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 ?
8501	2^176255-667	53059	Yves Minet	01/2012
8502	36471*2^176221+8647	53053	Paul Vanderveen	04/2016
8503	(19*10^53049-1)/9	53050	Serge Batalov	03/2009
8504	9*2^176203-5	53044	Lelio R Paula	03/2014
8505	2^176205-94395	53043	Lelio R Paula	08/2011
8506	(19*2^176224-1)/217916913	53042	Lelio R Paula	01/2014
8507	17^43103+14	53037	Lelio R Paula	01/2013
8508	(31*2^176188-1)/3555	53036	Lelio R Paula	01/2014
8509	2^176177+60947	53035	David Broadhurst	05/2002
8510	(22*10^53033-7)/3	53034	Erik Branger	09/2014
8511	13810^6909+6909^13810	53023	Hans Havermann	06/2016
8513	2^176108+16095	53014	Lelio R Paula	10/2009
8512	2^176107+18915	53014	Lelio R Paula	07/2012
8514	3^111080-9628	52999	Enzo Doria	02/2013
8515	2^176047-1551	52996	Yves Minet	08/2012
8516	2^176042+73519	52994	Enzo Doria	04/2016
8517	lucasV(1715,1,2^14)/65537	52986	Mike Oakes	04/2009
8518	2^175984-112259	52977	Enzo Doria	06/2014
8519	11^50870+10	52976	Lelio R Paula	01/2013
8520	(11*10^52956+19)/3	52957	Robert Price	03/2016
8521	gcd(V(949965),5F(189993)(F(189993)+1)+1)	52941	Serge Batalov	04/2015
8522	(-lucasV(1,2,351735)+2)/(37263)	52938	Mike Oakes	03/2017
8524	(98*10^52931-89)/99	52931	Ray Chandler	11/2010
8523	13774^6963+6963^13774	52931	Hans Havermann	06/2016
8525	2^175812-1367	52925	Yves Minet	05/2013
8526	2^175801+1155*175801	52922	Henri Lifchitz	01/2005
8527	11^50801-9090	52904	Enzo Doria	02/2013
8528	43^32374+12	52882	Robert Price	11/2013
8529	2^175628+13	52870	Lelio R Paula	01/2011
8530	2^175615-1747	52866	Yves Minet	09/2012
8531	9*2^175586-7	52858	Lelio R Paula	03/2014
8532	12174^12937+12937^12174	52854	Norbert Schneider	04/2016
8533	(15*2^175565+1)/8359	52848	Lelio R Paula	07/2012
8534	(2^175631-1)/330463093135534238072561/92733169	52839	Robert Kinser	03/2017
8535	14256^5077+5077^14256	52828	Hans Havermann	06/2016
8536	2^175467+82875	52821	Lelio R Paula	07/2012
8537	(67607*2^175426+1)/3	52813	Lelio R Paula	05/2014
8538	13^47400-60	52801	Lelio R Paula	01/2013
8539	4*10^52792+63	52793	Robert Price	06/2016
8541	(78557*2^175360+1)/3087	52791	Lelio R Paula	06/2014
8540	18^42055-2929	52791	Enzo Doria	03/2013
8542	9*5^75521+2	52788	Lelio R Paula	09/2014
8543	6^67814+31	52770	Lelio R Paula	10/2012
8544	70^28600+69	52770	Norbert Schneider	10/2012
8545	14^46038+97	52766	Lelio R Paula	01/2013
8546	(61*10^52763-7)/9	52764	Serge Batalov	02/2009
8547	2*5^75474+9	52755	Lelio R Paula	09/2014
8548	10^52753+2826430609	52754	Robert Price	05/2015
8549	10^52753+183997	52754	Patrick De Geest	01/2016
8550	10^52753-50153	52753	Patrick De Geest	03/2016
8551	19846^455+455^19846	52751	Anatoly F. Selevich	02/2007
8552	2^175217+72977	52746	Enzo Doria	04/2016
8553	p(11466)#/2-256	52746	Robert Price	05/2017
8554	(4*10^52740+41)/9	52740	Robert Price	11/2014
8555	2^175189+5385	52738	Lelio R Paula	08/2009
8556	2^175160+9385	52729	Lelio R Paula	07/2008
8557	12356^12885+12885^12356	52724	Norbert Schneider	03/2016
8558	2^175137+11	52722	Lelio R Paula	01/2011
8559	65^29077-64^29077	52715	Robert Price	08/2013
8560	2*10^52713-87	52714	Robert Price	06/2016
8561	2^175106-465	52713	Lelio R Paula	08/2009
8562	2^175089-58695	52708	Lelio R Paula	08/2009
8563	2^175045+195	52694	Lelio R Paula	02/2011
8564	2^175025+149	52688	Lelio R Paula	02/2011
8565	(19^41201+1)/20	52685	Paul Bourdelais	03/2010
8566	2*12^48815-5^48815	52681	Mike Oakes	10/2010
8567	335^20862-20862^335	52678	Norbert Schneider	09/2015
8568	2^174983-7605	52676	Lelio R Paula	07/2009
8569	4*10^52667+19	52668	Robert Price	04/2016
8570	(10^52667+77)/3	52667	Robert Price	01/2017
8571	11434^12977+12977^11434	52664	Norbert Schneider	04/2016
8572	2^174941-1203	52663	Lelio R Paula	07/2009
8573	2^174910+12705	52654	Lelio R Paula	07/2012
8574	3^110338+74	52645	Lelio R Paula	10/2012
8575	5^75303+12	52635	Lelio R Paula	10/2012
8576	2^174836+255255	52631	Lelio R Paula	07/2009
8577	20^40443+9	52618	Lelio R Paula	01/2013
8578	(11*2^174788+1)/9	52617	Lelio R Paula	01/2012
8579	(11*2^174786-1)/703	52615	Lelio R Paula	01/2014
8580	11^50520-1290	52612	Enzo Doria	11/2012
8581	(9913*2^174736-1)/333	52603	Lelio R Paula	03/2015
8582	13145^10024+10024^13145	52594	Hans Havermann	05/2016
8583	5003^14217-150	52592	Enzo Doria	07/2012
8584	19^41123+10	52587	Lelio R Paula	01/2013
8585	2^174683+12909	52585	Lelio R Paula	01/2011
8586	2^174643+59	52573	Lelio R Paula	01/2011
8587	(1017*2^174640-1)/773	52572	Lelio R Paula	03/2015
8588	13529^7662+7662^13529	52552	Hans Havermann	06/2016
8589	121421#+188767	52548	Makoto Morimoto	02/2016
8590	20^40375-5923	52530	Enzo Doria	03/2013
8591	(67607*2^174503+1)/90948079	52528	Lelio R Paula	05/2014
8592	(-lucasV(1,2,349014)+2)/(7508731047043)	52521	Mike Oakes	03/2017
8593	2^174462+345	52519	Lelio R Paula	07/2009
8594	t(178863)	52509	Robert Price	10/2014
8595	2^174416+855	52505	Lelio R Paula	07/2009
8596	6^67467-103	52500	Lelio R Paula	10/2012
8597	2^174329-11265	52479	Enzo Doria	06/2014
8598	2^174314-1241	52474	Yves Minet	05/2009
8599	52^30577-51	52471	Norbert Schneider	08/2014
8600	15692^2205+2205^15692	52465	Hans Havermann	06/2016
8601	(2^174281-7)/628817029615	52453	Lelio R Paula	02/2012
8602	(2^174240+5)/3	52451	Lelio R Paula	02/2012
8603	(15*2^174221+1)/403	52445	Lelio R Paula	07/2012
8604	26313!2-32	52443	Robert Price	10/2015
8605	(3*2^174214-1)/3748729	52438	Lelio R Paula	01/2014
8606	2*3^109900-5	52436	Lelio R Paula	03/2014
8608	4159^14488-150	52432	Enzo Doria	07/2012
8607	(89*10^52431-71)/9	52432	Robert Price	11/2015
8609	2^174170-3941	52431	Yves Minet	04/2017
8610	(7*2^174171-1)/685	52429	Lelio R Paula	01/2014
8612	(260137^9679+1)/260138	52409	Faysal YAtim	03/2008
8611	2^174098+79	52409	Lelio R Paula	01/2011
8613	35^33940-2214	52406	Enzo Doria	03/2013
8614	15^44557+2	52404	Ray Chandler	07/2011
8615	2^174049-439	52394	Yves Minet	01/2012
8616	6^67329+115	52393	Lelio R Paula	10/2012
8618	2^174041+262145	52392	Lelio R Paula	07/2009
8617	141^24377+2	52392	Lelio R Paula	05/2013
8619	lucasU(285,1,21339)-lucasU(285,1,21338)	52382	Mike Oakes	05/2009
8620	2^174001-5955	52380	Lelio R Paula	07/2009
8621	lucasV(-1,2,347969)	52375	Mike Oakes	02/2017
8622	3^109764-140	52371	Lelio R Paula	10/2012
8623	2*3^109761+7	52370	Lelio R Paula	03/2014
8624	2^173944-112253	52363	Enzo Doria	06/2014
8626	2^173940+1111	52362	Lelio R Paula	01/2011
8625	(3126^14983-1)/3125	52362	Richard Fischer	03/2015
8627	15214^2763+2763^15214	52358	Hans Havermann	05/2016
8628	13200^9247+9247^13200	52352	Hans Havermann	05/2016
8629	(1017*2^173867-1)/7175	52339	Lelio R Paula	03/2015
8630	13732^6465+6465^13732	52327	Hans Havermann	05/2016
8631	(2^173867-1)/52536637502689	52326	Donovan Johnson	06/2005
8632	2^173811-684877	52323	Paul Bourdelais	11/2012
8633	2^173807-5955	52322	Lelio R Paula	06/2009
8634	2^173796-1044689	52318	Paul Bourdelais	11/2012
8635	10^52317+64497	52318	Patrick De Geest	12/2012
8636	10^52317+64743	52318	Patrick De Geest	12/2012
8638	10^52317-71	52317	Robert Price	05/2011
8637	10821^12968+12968^10821	52317	Norbert Schneider	04/2016
8639	(2^173778-3)/57959	52308	Lelio R Paula	02/2012
8641	2^173727+9	52298	Lelio R Paula	01/2011
8640	(14^45631+13^45631)/27	52298	Robert Price	04/2013
8642	37856!3+6561	52293	Robert Price	11/2015
8643	4*3^109596+5	52292	Lelio R Paula	03/2014
8644	15436^2441+2441^15436	52291	Hans Havermann	05/2016
8645	43^32005+24	52280	Robert Price	11/2013
8646	2^173650-165	52274	Lelio R Paula	02/2011
8647	4*10^52272+93	52273	Robert Price	01/2017
8648	19^40873+84	52267	Lelio R Paula	01/2013
8649	2^173621+4242429	52266	Jason Earls	09/2008
8650	numbpart(46909^2-1)	52247	Serge Batalov	04/2017
8651	14^45579-31	52240	Lelio R Paula	01/2013
8652	(10223*2^173518+1)/903	52236	Lelio R Paula	05/2014
8653	20^40147-6123	52233	Enzo Doria	03/2013
8654	4^86754-3^(86754+1)	52232	Robert Price	04/2016
8655	2^173477-3433	52222	Yves Minet	04/2009
8656	(25*2^173446+1)/61	52213	Lelio R Paula	07/2012
8657	3^109431-38	52212	Lelio R Paula	10/2012
8658	2^173424-3959	52206	Yves Minet	04/2017
8659	13^46861-72	52201	Lelio R Paula	01/2013
8660	2^173373-1363	52191	Yves Minet	03/2009
8661	11^50114-1740	52189	Enzo Doria	11/2012
8662	13735^6304+6304^13735	52188	Hans Havermann	05/2016
8663	11^50111-1110	52186	Enzo Doria	11/2012
8664	lucasU(46,1,31387)+lucasU(46,1,31386)	52181	Mike Oakes	04/2009
8665	20^40105-8583	52178	Enzo Doria	03/2013
8666	(10322^13001+2679^13001)/13001^2	52175	Lelio R Paula	08/2008
8667	2^173314-3941	52173	Yves Minet	04/2017
8668	2^173294+1155	52167	Lelio R Paula	07/2012
8669	(19*2^173301-1)/23489	52166	Lelio R Paula	01/2014
8670	15146^2781+2781^15146	52166	Hans Havermann	06/2016
8671	11^50088-32	52162	Lelio R Paula	01/2013
8672	3^109320+236	52159	Lelio R Paula	10/2012
8673	2^173246-28635	52153	Lelio R Paula	06/2009
8674	2*10^52147+11	52148	Robert Price	01/2015
8675	2^173208-112625	52141	Enzo Doria	06/2014
8676	(9179*2^173206-1)/2035	52141	Lelio R Paula	03/2015
8677	15^44333-76	52140	Lelio R Paula	01/2013
8678	2^173187-3189	52135	Yves Minet	10/2014
8679	2^173167+75579	52129	Enzo Doria	04/2016
8680	(2^173169+7)/92793	52125	Lelio R Paula	02/2012
8681	9*7^61671+4	52119	Lelio R Paula	09/2014
8683	2^173130-9221	52118	Lelio R Paula	07/2008
8682	(17*2^173129-1)/3	52118	Lelio R Paula	01/2014
8684	2^173100-112559	52109	Enzo Doria	06/2014
8685	2^173091-112339	52106	Enzo Doria	06/2014
8686	11^50030+28	52101	Lelio R Paula	01/2013
8687	(59*10^52099+13)/9	52100	Robert Price	09/2015
8688	2^173064-1829	52098	Yves Minet	09/2012
8689	2^173062-1361	52097	Yves Minet	08/2012
8690	3^109190-70	52097	Lelio R Paula	10/2012
8691	2^173059+90195	52096	Lelio R Paula	07/2012
8692	2^173048-112625	52093	Enzo Doria	06/2014
8693	92^26524+91	52088	Norbert Schneider	04/2013
8694	41^32295-40	52085	Theodore Burton	02/2007
8695	2^173002+177	52079	Lelio R Paula	02/2011
8696	p(11334)#/2+8	52075	Robert Price	01/2017
8697	2^172965-112363	52068	Enzo Doria	06/2014
8698	9*2^172935+7	52060	Lelio R Paula	03/2014
8699	11^49978-8190	52047	Enzo Doria	02/2013
8700	10^52041+633	52042	Patrick De Geest	11/2012
8701	10^52041-93	52041	Robert Price	05/2011
8702	(21*2^172815-1)/869	52021	Lelio R Paula	01/2014
8703	(182*10^52018+1)/3	52020	Robert Price	02/2017
8704	4*6^66843-5	52015	Lelio R Paula	09/2014
8705	19^40670-54	52007	Lelio R Paula	01/2013
8706	2^172756-112883	52005	Enzo Doria	06/2014
8707	11832^12763-12763^11832	51985	Norbert Schneider	02/2017
8708	7^61511-36	51983	Lelio R Paula	10/2012
8709	2^172640-75	51970	Lelio R Paula	01/2011
8710	gcd(V(932265),5F(186453)(F(186453)-1)+1)	51953	Serge Batalov	04/2015
8711	12240^12709-12709^12240	51952	Norbert Schneider	01/2017
8712	t(173589)	51951	Robert Price	12/2014
8713	7^61469+34	51948	Lelio R Paula	10/2012
8714	9*2^172553-7	51945	Lelio R Paula	03/2014
8715	11542^12787+12787^11542	51945	Norbert Schneider	01/2016
8716	35^33640-7086	51943	Enzo Doria	03/2013
8717	(7*2^172534+1)/2479	51936	Lelio R Paula	07/2012
8718	(2^86243+43467)^2+(2^86243+43467)+41	51924	Makoto Morimoto	05/2016
8719	(2^86243+84085)^2+(2^86243+84085)+41	51924	Makoto Morimoto	05/2016
8720	((2^86243+75146)^2+(2^86243+75146)+41)/61	51922	Makoto Morimoto	05/2016
8721	((2^86243+8692)^2+(2^86243+8692)+41)/3011	51920	Makoto Morimoto	05/2016
8722	((2^86243+30085)^2+(2^86243+30085)+41)/41/199	51920	Makoto Morimoto	05/2016
8723	((2^86243+36540)^2+(2^86243+36540)+41)/43/647	51920	Makoto Morimoto	05/2016
8725	2^172470+7	51919	Lelio R Paula	01/2011
8724	((2^86243+76136)^2+(2^86243+76136)+41)/60509	51919	Makoto Morimoto	05/2016
8726	((2^86243+50999)^2+(2^86243+50999)+41)/2496869	51918	Makoto Morimoto	05/2016
8727	((2^86243+80760)^2+(2^86243+80760)+41)/930481	51918	Makoto Morimoto	05/2016
8728	((2^86243+26732)^2+(2^86243+26732)+41)/223/96517	51917	Makoto Morimoto	05/2016
8729	((2^86243+51479)^2+(2^86243+51479)+41)/1607/22027	51916	Makoto Morimoto	05/2016
8732	2^172455+15	51915	Lelio R Paula	01/2011
8730	((2^86243+27637)^2+(2^86243+27637)+41)/2693/518431	51915	Makoto Morimoto	05/2016
8731	((2^86243+82275)^2+(2^86243+82275)+41)/71/9309929	51915	Makoto Morimoto	05/2016
8733	((2^86243+57757)^2+(2^86243+57757)+41)/30871/622729	51914	Makoto Morimoto	05/2016
8734	((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/65293	51913	Makoto Morimoto	05/2016
8735	((2^86243+8693)^2+(2^86243+8693)+41)/494107/2933891	51912	Makoto Morimoto	05/2016
8736	((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/1472623	51911	Makoto Morimoto	05/2016
8737	((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/2171293	51911	Makoto Morimoto	05/2016
8738	((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/12566509	51909	Makoto Morimoto	05/2016
8739	5^74263+54	51908	Lelio R Paula	10/2012
8740	13804^5755+5755^13804	51904	Hans Havermann	05/2016
8741	7*2^172403-3	51900	Henri Lifchitz	06/2003
8742	t(196078)	51892	Robert Price	02/2014
8743	2*3^108759-7	51892	Lelio R Paula	03/2014
8744	(94*10^51889+11)/3	51891	Robert Price	02/2017
8745	(73*10^51889+17)/9	51890	Robert Price	10/2015
8746	35^33603-4026	51886	Enzo Doria	03/2013
8747	2^172350-107	51883	Lelio R Paula	02/2011
8748	14419^3960+3960^14419	51876	Hans Havermann	05/2016
8749	2^172325-113185	51875	Enzo Doria	07/2014
8750	10^51872+100683	51873	Patrick De Geest	06/2016

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