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 ?
9501	2^184044-111269	55403	Enzo Doria	05/2014
9502	14051^8766+8766^14051	55401	Hans Havermann	07/2016
9503	98^27819+27819^98	55394	Serge Batalov	05/2014
9504	(178*10^55390-7)/9	55392	Robert Price	08/2017
9505	58046^9+9^58046	55390	Andrey Kulsha	02/2004
9506	7^65536+2*59232-2	55385	Jiahao He	07/2017
9507	2^183980+75241	55384	Enzo Doria	04/2016
9508	10^55372+37	55373	Robert Price	01/2011
9509	10^55372-49967	55372	Patrick De Geest	12/2012
9510	(13*10^55367+17)/3	55368	Robert Price	06/2015
9511	2*6^71150+7	55366	Lelio R Paula	09/2014
9512	19^43296-62	55365	Lelio R Paula	02/2013
9513	19^43295+10	55364	Lelio R Paula	02/2013
9514	(29*10^55362-11)/9	55363	Robert Price	04/2015
9515	(37*10^55359+53)/9	55360	Robert Price	05/2015
9516	19^43283+72	55349	Lelio R Paula	02/2013
9517	2^183800-65	55330	Lelio R Paula	03/2011
9518	21001^12801-110	55329	Enzo Doria	07/2012
9519	33^36433-32^36433	55325	Robert Price	04/2012
9520	(17*2^183729+1)/145	55308	Lelio R Paula	07/2012
9521	9932^13837-13837^9932	55307	Norbert Schneider	11/2018
9523	9^57952+8^(57952-1)	55301	Robert Price	03/2016
9522	14872^5229+5229^14872	55301	Hans Havermann	08/2016
9524	61^30972-2	55296	Lelio R Paula	08/2013
9525	2^183671-112537	55291	Enzo Doria	06/2014
9526	(2^183687+7)/497939745	55287	Lelio R Paula	02/2012
9527	3^115873+56	55286	Lelio R Paula	10/2012
9528	13^49629-84	55284	Lelio R Paula	01/2013
9529	2^183632-5	55279	Henri Lifchitz	08/2005
9530	13981^8988+8988^13981	55277	Hans Havermann	07/2016
9531	10688^13719-13719^10688	55273	Norbert Schneider	09/2018
9532	(5*2^183585+1)/13	55265	Lelio R Paula	07/2012
9533	2^183576+171	55262	Lelio R Paula	03/2011
9534	13^49604+82	55257	Lelio R Paula	01/2013
9535	(11*10^55254+1)/3	55255	Erik Branger	03/2014
9536	12609^13474-13474^12609	55253	Norbert Schneider	05/2018
9537	3^115802-26	55252	Lelio R Paula	10/2012
9538	2^183534-3645	55250	Lelio R Paula	01/2011
9539	(15*2^183533-1)/113	55249	Lelio R Paula	01/2014
9540	5^79032-13766	55241	Enzo Doria	02/2013
9541	8*3^115759-7	55232	Lelio R Paula	03/2014
9542	6^70974-137	55229	Lelio R Paula	10/2012
9543	2^183466+524287	55229	Paul Underwood	08/2018
9544	2^183446-113073	55223	Enzo Doria	07/2014
9545	2^183441+577294575	55222	Lelio R Paula	03/2013
9546	5^79000-6	55219	Lelio R Paula	10/2012
9547	2^183413-901	55213	Yves Minet	01/2012
9548	19^43168-50	55202	Lelio R Paula	02/2013
9549	2^183340+19683	55191	Lelio R Paula	02/2012
9550	6^70923+35	55189	Lelio R Paula	10/2012
9551	2^183317-4035	55184	Lelio R Paula	01/2011
9552	2^183284-15	55174	Lelio R Paula	03/2011
9553	2^183255+149	55166	Lelio R Paula	02/2011
9554	4*10^55165+87	55166	Robert Price	05/2016
9555	(3^115574+4)/63037	55139	Lelio R Paula	03/2012
9556	2^183165-112333	55139	Enzo Doria	06/2014
9557	(109^27061-1)/108	55133	Richard Fischer	09/2017
9558	2^183142+855	55132	Lelio R Paula	01/2011
9559	(49*10^55129+383)/9	55130	Robert Price	04/2017
9560	2^183019+255255	55095	Lelio R Paula	01/2011
9561	(10^55084-19)/9	55084	Robert Price	10/2017
9562	3*10^55077+7	55078	Erik Branger	11/2013
9563	(62*10^55075-71)/9	55076	Robert Price	09/2015
9564	27499!2-32	55070	Robert Price	10/2015
9565	15307^3958+3958^15307	55067	Hans Havermann	08/2016
9566	155^25137-154	55059	Norbert Schneider	12/2018
9567	70^29836-69	55051	Norbert Schneider	10/2012
9568	18^43854-83	55049	Lelio R Paula	02/2013
9569	7^65126+58	55038	Lelio R Paula	10/2012
9570	2^182827-1615	55037	Lelio R Paula	11/2009
9571	7*10^55030-9	55031	Dmitry Domanov	11/2010
9572	9027^13912-13912^9027	55030	Norbert Schneider	08/2018
9573	2^182768-4055	55019	Yves Minet	02/2018
9574	6^70702+23	55017	Lelio R Paula	10/2012
9575	(23*2^182753+1)/151	55014	Lelio R Paula	07/2012
9576	2^182743-1615	55012	Lelio R Paula	11/2009
9577	(24737*2^182736+1)/399	55011	Lelio R Paula	05/2014
9578	3^115280-9568	55003	Enzo Doria	02/2013
9579	2^182656-12849	54985	Enzo Doria	10/2012
9580	12791^13388-13388^12791	54984	Norbert Schneider	03/2018
9581	9*19^42995+16	54981	Curtis Bright	05/2015
9582	2^182627+28425	54977	Lelio R Paula	11/2009
9583	2^182597-113053	54968	Enzo Doria	07/2014
9584	(3^115213+2)/30906725	54964	Lelio R Paula	03/2012
9585	2^182581-1975	54963	Yves Minet	09/2012
9586	(2*10^54960-179)/3	54960	Robert Price	11/2017
9587	27449!!-16	54959	Robert Price	06/2015
9588	(22*10^54958-73)/3	54959	Robert Price	09/2017
9590	4^91283-3^91283	54958	Jean-Louis Charton	01/2004
9589	2^182565+107	54958	Lelio R Paula	11/2009
9591	2^182560+2053	54957	Lelio R Paula	12/2010
9592	126892#-p(126892)	54927	Henri Lifchitz	12/2018
9593	2^182451-182451	54924	Henri Lifchitz	10/2004
9594	2^182444+81	54922	Henri Lifchitz	10/2005
9595	7589^14154-14154^7589	54921	Norbert Schneider	01/2019
9596	2^182433+74105	54918	Enzo Doria	04/2016
9597	20^42206-5243	54912	Enzo Doria	03/2013
9598	2^182394+85	54907	Lelio R Paula	02/2011
9599	2^182374-112287	54901	Enzo Doria	06/2014
9600	(47^32833-33^32833)/14	54899	Serge Batalov	12/2016
9601	10188^13697-13697^10188	54899	Norbert Schneider	09/2018
9602	2^182363-113167	54897	Enzo Doria	07/2014
9603	2^182359-112221	54896	Enzo Doria	06/2014
9604	(F(1905)^139-F(1904)^139)/F(1903)	54893	Wayne Halsdorf	05/2010
9605	(17*2^182274+1)/1467	54869	Lelio R Paula	01/2012
9606	18^43698-5	54853	Lelio R Paula	02/2013
9607	2^182209-1893	54851	Yves Minet	09/2012
9608	2^182194-3443	54846	Yves Minet	12/2016
9609	15023^4468+4468^15023	54836	Hans Havermann	08/2016
9610	2^182135+90143	54829	Yves Minet	10/2010
9611	2^182119+74333	54824	Enzo Doria	04/2016
9612	14289^6860+6860^14289	54818	Hans Havermann	08/2016
9613	3^114892-114892^3	54818	Norbert Schneider	03/2017
9614	2^182070-47355	54809	Lelio R Paula	01/2011
9615	3^114869+76	54807	Lelio R Paula	10/2012
9616	8^60681-60681^8	54801	Norbert Schneider	12/2016
9617	1897^16710+16710^1897	54777	Serge Batalov	05/2014
9618	Phi(61868,59)	54776	Enzo Doria	04/2012
9619	113^26679+2	54775	Lelio R Paula	05/2013
9620	3^114789-74	54769	Lelio R Paula	10/2012
9621	15^46567+98	54768	Lelio R Paula	02/2013
9622	(2*10^54767-71)/3	54767	Robert Price	01/2017
9623	(298*10^54765-7)/3	54767	Robert Price	06/2017
9624	(21*2^181931-1)/169997	54763	Lelio R Paula	01/2014
9626	2^181913+29	54762	Henri Lifchitz	06/2005
9625	(31*10^54761-121)/9	54762	Robert Price	06/2016
9627	2^181887+189	54754	Lelio R Paula	02/2011
9628	2^181874+181874^2-1	54750	Robert Price	04/2014
9629	(2^181865+9)/7339	54743	Lelio R Paula	02/2012
9630	5^78314-92	54740	Lelio R Paula	10/2012
9631	(163*10^54727-1)/9	54729	Serge Batalov	12/2014
9632	15^46531+74	54725	Lelio R Paula	02/2013
9633	277^22400-348	54712	Enzo Doria	07/2012
9634	6^70302+101	54706	Lelio R Paula	10/2012
9635	3^114622-10408	54689	Enzo Doria	02/2013
9637	(23*2^181674+1)/489	54688	Lelio R Paula	01/2012
9636	2^181669-1551	54688	Yves Minet	08/2012
9638	(57352^11491-1)/57351	54676	Serge Batalov	04/2015
9639	(31*2^181629-1)/10734721	54671	Lelio R Paula	01/2014
9640	(F(1048)^251-F(1047)^251)/F(1046)	54668	Wayne Halsdorf	05/2010
9641	13^49073+46	54665	Lelio R Paula	01/2013
9642	(57042^11491-1)/57041	54649	Serge Batalov	04/2015
9644	20^42000+73	54644	Lelio R Paula	02/2013
9643	(67607*2^181517+1)/1655	54644	Lelio R Paula	05/2014
9645	33*10^54634+7	54636	Robert Price	07/2016
9646	20^41988+61	54628	Lelio R Paula	01/2013
9647	20^41988-8123	54628	Enzo Doria	03/2013
9648	2^181420+21181	54613	Yves Minet	03/2011
9649	9854^13675-13675^9854	54613	Norbert Schneider	08/2018
9650	(19*10^54608+161)/9	54609	Robert Price	07/2016
9651	19^42696-24	54598	Lelio R Paula	02/2013
9652	(44*10^54596-503)/9	54597	Robert Price	10/2017
9653	(74*10^54583+61)/9	54584	Robert Price	10/2015
9654	2^181316-94395	54582	Lelio R Paula	09/2011
9655	14751^5006+5006^14751	54572	Hans Havermann	08/2016
9656	14^47609+39	54567	Lelio R Paula	02/2013
9657	12696^13295-13295^12696	54559	Norbert Schneider	01/2018
9658	(2^124979+lucasV(2,-2,124979)+1)/3	54552	Paul Vanderveen	12/2017
9660	3^114327-74	54548	Lelio R Paula	10/2012
9659	(44*10^54547-161)/9	54548	Robert Price	11/2017
9661	gcd(V(995625),5F(199125)(F(199125)-1)+1)	54546	Serge Batalov	04/2015
9662	(17*10^54537-47)/3	54538	Robert Price	05/2017
9663	2^181155-1155*181155	54534	Henri Lifchitz	02/2005
9664	Phi(61672,83)	54533	Enzo Doria	05/2012
9665	(2*10^54527-197)/3	54527	Robert Price	11/2017
9666	9*2^181128+7	54526	Lelio R Paula	03/2014
9667	89*10^54518-7	54520	Robert Price	03/2017
9668	2^181090-113247	54514	Enzo Doria	07/2014
9669	14031^7670+7670^14031	54508	Hans Havermann	08/2016
9670	14210^6849+6849^14210	54505	Hans Havermann	08/2016
9671	2^181043-199	54500	Lelio R Paula	02/2011
9672	12^50499+5	54498	Lelio R Paula	01/2013
9673	12^50491+5	54489	Lelio R Paula	01/2013
9674	6^70016-145	54484	Lelio R Paula	10/2012
9675	11^52313-9600	54479	Enzo Doria	02/2013
9676	2^64459+3^64459+5^64459+7^64459	54475	Henri Lifchitz	08/2001
9677	2^180946-111041	54471	Enzo Doria	05/2014
9678	(64*10^54467+287)/9	54468	Robert Price	04/2016
9679	(32*10^54458+319)/9	54459	Robert Price	10/2017
9680	5^77907-2*3^77907	54455	Mike Oakes	11/2009
9681	20^41853-5623	54453	Enzo Doria	03/2013
9682	14^47506-75	54448	Lelio R Paula	02/2013
9683	(25*10^54443-67)/3	54444	Robert Price	11/2017
9684	2^180839-113437	54438	Enzo Doria	08/2014
9685	3^114085+28	54433	Lelio R Paula	10/2012
9686	Phi(141230,10)	54432	Ray Chandler	08/2009
9687	6^69946-55	54429	Lelio R Paula	10/2012
9688	p(11796)#/2-1024	54427	Robert Price	09/2017
9689	5*2^180796+3	54426	Lelio R Paula	03/2014
9690	(23*2^180782-1)/91	54421	Lelio R Paula	01/2014
9691	9*6^69928-7	54416	Lelio R Paula	09/2014
9692	92^27701-91^27701	54399	Robert Price	08/2015
9693	(2^180687-3)*6-7	54393	Gilbert Mozzo	04/2016
9694	(5*10^54388-11)/3	54389	Erik Branger	12/2013
9695	20^41799-3043	54382	Enzo Doria	03/2013
9696	13860^8387+8387^13860	54382	Hans Havermann	08/2016
9697	(F(19)^15017-F(18)^15017)/F(17)	54378	Wayne Halsdorf	05/2010
9698	7^64329-18	54365	Lelio R Paula	10/2012
9699	2^180551-967	54352	Yves Minet	01/2012
9700	9075^13732-13732^9075	54350	Norbert Schneider	09/2018
9701	15^46209-74	54347	Lelio R Paula	02/2013
9702	10^54345+29739	54346	Patrick De Geest	08/2013
9703	10^54345-141381	54345	Patrick De Geest	09/2013
9704	lucasU(2098,1,16360)-lucasU(2098,1,16359)	54342	Mike Oakes	05/2009
9705	177^24171-2	54336	Lelio R Paula	10/2017
9706	2^180496+15	54335	Lelio R Paula	02/2011
9707	1845^16636+16636^1845	54334	Serge Batalov	05/2014
9708	11^52169-70	54329	Lelio R Paula	01/2013
9709	2^180446-4031	54320	Yves Minet	02/2018
9710	13693^9262+9262^13693	54317	Hans Havermann	06/2016
9711	2^180429-113101	54315	Enzo Doria	07/2014
9712	2^180423-112051	54313	Enzo Doria	05/2014
9713	16112^2349+2349^16112	54312	Hans Havermann	06/2016
9714	(79^28621-1)/78	54311	Paul Bourdelais	08/2017
9715	(13^48751+4^48751)/17	54305	Robert Price	05/2013
9716	2^180370+12915	54297	Lelio R Paula	09/2012
9717	(10^54290+41)/3	54290	Robert Price	01/2017
9718	15108^3917+3917^15108	54283	Hans Havermann	06/2016
9719	2^180317-3019	54281	Yves Minet	10/2014
9720	2^180314+855	54280	Lelio R Paula	10/2009
9721	19^42425+94	54252	Lelio R Paula	02/2013
9722	2^180180-1005449	54240	Paul Bourdelais	11/2012
9723	2^180173-2773	54238	Yves Minet	07/2014
9724	13367^11418+11418^13367	54238	Hans Havermann	06/2016
9725	427^20614+20614^427	54224	Norbert Schneider	06/2016
9726	2^180124-87959	54223	Gary Barnes	08/2009
9727	2^180111-113101	54219	Enzo Doria	07/2014
9728	2^180102-4475	54217	Yves Minet	03/2019
9729	2^180101-114871	54216	Enzo Doria	05/2015
9730	(11*2^180099+1)/51617	54212	Lelio R Paula	07/2012
9732	2^180070+465	54207	Lelio R Paula	09/2012
9731	13683^9154+9154^13683	54207	Hans Havermann	06/2016
9733	8105225132^180009-95312^9531-1	54198	Jiong Sun	12/2003
9734	2^180014+613	54190	Jason Earls	04/2008
9735	2^180007+101	54188	Lelio R Paula	02/2011
9736	2^180001+41877	54186	Jim Fougeron	08/2002
9737	2^180000+130153	54186	Jim Fougeron	09/2002
9738	3^113565-74	54185	Lelio R Paula	10/2012
9739	50^31891-49	54182	Norbert Schneider	07/2014
9740	(5*2^179991-1)/11427	54180	Lelio R Paula	01/2014
9741	3^113548+26	54177	Lelio R Paula	10/2012
9742	(lucasV(1,2,360029)-2)/(3^3522251725981)	54177	Mike Oakes	04/2017
9743	181^23996-2	54176	Lelio R Paula	10/2017
9744	4159^14969-138	54173	Enzo Doria	07/2012
9746	2^179955+5775	54172	Lelio R Paula	10/2009
9745	2^179953-231313	54172	Enzo Doria	05/2014
9747	5^77485+6	54160	Lelio R Paula	10/2012
9748	18^43141+85	54154	Lelio R Paula	02/2013
9749	10^54149+187647	54150	Patrick De Geest	07/2017
9750	10^54149-800001	54149	Robert Price	06/2017

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PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)