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 ?
9251	(15*2^175565+1)/8359	52848	Lelio R Paula	07/2012
9252	(2^175631-1)/330463093135534238072561/92733169	52839	Robert Kinser	03/2017
9253	14256^5077+5077^14256	52828	Hans Havermann	06/2016
9254	2^175467+82875	52821	Lelio R Paula	07/2012
9255	(7*10^52819+167)/3	52820	Robert Kinser	10/2017
9256	(67607*2^175426+1)/3	52813	Lelio R Paula	05/2014
9257	13^47400-60	52801	Lelio R Paula	01/2013
9258	4*10^52792+63	52793	Robert Price	06/2016
9260	(78557*2^175360+1)/3087	52791	Lelio R Paula	06/2014
9259	18^42055-2929	52791	Enzo Doria	03/2013
9261	9*5^75521+2	52788	Lelio R Paula	09/2014
9262	6^67814+31	52770	Lelio R Paula	10/2012
9263	70^28600+69	52770	Norbert Schneider	10/2012
9264	14^46038+97	52766	Lelio R Paula	01/2013
9265	(61*10^52763-7)/9	52764	Serge Batalov	02/2009
9266	2*5^75474+9	52755	Lelio R Paula	09/2014
9267	10^52753+2826430609	52754	Robert Price	05/2015
9268	10^52753+183997	52754	Patrick De Geest	01/2016
9269	10^52753-50153	52753	Patrick De Geest	03/2016
9270	19846^455+455^19846	52751	Anatoly F. Selevich	02/2007
9271	2^175217+72977	52746	Enzo Doria	04/2016
9272	p(11466)#/2-256	52746	Robert Price	05/2017
9273	(4*10^52740+41)/9	52740	Robert Price	11/2014
9274	2^175189+5385	52738	Lelio R Paula	08/2009
9275	2^175160+9385	52729	Lelio R Paula	07/2008
9276	12356^12885+12885^12356	52724	Norbert Schneider	03/2016
9277	2^175137+11	52722	Lelio R Paula	01/2011
9278	65^29077-64^29077	52715	Robert Price	08/2013
9279	2*10^52713-87	52714	Robert Price	06/2016
9280	2^175106-465	52713	Lelio R Paula	08/2009
9281	2^175089-58695	52708	Lelio R Paula	08/2009
9282	2^175045+195	52694	Lelio R Paula	02/2011
9283	195^23010-2	52694	Lelio R Paula	10/2017
9284	2^175025+149	52688	Lelio R Paula	02/2011
9286	(19^41201+1)/20	52685	Paul Bourdelais	03/2010
9285	(436*10^52683-13)/9	52685	Robert Price	10/2017
9287	2*12^48815-5^48815	52681	Mike Oakes	10/2010
9288	335^20862-20862^335	52678	Norbert Schneider	09/2015
9289	2^174983-7605	52676	Lelio R Paula	07/2009
9290	4*10^52667+19	52668	Robert Price	04/2016
9291	(10^52667+77)/3	52667	Robert Price	01/2017
9292	11434^12977+12977^11434	52664	Norbert Schneider	04/2016
9293	2^174941-1203	52663	Lelio R Paula	07/2009
9294	8501^13400-13400^8501	52655	Norbert Schneider	03/2018
9295	2^174910+12705	52654	Lelio R Paula	07/2012
9296	3^110338+74	52645	Lelio R Paula	10/2012
9297	5^75303+12	52635	Lelio R Paula	10/2012
9298	2^174836+255255	52631	Lelio R Paula	07/2009
9299	(66^28921+1)/67	52622	Paul Bourdelais	08/2017
9300	20^40443+9	52618	Lelio R Paula	01/2013
9301	(11*2^174788+1)/9	52617	Lelio R Paula	01/2012
9302	(11*2^174786-1)/703	52615	Lelio R Paula	01/2014
9303	11^50520-1290	52612	Enzo Doria	11/2012
9304	(10^52608-19)/9	52608	Robert Price	10/2017
9305	(9913*2^174736-1)/333	52603	Lelio R Paula	03/2015
9306	13145^10024+10024^13145	52594	Hans Havermann	05/2016
9307	5003^14217-150	52592	Enzo Doria	07/2012
9308	2^174698-4055	52590	Yves Minet	02/2018
9309	19^41123+10	52587	Lelio R Paula	01/2013
9310	2^174683+12909	52585	Lelio R Paula	01/2011
9311	2^174643+59	52573	Lelio R Paula	01/2011
9312	(1017*2^174640-1)/773	52572	Lelio R Paula	03/2015
9313	13529^7662+7662^13529	52552	Hans Havermann	06/2016
9314	121421#+188767	52548	Makoto Morimoto	02/2016
9315	20^40375-5923	52530	Enzo Doria	03/2013
9316	(67607*2^174503+1)/90948079	52528	Lelio R Paula	05/2014
9317	(-lucasV(1,2,349014)+2)/(7508731047043)	52521	Mike Oakes	03/2017
9318	2^174462+345	52519	Lelio R Paula	07/2009
9319	t(178863)	52509	Robert Price	10/2014
9320	2^174416+855	52505	Lelio R Paula	07/2009
9321	6^67467-103	52500	Lelio R Paula	10/2012
9322	(2^174533-1)/(193594572654550537*91917886778031629891960890057)	52494	Dario Alpern	06/2017
9323	2^174329-11265	52479	Enzo Doria	06/2014
9324	2^174314-1241	52474	Yves Minet	05/2009
9325	52^30577-51	52471	Norbert Schneider	08/2014
9326	9403^13206-13206^9403	52471	Norbert Schneider	12/2017
9327	15692^2205+2205^15692	52465	Hans Havermann	06/2016
9328	(2^174281-7)/628817029615	52453	Lelio R Paula	02/2012
9329	(2^174240+5)/3	52451	Lelio R Paula	02/2012
9330	(86*10^52450-221)/9	52451	Robert Price	06/2017
9331	(62*10^52448-197)/9	52449	Robert Price	10/2017
9332	(15*2^174221+1)/403	52445	Lelio R Paula	07/2012
9333	26313!2-32	52443	Robert Price	10/2015
9334	(3*2^174214-1)/3748729	52438	Lelio R Paula	01/2014
9335	2*3^109900-5	52436	Lelio R Paula	03/2014
9337	4159^14488-150	52432	Enzo Doria	07/2012
9336	(89*10^52431-71)/9	52432	Robert Price	11/2015
9338	2^174170-3941	52431	Yves Minet	04/2017
9339	(7*2^174171-1)/685	52429	Lelio R Paula	01/2014
9340	(260137^9679+1)/260138	52409	Faysal YAtim	03/2008
9341	2^174098+79	52409	Lelio R Paula	01/2011
9342	35^33940-2214	52406	Enzo Doria	03/2013
9343	15^44557+2	52404	Ray Chandler	07/2011
9344	2^174049-439	52394	Yves Minet	01/2012
9345	6^67329+115	52393	Lelio R Paula	10/2012
9347	2^174041+262145	52392	Lelio R Paula	07/2009
9346	141^24377+2	52392	Lelio R Paula	05/2013
9348	lucasU(285,1,21339)-lucasU(285,1,21338)	52382	Mike Oakes	05/2009
9349	2^174001-5955	52380	Lelio R Paula	07/2009
9350	lucasV(-1,2,347969)	52375	Mike Oakes	02/2017
9351	3^109764-140	52371	Lelio R Paula	10/2012
9353	2*3^109761+7	52370	Lelio R Paula	03/2014
9352	9863^13112-13112^9863	52370	Norbert Schneider	10/2017
9355	(145^24229+1)/146	52366	Richard Fischer	02/2018
9354	8094^13399-13399^8094	52366	Norbert Schneider	03/2018
9356	2^173944-112253	52363	Enzo Doria	06/2014
9358	2^173940+1111	52362	Lelio R Paula	01/2011
9357	(3126^14983-1)/3125	52362	Richard Fischer	03/2015
9359	15214^2763+2763^15214	52358	Hans Havermann	05/2016
9360	13200^9247+9247^13200	52352	Hans Havermann	05/2016
9361	(1017*2^173867-1)/7175	52339	Lelio R Paula	03/2015
9362	13732^6465+6465^13732	52327	Hans Havermann	05/2016
9363	(2^173867-1)/52536637502689	52326	Donovan Johnson	06/2005
9364	2^173811-684877	52323	Paul Bourdelais	11/2012
9365	2^173807-5955	52322	Lelio R Paula	06/2009
9366	2^173796-1044689	52318	Paul Bourdelais	11/2012
9367	10^52317+64497	52318	Patrick De Geest	12/2012
9368	10^52317+64743	52318	Patrick De Geest	12/2012
9370	10^52317-71	52317	Robert Price	05/2011
9369	10821^12968+12968^10821	52317	Norbert Schneider	04/2016
9371	(298*10^52308-7)/3	52310	Robert Price	06/2017
9372	(2^173778-3)/57959	52308	Lelio R Paula	02/2012
9373	10232^13043-13043^10232	52302	Norbert Schneider	08/2017
9374	2^173727+9	52298	Lelio R Paula	01/2011
9375	(14^45631+13^45631)/27	52298	Robert Price	04/2013
9376	37856!3+6561	52293	Robert Price	11/2015
9377	4*3^109596+5	52292	Lelio R Paula	03/2014
9378	15436^2441+2441^15436	52291	Hans Havermann	05/2016
9379	43^32005+24	52280	Robert Price	11/2013
9380	2^173650-165	52274	Lelio R Paula	02/2011
9381	4*10^52272+93	52273	Robert Price	01/2017
9382	19^40873+84	52267	Lelio R Paula	01/2013
9383	2^173621+4242429	52266	Jason Earls	09/2008
9384	9999^13064-13064^9999	52256	Norbert Schneider	09/2017
9385	numbpart(46909^2-1)	52247	Serge Batalov	04/2017
9386	14^45579-31	52240	Lelio R Paula	01/2013
9387	(10223*2^173518+1)/903	52236	Lelio R Paula	05/2014
9388	20^40147-6123	52233	Enzo Doria	03/2013
9389	4^86754-3^(86754+1)	52232	Robert Price	04/2016
9390	2^173477-3433	52222	Yves Minet	04/2009
9391	(22*10^52217-73)/3	52218	Robert Price	09/2017
9392	(25*2^173446+1)/61	52213	Lelio R Paula	07/2012
9393	3^109431-38	52212	Lelio R Paula	10/2012
9394	2^173424-3959	52206	Yves Minet	04/2017
9395	13^46861-72	52201	Lelio R Paula	01/2013
9396	2^173373-1363	52191	Yves Minet	03/2009
9397	11^50114-1740	52189	Enzo Doria	11/2012
9398	13735^6304+6304^13735	52188	Hans Havermann	05/2016
9399	11^50111-1110	52186	Enzo Doria	11/2012
9400	lucasU(46,1,31387)+lucasU(46,1,31386)	52181	Mike Oakes	04/2009
9401	20^40105-8583	52178	Enzo Doria	03/2013
9402	(10322^13001+2679^13001)/13001^2	52175	Lelio R Paula	08/2008
9403	2^173314-3941	52173	Yves Minet	04/2017
9404	2^173294+1155	52167	Lelio R Paula	07/2012
9406	(19*2^173301-1)/23489	52166	Lelio R Paula	01/2014
9405	15146^2781+2781^15146	52166	Hans Havermann	06/2016
9407	11^50088-32	52162	Lelio R Paula	01/2013
9408	3^109320+236	52159	Lelio R Paula	10/2012
9409	2^173246-28635	52153	Lelio R Paula	06/2009
9410	2*10^52147+11	52148	Robert Price	01/2015
9411	2^173208-112625	52141	Enzo Doria	06/2014
9412	(9179*2^173206-1)/2035	52141	Lelio R Paula	03/2015
9413	15^44333-76	52140	Lelio R Paula	01/2013
9414	2^173187-3189	52135	Yves Minet	10/2014
9415	2^173167+75579	52129	Enzo Doria	04/2016
9416	(2^173169+7)/92793	52125	Lelio R Paula	02/2012
9417	(25*10^52119+23)/3	52120	Robert Price	06/2017
9418	9*7^61671+4	52119	Lelio R Paula	09/2014
9420	2^173130-9221	52118	Lelio R Paula	07/2008
9419	(17*2^173129-1)/3	52118	Lelio R Paula	01/2014
9421	215^22342-216	52112	Karsten Bonath	04/2018
9422	2^173100-112559	52109	Enzo Doria	06/2014
9423	2^173091-112339	52106	Enzo Doria	06/2014
9424	11^50030+28	52101	Lelio R Paula	01/2013
9425	(59*10^52099+13)/9	52100	Robert Price	09/2015
9426	2^173064-1829	52098	Yves Minet	09/2012
9427	2^173062-1361	52097	Yves Minet	08/2012
9428	3^109190-70	52097	Lelio R Paula	10/2012
9429	2^173059+90195	52096	Lelio R Paula	07/2012
9430	2^173048-112625	52093	Enzo Doria	06/2014
9431	92^26524+91	52088	Norbert Schneider	04/2013
9432	41^32295-40	52085	Theodore Burton	02/2007
9433	2^173002+177	52079	Lelio R Paula	02/2011
9434	p(11334)#/2+8	52075	Robert Price	01/2017
9435	2^172965-112363	52068	Enzo Doria	06/2014
9436	9*2^172935+7	52060	Lelio R Paula	03/2014
9437	11^49978-8190	52047	Enzo Doria	02/2013
9438	10^52041+633	52042	Patrick De Geest	11/2012
9439	8494^13245-13245^8494	52042	Norbert Schneider	01/2018
9440	10^52041-93	52041	Robert Price	05/2011
9441	(21*2^172815-1)/869	52021	Lelio R Paula	01/2014
9442	(182*10^52018+1)/3	52020	Robert Price	02/2017
9443	4*6^66843-5	52015	Lelio R Paula	09/2014
9444	7732^13377-13377^7732	52014	Norbert Schneider	03/2018
9445	19^40670-54	52007	Lelio R Paula	01/2013
9446	2^172756-112883	52005	Enzo Doria	06/2014
9447	11832^12763-12763^11832	51985	Norbert Schneider	02/2017
9448	7^61511-36	51983	Lelio R Paula	10/2012
9449	10591^12914-12914^10591	51979	Norbert Schneider	05/2017
9450	2^172640-75	51970	Lelio R Paula	01/2011
9451	7750^13359-13359^7750	51958	Norbert Schneider	03/2018
9452	gcd(V(932265),5F(186453)(F(186453)-1)+1)	51953	Serge Batalov	04/2015
9453	12240^12709-12709^12240	51952	Norbert Schneider	01/2017
9454	t(173589)	51951	Robert Price	12/2014
9455	7^61469+34	51948	Lelio R Paula	10/2012
9456	9*2^172553-7	51945	Lelio R Paula	03/2014
9457	11542^12787+12787^11542	51945	Norbert Schneider	01/2016
9458	35^33640-7086	51943	Enzo Doria	03/2013
9459	(7*2^172534+1)/2479	51936	Lelio R Paula	07/2012
9460	(2^86243+43467)^2+(2^86243+43467)+41	51924	Makoto Morimoto	05/2016
9461	(2^86243+84085)^2+(2^86243+84085)+41	51924	Makoto Morimoto	05/2016
9462	((2^86243+75146)^2+(2^86243+75146)+41)/61	51922	Makoto Morimoto	05/2016
9463	((2^86243+8692)^2+(2^86243+8692)+41)/3011	51920	Makoto Morimoto	05/2016
9464	((2^86243+30085)^2+(2^86243+30085)+41)/41/199	51920	Makoto Morimoto	05/2016
9465	((2^86243+36540)^2+(2^86243+36540)+41)/43/647	51920	Makoto Morimoto	05/2016
9467	2^172470+7	51919	Lelio R Paula	01/2011
9466	((2^86243+76136)^2+(2^86243+76136)+41)/60509	51919	Makoto Morimoto	05/2016
9468	((2^86243+50999)^2+(2^86243+50999)+41)/2496869	51918	Makoto Morimoto	05/2016
9469	((2^86243+80760)^2+(2^86243+80760)+41)/930481	51918	Makoto Morimoto	05/2016
9470	((2^86243+26732)^2+(2^86243+26732)+41)/223/96517	51917	Makoto Morimoto	05/2016
9471	((2^86243+51479)^2+(2^86243+51479)+41)/1607/22027	51916	Makoto Morimoto	05/2016
9474	2^172455+15	51915	Lelio R Paula	01/2011
9472	((2^86243+27637)^2+(2^86243+27637)+41)/2693/518431	51915	Makoto Morimoto	05/2016
9473	((2^86243+82275)^2+(2^86243+82275)+41)/71/9309929	51915	Makoto Morimoto	05/2016
9475	((2^86243+57757)^2+(2^86243+57757)+41)/30871/622729	51914	Makoto Morimoto	05/2016
9476	((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/65293	51913	Makoto Morimoto	05/2016
9477	((2^86243+8693)^2+(2^86243+8693)+41)/494107/2933891	51912	Makoto Morimoto	05/2016
9478	((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/1472623	51911	Makoto Morimoto	05/2016
9479	((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/2171293	51911	Makoto Morimoto	05/2016
9480	((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/12566509	51909	Makoto Morimoto	05/2016
9481	5^74263+54	51908	Lelio R Paula	10/2012
9482	13804^5755+5755^13804	51904	Hans Havermann	05/2016
9483	7*2^172403-3	51900	Henri Lifchitz	06/2003
9484	t(196078)	51892	Robert Price	02/2014
9485	2*3^108759-7	51892	Lelio R Paula	03/2014
9486	(94*10^51889+11)/3	51891	Robert Price	02/2017
9487	(73*10^51889+17)/9	51890	Robert Price	10/2015
9488	35^33603-4026	51886	Enzo Doria	03/2013
9489	2^172350-107	51883	Lelio R Paula	02/2011
9490	14419^3960+3960^14419	51876	Hans Havermann	05/2016
9491	2^172325-113185	51875	Enzo Doria	07/2014
9492	10^51872+100683	51873	Patrick De Geest	06/2016
9493	10^51872-1000000001	51872	Robert Price	05/2016
9494	10^51872-100149	51872	Patrick De Geest	06/2016
9495	2147092^8192+63	51871	Jens K. Andersen	04/2009
9496	13^46564-24	51870	Lelio R Paula	01/2013
9497	10524^12893-12893^10524	51858	Norbert Schneider	05/2017
9498	13981^5110+5110^13981	51848	Hans Havermann	05/2016
9499	2^172228+76261	51846	Enzo Doria	04/2016
9500	11^49772-1260	51833	Enzo Doria	11/2012

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