-1)/61	67019	Lelio R Paula	04/2015
6401	2^222614-111041	67014	Enzo Doria	05/2014
6402	2^222520-1907	66986	Yves Minet	03/2013
6403	(4^111231+23)/3	66968	Robert Price	02/2017
6404	2^222408-111275	66952	Enzo Doria	05/2014
6405	10^66949-9^66949	66949	Jean-Louis Charton	12/2005
6406	2^222378-1005	66943	Lelio R Paula	04/2012
6407	(9*2^222366+1)/73	66938	Lelio R Paula	08/2012
6408	7^79202-6^(79202+1)	66934	Robert Price	06/2016
6409	2^222325-112255	66927	Enzo Doria	06/2014
6410	20^51428+33	66910	Lelio R Paula	08/2013
6411	2^222224-18509	66897	Enzo Doria	05/2013
6412	2^222192-869688105	66887	Lelio R Paula	02/2016
6413	11^64219-64	66878	Lelio R Paula	07/2013
6414	2^222151-17295	66875	Lelio R Paula	04/2012
6415	gcd(V(799885),5F(159977)(F(159977)+1)+1)	66867	Serge Batalov	04/2015
6416	2^222085-111031	66855	Enzo Doria	05/2014
6417	8*10^66848-13	66849	Robert Price	05/2017
6418	(3^140087+4)/13	66838	Lelio R Paula	04/2012
6419	(3^140102+4)/8843609437	66836	Lelio R Paula	04/2012
6420	19^52265+52	66835	Lelio R Paula	08/2013
6421	2*10^66826-27	66827	Robert Price	02/2017
6422	4*6^85867+5	66819	Lelio R Paula	09/2014
6423	15^56800+8	66802	Lelio R Paula	08/2013
6424	(2^221891-2^110946+1)/5	66796		11/2006
6425	10^66793+69441	66794	Patrick De Geest	05/2013
6426	10^66793-63	66793	Robert Price	05/2011
6427	35^43256-1704	66791	Enzo Doria	03/2013
6428	3^139976+2^(139976-1)	66786	Robert Price	05/2016
6429	7^79023-54	66783	Lelio R Paula	06/2013
6430	104^33109-103	66782	Norbert Schneider	11/2016
6431	(34*10^66778-7)/9/37/358901	66772	Makoto Morimoto	04/2016
6432	(-lucasV(1,2,443622)+2)/(7281487)	66766	Mike Oakes	04/2017
6434	2^221768+183	66759	Lelio R Paula	02/2012
6433	gcd(V(1197915),5F(239583)(F(239583)+1)+1)	66759	Serge Batalov	04/2015
6435	(154*10^66755-1)/9	66757	Serge Batalov	12/2014
6436	11^64097+48	66751	Lelio R Paula	07/2013
6437	(lucasV(1,2,443547)-2)/(713791327221773)	66749	Mike Oakes	04/2017
6438	(3*2^221696-1)/13	66737	Lelio R Paula	01/2014
6439	8*6^85758-7	66734	Lelio R Paula	09/2014
6440	135^31325+2	66733	Lelio R Paula	05/2013
6441	(49*10^66729+41)/9	66730	Robert Price	07/2015
6442	(349*10^66720-7)/9	66722	Robert Price	03/2017
6443	(-lucasV(1,2,443285)+2)/(3^2*307)	66718	Mike Oakes	04/2017
6444	(25*10^66714+71)/3	66715	Robert Price	01/2017
6445	11^64061-780	66713	Enzo Doria	11/2012
6446	7^78929+4	66703	Lelio R Paula	06/2013
6447	11^64048-930	66700	Enzo Doria	11/2012
6448	2*7^78921+5	66697	Lelio R Paula	09/2014
6449	(25*2^221526+1)/409	66685	Lelio R Paula	08/2012
6450	(2^221509-1)/292391881	66673	Jens K. Andersen	02/2009
6451	2^221479+72953	66672	Enzo Doria	04/2016
6452	10^66666+275403	66667	Patrick De Geest	03/2010
6453	10^66666-115521	66666	Patrick De Geest	03/2010
6454	(18*10^66657-81)/99	66657	Ray Chandler	01/2011
6455	4*10^66653+21	66654	Robert Price	08/2016
6456	(10^66650+149)/3	66650	Serge Batalov	12/2014
6457	9^69842+38^69842-24^69842-3*2^69842	66647	Mike Oakes	12/2010
6458	2^221391-2145	66646	Lelio R Paula	04/2012
6459	(5*10^66613-119)/3	66614	Robert Price	04/2016
6460	2^221273-113233	66610	Enzo Doria	07/2014
6461	3^139571-46	66593	Lelio R Paula	06/2013
6462	2^221181-869688105	66583	Lelio R Paula	02/2016
6463	(61*10^66575-7)/9	66576	Ray Chandler	02/2012
6464	2^221126+133	66566	Lelio R Paula	02/2012
6465	12^61680+91	66564	Lelio R Paula	07/2013
6466	(lucasV(1,2,442258)+2)/103	66564	Mike Oakes	04/2017
6467	(13*10^66551-73)/3	66552	Robert Price	12/2016
6468	11^63901-1590	66547	Enzo Doria	12/2012
6469	11^63901-1500	66547	Enzo Doria	12/2012
6470	6^85517+23	66546	Lelio R Paula	07/2013
6471	17^54069-40	66530	Lelio R Paula	08/2013
6472	(2^110503+4725)^2+(2^110503+4725)+41	66530	Makoto Morimoto	05/2016
6473	(2^110503+8099)^2+(2^110503+8099)+41	66530	Makoto Morimoto	05/2016
6475	(2^221008-1017)/78533	66526	Lelio R Paula	04/2012
6474	3^139432+26	66526	Lelio R Paula	06/2013
6476	((2^110503+5139)^2+(2^110503+5139)+41)/20865797	66523	Makoto Morimoto	05/2016
6477	((2^110503+6647)^2+(2^110503+6647)+41)/197/17327	66523	Makoto Morimoto	05/2016
6478	6^85481+85481	66518	Henri Lifchitz	08/2014
6479	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
6480	13^59687+66	66488	Lelio R Paula	07/2013
6481	(49*10^66485-31)/9	66486	Robert Price	07/2015
6482	(46*10^66469+17)/9	66470	Robert Price	06/2015
6483	2^220790+97	66465	Lelio R Paula	02/2012
6484	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
6485	40009^14441-102	66460	Enzo Doria	07/2012
6486	2^220736-143	66449	Lelio R Paula	02/2012
6487	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
6488	2^220675+69	66430	Lelio R Paula	02/2012
6489	2^220633-111381	66418	Enzo Doria	05/2014
6490	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
6491	2^220596-15813	66407	Enzo Doria	04/2013
6492	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
6493	2^220549-1859173	66392	Enzo Doria	04/2016
6494	2^220478-161	66371	Lelio R Paula	02/2012
6495	5^94938-14636	66359	Enzo Doria	02/2013
6496	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
6497	2^220253-114871	66303	Enzo Doria	05/2015
6498	12^61432+95	66297	Lelio R Paula	07/2013
6499	2^220192-111563	66285	Enzo Doria	05/2014
6500	2^220188-111449	66284	Enzo Doria	05/2014

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Probable Primes Top 10000

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