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	(F(1905)^139-F(1904)^139)/F(1903)	54893	Wayne Halsdorf	05/2010
8502	(17*2^182274+1)/1467	54869	Lelio R Paula	01/2012
8503	18^43698-5	54853	Lelio R Paula	02/2013
8504	2^182209-1893	54851	Yves Minet	09/2012
8505	2^182194-3443	54846	Yves Minet	12/2016
8506	15023^4468+4468^15023	54836	Hans Havermann	08/2016
8507	2^182135+90143	54829	Yves Minet	10/2010
8508	2^182119+74333	54824	Enzo Doria	04/2016
8509	14289^6860+6860^14289	54818	Hans Havermann	08/2016
8510	3^114892-114892^3	54818	Norbert Schneider	03/2017
8511	2^182070-47355	54809	Lelio R Paula	01/2011
8512	3^114869+76	54807	Lelio R Paula	10/2012
8513	8^60681-60681^8	54801	Norbert Schneider	12/2016
8514	1897^16710+16710^1897	54777	Serge Batalov	05/2014
8515	Phi(61868,59)	54776	Enzo Doria	04/2012
8516	113^26679+2	54775	Lelio R Paula	05/2013
8517	3^114789-74	54769	Lelio R Paula	10/2012
8518	15^46567+98	54768	Lelio R Paula	02/2013
8519	(2*10^54767-71)/3	54767	Robert Price	01/2017
8520	(298*10^54765-7)/3	54767	Robert Price	06/2017
8521	(21*2^181931-1)/169997	54763	Lelio R Paula	01/2014
8523	2^181913+29	54762	Henri Lifchitz	06/2005
8522	(31*10^54761-121)/9	54762	Robert Price	06/2016
8524	2^181887+189	54754	Lelio R Paula	02/2011
8525	2^181874+181874^2-1	54750	Robert Price	04/2014
8526	(2^181865+9)/7339	54743	Lelio R Paula	02/2012
8527	5^78314-92	54740	Lelio R Paula	10/2012
8528	(163*10^54727-1)/9	54729	Serge Batalov	12/2014
8529	15^46531+74	54725	Lelio R Paula	02/2013
8530	277^22400-348	54712	Enzo Doria	07/2012
8531	6^70302+101	54706	Lelio R Paula	10/2012
8532	3^114622-10408	54689	Enzo Doria	02/2013
8534	(23*2^181674+1)/489	54688	Lelio R Paula	01/2012
8533	2^181669-1551	54688	Yves Minet	08/2012
8535	(57352^11491-1)/57351	54676	Serge Batalov	04/2015
8536	(31*2^181629-1)/10734721	54671	Lelio R Paula	01/2014
8537	(F(1048)^251-F(1047)^251)/F(1046)	54668	Wayne Halsdorf	05/2010
8538	13^49073+46	54665	Lelio R Paula	01/2013
8539	(57042^11491-1)/57041	54649	Serge Batalov	04/2015
8541	20^42000+73	54644	Lelio R Paula	02/2013
8540	(67607*2^181517+1)/1655	54644	Lelio R Paula	05/2014
8542	33*10^54634+7	54636	Robert Price	07/2016
8543	20^41988+61	54628	Lelio R Paula	01/2013
8544	20^41988-8123	54628	Enzo Doria	03/2013
8545	2^181420+21181	54613	Yves Minet	03/2011
8546	(19*10^54608+161)/9	54609	Robert Price	07/2016
8547	19^42696-24	54598	Lelio R Paula	02/2013
8548	(74*10^54583+61)/9	54584	Robert Price	10/2015
8549	2^181316-94395	54582	Lelio R Paula	09/2011
8550	14751^5006+5006^14751	54572	Hans Havermann	08/2016
8551	14^47609+39	54567	Lelio R Paula	02/2013
8552	3^114327-74	54548	Lelio R Paula	10/2012
8553	gcd(V(995625),5F(199125)(F(199125)-1)+1)	54546	Serge Batalov	04/2015
8554	(17*10^54537-47)/3	54538	Robert Price	05/2017
8555	2^181155-1155*181155	54534	Henri Lifchitz	02/2005
8556	Phi(61672,83)	54533	Enzo Doria	05/2012
8557	9*2^181128+7	54526	Lelio R Paula	03/2014
8558	89*10^54518-7	54520	Robert Price	03/2017
8559	2^181090-113247	54514	Enzo Doria	07/2014
8560	14031^7670+7670^14031	54508	Hans Havermann	08/2016
8561	14210^6849+6849^14210	54505	Hans Havermann	08/2016
8562	2^181043-199	54500	Lelio R Paula	02/2011
8563	12^50499+5	54498	Lelio R Paula	01/2013
8564	12^50491+5	54489	Lelio R Paula	01/2013
8565	6^70016-145	54484	Lelio R Paula	10/2012
8566	11^52313-9600	54479	Enzo Doria	02/2013
8567	2^64459+3^64459+5^64459+7^64459	54475	Henri Lifchitz	08/2001
8568	2^180946-111041	54471	Enzo Doria	05/2014
8569	(64*10^54467+287)/9	54468	Robert Price	04/2016
8570	5^77907-2*3^77907	54455	Mike Oakes	11/2009
8571	20^41853-5623	54453	Enzo Doria	03/2013
8572	14^47506-75	54448	Lelio R Paula	02/2013
8573	2^180839-113437	54438	Enzo Doria	08/2014
8574	3^114085+28	54433	Lelio R Paula	10/2012
8575	Phi(141230,10)	54432	Ray Chandler	08/2009
8576	6^69946-55	54429	Lelio R Paula	10/2012
8577	p(11796)#/2-1024	54427	Robert Price	09/2017
8578	5*2^180796+3	54426	Lelio R Paula	03/2014
8579	(23*2^180782-1)/91	54421	Lelio R Paula	01/2014
8580	9*6^69928-7	54416	Lelio R Paula	09/2014
8581	92^27701-91^27701	54399	Robert Price	08/2015
8582	(2^180687-3)*6-7	54393	Gilbert Mozzo	04/2016
8583	(5*10^54388-11)/3	54389	Erik Branger	12/2013
8584	20^41799-3043	54382	Enzo Doria	03/2013
8585	13860^8387+8387^13860	54382	Hans Havermann	08/2016
8586	(F(19)^15017-F(18)^15017)/F(17)	54378	Wayne Halsdorf	05/2010
8587	7^64329-18	54365	Lelio R Paula	10/2012
8588	2^180551-967	54352	Yves Minet	01/2012
8589	15^46209-74	54347	Lelio R Paula	02/2013
8590	10^54345+29739	54346	Patrick De Geest	08/2013
8591	10^54345-141381	54345	Patrick De Geest	09/2013
8592	lucasU(2098,1,16360)-lucasU(2098,1,16359)	54342	Mike Oakes	05/2009
8593	177^24171-2	54336	Lelio R Paula	10/2017
8594	2^180496+15	54335	Lelio R Paula	02/2011
8595	1845^16636+16636^1845	54334	Serge Batalov	05/2014
8596	11^52169-70	54329	Lelio R Paula	01/2013
8597	13693^9262+9262^13693	54317	Hans Havermann	06/2016
8598	2^180429-113101	54315	Enzo Doria	07/2014
8599	2^180423-112051	54313	Enzo Doria	05/2014
8600	16112^2349+2349^16112	54312	Hans Havermann	06/2016
8601	(79^28621-1)/78	54311	Paul Bourdelais	08/2017
8602	(13^48751+4^48751)/17	54305	Robert Price	05/2013
8603	2^180370+12915	54297	Lelio R Paula	09/2012
8604	(10^54290+41)/3	54290	Robert Price	01/2017
8605	15108^3917+3917^15108	54283	Hans Havermann	06/2016
8606	2^180317-3019	54281	Yves Minet	10/2014
8607	2^180314+855	54280	Lelio R Paula	10/2009
8608	19^42425+94	54252	Lelio R Paula	02/2013
8609	2^180180-1005449	54240	Paul Bourdelais	11/2012
8610	2^180173-2773	54238	Yves Minet	07/2014
8611	13367^11418+11418^13367	54238	Hans Havermann	06/2016
8612	427^20614+20614^427	54224	Norbert Schneider	06/2016
8613	2^180124-87959	54223	Gary Barnes	08/2009
8614	2^180111-113101	54219	Enzo Doria	07/2014
8615	2^180101-114871	54216	Enzo Doria	05/2015
8616	(11*2^180099+1)/51617	54212	Lelio R Paula	07/2012
8618	2^180070+465	54207	Lelio R Paula	09/2012
8617	13683^9154+9154^13683	54207	Hans Havermann	06/2016
8619	8105225132^180009-95312^9531-1	54198	Jiong Sun	12/2003
8620	2^180014+613	54190	Jason Earls	04/2008
8621	2^180007+101	54188	Lelio R Paula	02/2011
8622	2^180001+41877	54186	Jim Fougeron	08/2002
8623	2^180000+130153	54186	Jim Fougeron	09/2002
8624	3^113565-74	54185	Lelio R Paula	10/2012
8625	50^31891-49	54182	Norbert Schneider	07/2014
8626	(5*2^179991-1)/11427	54180	Lelio R Paula	01/2014
8627	3^113548+26	54177	Lelio R Paula	10/2012
8628	(lucasV(1,2,360029)-2)/(3^3522251725981)	54177	Mike Oakes	04/2017
8629	181^23996-2	54176	Lelio R Paula	10/2017
8630	4159^14969-138	54173	Enzo Doria	07/2012
8632	2^179955+5775	54172	Lelio R Paula	10/2009
8631	2^179953-231313	54172	Enzo Doria	05/2014
8633	5^77485+6	54160	Lelio R Paula	10/2012
8634	18^43141+85	54154	Lelio R Paula	02/2013
8635	10^54149+187647	54150	Patrick De Geest	07/2017
8638	3^113489-340	54149	Lelio R Paula	10/2012
8636	10^54149-800001	54149	Robert Price	06/2017
8637	10^54149-36501	54149	Patrick De Geest	07/2017
8639	7^64070+90	54146	Lelio R Paula	10/2012
8640	18^43131+71	54142	Lelio R Paula	02/2013
8641	2^179826-131	54134	Lelio R Paula	02/2011
8642	2^179815-112735	54130	Enzo Doria	06/2014
8643	2^179806+73849	54127	Enzo Doria	04/2016
8644	2^179790+33	54123	Donovan Johnson	02/2006
8645	14287^6138+6138^14287	54120	Hans Havermann	06/2016
8646	(17*10^54117+1)/9	54118	Serge Batalov	05/2010
8647	2^179763-189	54115	Lelio R Paula	02/2011
8648	(21181*2^179770+1)/3029105	54115	Lelio R Paula	05/2014
8649	1828^16589+16589^1828	54113	Serge Batalov	05/2014
8651	20^41588-5883	54108	Enzo Doria	03/2013
8650	50^31847-49	54108	Norbert Schneider	07/2014
8652	2^179733-6855	54106	Lelio R Paula	10/2009
8653	20^41584-5583	54103	Enzo Doria	03/2013
8654	10^54084+3*3^54084	54085	Mike Oakes	05/2010
8655	2^179613-1795	54069	Lelio R Paula	10/2009
8656	2^179589-1011523	54062	Paul Bourdelais	11/2012
8657	2^179574-2531	54058	Yves Minet	07/2014
8658	(41*10^54051-23)/9	54052	Robert Price	05/2015
8659	117^26131-116	54044	Norbert Schneider	10/2013
8660	(10^54038-31)/3	54038	Serge Batalov	12/2014
8661	11^51885-84	54033	Lelio R Paula	01/2013
8662	14990^4011+4011^14990	54013	Hans Havermann	07/2016
8663	(19*2^179414+1)/7	54010	Lelio R Paula	07/2012
8664	3^113182-10408	54002	Enzo Doria	02/2013
8665	35^34970-8786	53997	Enzo Doria	03/2013
8666	2^179371-1637587	53997	Enzo Doria	05/2015
8667	19^42225-92	53996	Lelio R Paula	01/2013
8668	(3^113188+7)/73917675784	53994	Lelio R Paula	03/2012
8669	7*3^113162+8	53993	Lelio R Paula	03/2014
8670	(10^53991+179)/9	53991	Serge Batalov	12/2014
8671	2^179350-2145	53990	Lelio R Paula	10/2009
8672	(-lucasV(1,2,358718)-2)/(51719)	53990	Mike Oakes	04/2017
8673	8^59782-6^59782-3^59782	53989	Mike Oakes	11/2009
8674	3*7^63861+8	53970	Lelio R Paula	09/2014
8675	2^179274+71389	53967	Enzo Doria	04/2016
8676	2^179259-58695	53963	Lelio R Paula	10/2009
8677	6^69345+61	53961	Lelio R Paula	10/2012
8678	(-lucasV(1,2,358635)+2)/(71793172321719602511716271)	53957	Mike Oakes	04/2017
8679	(40216^11719-1)/40215	53955	Serge Batalov	04/2015
8680	89*10^53951-9	53953	Robert Price	05/2017
8681	14^47067-3	53945	Lelio R Paula	01/2013
8682	p(11700)#/2-512	53937	Robert Price	07/2017
8683	(2^179168-5)/59	53934	Lelio R Paula	02/2012
8684	2^179128+8415	53923	Lelio R Paula	07/2012
8685	2^179120+2533	53921	Henri Lifchitz	09/2004
8686	(2^179126+78557)/4649321187	53913	Lelio R Paula	05/2012
8687	74^28842+73	53913	Norbert Schneider	11/2012
8688	1271^17368+17368^1271	53913	Serge Batalov	05/2014
8689	2^179079+53	53909	Lelio R Paula	02/2011
8690	17^43807+54	53903	Lelio R Paula	01/2013
8691	17^43807+30	53903	Lelio R Paula	01/2013
8692	3^112951-310	53892	Lelio R Paula	10/2012
8693	Phi(7,2957!)	53888	Robert Price	05/2015
8694	(10223*2^178975+1)/33985	53877	Lelio R Paula	05/2014
8695	2^178944-219209	53868	Enzo Doria	11/2012
8696	(10^53859+149)/3	53859	Serge Batalov	12/2014
8697	2^178910-191	53858	Lelio R Paula	02/2011
8698	16170^2141+2141^16170	53857	Hans Havermann	07/2016
8699	(5*10^53855-107)/3	53856	Robert Price	01/2017
8700	(72*10^53847-27)/99	53847	Patrick De Geest	08/2004
8701	2^178841-869688105	53837	Lelio R Paula	06/2012
8702	2*10^53834-27	53835	Robert Price	02/2017
8703	2^178821-1011523	53831	Paul Bourdelais	11/2012
8704	2^178819-15	53830	Lelio R Paula	02/2011
8705	(14450!-1)/225296581	53829	Donovan Johnson	04/2006
8706	2^178761-465	53813	Lelio R Paula	10/2009
8707	18900^703+703^18900	53808	Anatoly F. Selevich	02/2007
8708	13918^7343+7343^13918	53806	Hans Havermann	08/2016
8709	10^53804+31749	53805	Patrick De Geest	12/2012
8711	10^53804-71	53804	Robert Price	05/2011
8710	t(178994)	53804	Robert Price	03/2015
8712	(2^178693-lucasV(1,2,178693)+1)/2	53792	Mike Oakes	11/2016
8713	2^178671-113215	53786	Enzo Doria	07/2014
8714	15110^3621+3621^15110	53774	Hans Havermann	07/2016
8715	2^178611+95	53768	Lelio R Paula	02/2011
8716	2^178597+5711	53764	Lelio R Paula	10/2011
8717	2^178598+12915	53764	Lelio R Paula	07/2012
8718	(9179*2^178579-1)/303	53760	Lelio R Paula	03/2015
8719	5*7^63589+2	53740	Lelio R Paula	09/2014
8720	2^178516-112515	53739	Enzo Doria	06/2014
8721	20^41302-27	53736	Lelio R Paula	01/2013
8722	6^69054-39209	53735	Mike Oakes	12/2010
8723	13086^12769+12769^13086	53734	Hans Havermann	07/2016
8724	2^178455+76043	53721	Enzo Doria	04/2016
8725	(10^53718-7)/3	53718	Makoto Kamada	10/2004
8726	(67607*2^178426+1)/3	53716	Lelio R Paula	05/2014
8727	9*10^53707+11	53708	Robert Kinser	01/2017
8728	94601!8-2	53708	Robert Price	04/2017
8729	13214^11595+11595^13214	53706	Hans Havermann	07/2016
8730	Phi(134350,10)/537401/8011962251	53705	Maksym Voznyy	10/2011
8731	2^178367-379	53694	Yves Minet	03/2013
8732	(2^178364-5)/11	53692	Lelio R Paula	02/2012
8733	4339^14760-168	53688	Enzo Doria	06/2012
8734	12^49746-11	53685	Lelio R Paula	01/2013
8735	12950^13051-13051^12950	53670	Norbert Schneider	08/2017
8736	(9913*2^178266-1)/2247	53665	Lelio R Paula	03/2015
8737	13725^8128+8128^13725	53665	Hans Havermann	07/2016
8738	2^178250-113261	53659	Enzo Doria	07/2014
8739	2^178226+11715	53652	Lelio R Paula	10/2009
8740	35^34742-1976	53645	Enzo Doria	03/2013
8741	20^41228-563	53639	Enzo Doria	03/2013
8742	359^20992+20992^359	53637	Norbert Schneider	08/2014
8743	(27*2^178183-1)/29065	53636	Lelio R Paula	01/2014
8744	(3^112414+7)/37381696	53628	Lelio R Paula	03/2012
8745	17994^955+955^17994	53623	Anatoly F. Selevich	10/2006
8746	2^178117-1551	53619	Yves Minet	08/2012
8747	2^178099-11287	53614	Enzo Doria	06/2014
8748	(15*2^178080-1)/309071	53604	Lelio R Paula	01/2014
8749	5^76672-13766	53592	Enzo Doria	02/2013
8750	6^68868-137	53590	Lelio R Paula	10/2012

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Probable Primes Top 10000

(183432 PRPs in the top)