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	(7^69247-4^69247)/3	58521	Robert Price	06/2012
9502	2^194358-1167	58508	Lelio R Paula	05/2011
9503	(2^194366+7)/1373	58507	Lelio R Paula	02/2012
9504	15091^7518+7518^15091	58495	Hans Havermann	04/2019
9505	15852^4895+4895^15852	58490	Hans Havermann	04/2019
9506	(493*10^58486-7)/9	58488	Robert Price	07/2016
9507	3^122579-340	58486	Lelio R Paula	10/2012
9508	(11*10^58458-149)/3	58459	Robert Price	01/2017
9509	(47*10^58456+133)/9	58457	Robert Price	04/2017
9510	2^194186+85	58456	Lelio R Paula	04/2011
9511	3^122506-2^(122506-1)	58451	Robert Price	01/2016
9512	(74^31267-1)/73	58444	Paul Bourdelais	08/2017
9513	177^25998-2	58443	Lelio R Paula	10/2017
9514	15^49690-26	58440	Lelio R Paula	03/2013
9515	10^58437+110721	58438	Patrick De Geest	12/2012
9516	10^58437-11	58437	Robert Price	05/2011
9517	2^194095+69	58429	Lelio R Paula	04/2011
9518	(29*10^58417-77)/3	58418	Robert Price	01/2017
9519	2^194034+177	58411	Lelio R Paula	04/2011
9520	789^20158+20158^789	58400	Norbert Schneider	06/2016
9521	14^50949+75	58395	Lelio R Paula	03/2013
9522	2^193974-114761	58392	Enzo Doria	05/2015
9523	2^193965+5	58390	Henri Lifchitz	12/2002
9524	(5*10^58384-29)/3	58385	Robert Price	02/2017
9525	3^122360+80	58381	Lelio R Paula	10/2012
9526	10103^14577-114	58373	Enzo Doria	07/2012
9527	(22699*2^193883+1)/21	58368	Lelio R Paula	06/2014
9528	(31*2^193886+1)/140765	58362	Lelio R Paula	07/2012
9529	11^56041-1560	58361	Enzo Doria	11/2012
9530	(2^193881+9)/17699	58360	Lelio R Paula	02/2012
9531	3^122313+58	58359	Lelio R Paula	10/2012
9532	6^74996-119	58359	Lelio R Paula	10/2012
9533	(11*2^193859+1)/13	58358	Lelio R Paula	07/2012
9534	2^193861-112255	58358	Enzo Doria	06/2014
9535	(22699*2^193854+1)/4927	58357	Lelio R Paula	06/2014
9536	18^46487+37	58354	Lelio R Paula	03/2013
9537	17^47419+54	58347	Lelio R Paula	03/2013
9538	2^193812-4799	58344	Yves Minet	05/2019
9539	15486^5851+5851^15486	58340	Hans Havermann	04/2019
9540	(31*2^193791+1)/3	58338	Lelio R Paula	02/2012
9541	(27*2^193805-1)/982249	58337	Lelio R Paula	01/2014
9542	14088^13825+13825^14088	58334	Hans Havermann	04/2019
9543	144^27025-143	58330	Norbert Schneider	11/2018
9544	11900^14311-14311^11900	58326	Norbert Schneider	05/2019
9545	15297^6494+6494^15297	58321	Hans Havermann	04/2019
9546	16293^3794+3794^16293	58315	Hans Havermann	04/2019
9547	3^122219-2^122219	58314	Mike Oakes	09/2003
9548	(199*10^58306+11)/3	58308	Robert Price	05/2017
9549	2^193674-18825	58302	Lelio R Paula	05/2011
9550	14897^8172+8172^14897	58282	Hans Havermann	04/2019
9551	5*10^58275+3	58276	Dmitry Domanov	11/2010
9552	2^193578-112913	58273	Enzo Doria	06/2014
9554	2^193541+1299	58262	Lelio R Paula	05/2011
9553	8361^14854-14854^8361	58262	Norbert Schneider	07/2019
9555	10^58250+93	58251	Robert Price	01/2011
9556	10^58250-175607	58250	Patrick De Geest	12/2012
9557	(107^28703+1)/108	58248	Richard Fischer	05/2018
9558	2^193492+8415	58247	Lelio R Paula	10/2012
9559	2^193444+157	58233	Lelio R Paula	04/2011
9560	Phi(28754,28754)	58231	Henri Lifchitz	08/2013
9561	2^193430-111881	58229	Enzo Doria	05/2014
9562	10^58225+124579	58226	Patrick De Geest	12/2012
9563	10^58225-93	58225	Robert Price	05/2011
9564	2^193375-295	58212	Yves Minet	05/2013
9565	14018^14037-14037^14018	58208	Norbert Schneider	10/2018
9566	2^193345+77267	58203	Enzo Doria	05/2016
9567	21^44017-20^44017	58201	Robert Price	05/2012
9568	(17*2^193329-1)/9	58199	Lelio R Paula	01/2014
9569	17^47291+20	58190	Lelio R Paula	03/2013
9570	p(12528)#/2-128	58170	Robert Price	05/2017
9571	2^193214-135	58164	Lelio R Paula	04/2011
9572	19^45483-80	58162	Lelio R Paula	03/2013
9573	(4*10^58155+83)/3	58156	Robert Price	01/2017
9575	14^50739-13	58154	Lelio R Paula	03/2013
9574	(1017*2^193184-1)/4823	58154	Lelio R Paula	04/2015
9576	(2*10^58151+457)/9	58151	Robert Price	01/2017
9577	(9179*2^193183-1)/3999267879	58149	Lelio R Paula	04/2015
9578	14555^9874+9874^14555	58140	Hans Havermann	05/2019
9579	(19*2^193114-1)/1186755	58129	Lelio R Paula	01/2014
9581	2^193091-1237	58127	Yves Minet	08/2012
9580	9*7^68780-2	58127	Lelio R Paula	09/2014
9582	2473^17130+17130^2473	58126	Norbert Schneider	10/2018
9583	2^193083-869688105	58124	Lelio R Paula	10/2012
9584	2^193058-45	58117	Lelio R Paula	04/2011
9585	(14016^14016+14017^14017)/(23710319913)	58115	David Broadhurst	09/2009
9586	11^55795-42	58105	Lelio R Paula	03/2013
9587	3^121779-16	58104	Lelio R Paula	10/2012
9588	(13*10^58103+191)/3	58104	Robert Price	08/2017
9589	15865^4594+4594^15865	58101	Hans Havermann	05/2019
9590	2^192986+195	58095	Lelio R Paula	04/2011
9591	7^68740+2*3^68740	58093	Mike Oakes	07/2010
9592	(85*10^58091-1)/3	58093	Robert Price	07/2017
9593	(404*10^58087-53)/9	58089	Robert Price	11/2017
9594	12^53821+11	58083	Lelio R Paula	02/2013
9595	119^27979-118	58072	Norbert Schneider	10/2013
9596	14380^10899+10899^14380	58058	Hans Havermann	04/2019
9597	(10223*2^192828+1)/243	58049	Lelio R Paula	05/2014
9598	2^192808-1127	58041	Yves Minet	05/2013
9599	(27*2^192803+1)/9827	58037	Lelio R Paula	07/2012
9601	(2^192781+lucasV(1,2,192781)+1)/4	58033	Mike Oakes	11/2016
9600	3*10^58032-23	58033	Robert Price	11/2017
9602	2^192678+72943	58002	Enzo Doria	04/2016
9603	(13*10^57997-37)/3	57998	Robert Price	08/2017
9604	2^192657-3189	57996	Yves Minet	10/2014
9605	6^74525-149	57992	Lelio R Paula	10/2012
9606	42^35723-41	57988	Norbert Schneider	06/2014
9607	(29*2^192625-1)/183	57986	Lelio R Paula	01/2014
9608	(3^121520-8)/3847	57977	Lelio R Paula	03/2012
9609	(2^192596-5)/139	57976	Lelio R Paula	02/2012
9610	10^57975+67833	57976	Patrick De Geest	09/2013
9611	10^57975-47693	57975	Patrick De Geest	09/2013
9612	(F(7707)^37-F(7706)^37)/F(7705)	57972	Wayne Halsdorf	03/2012
9613	14025^13592+13592^14025	57970	Hans Havermann	04/2019
9614	(29*10^57967+673)/9	57968	Robert Price	10/2017
9615	(3^121492-5)/4	57966	Lelio R Paula	03/2012
9616	2^192549+35	57964	Lelio R Paula	04/2011
9617	28799!2+2	57962	Robert Price	10/2012
9618	(7*2^192534-1)/1347	57957	Lelio R Paula	01/2014
9619	11108^14323-14323^11108	57946	Norbert Schneider	05/2019
9620	7001^15069-100	57943	Enzo Doria	07/2012
9621	L(277273)/11090921	57940	Donovan Johnson	11/2005
9622	(2^192469-1017)/35	57938	Lelio R Paula	02/2012
9623	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
9624	12752^14111-14111^12752	57934	Norbert Schneider	01/2019
9625	2^192443+1385	57932	Lelio R Paula	05/2011
9626	132^27317-131	57928	Norbert Schneider	03/2015
9627	41522!3-59049	57912	Robert Price	12/2015
9628	(3*2^192380-1)/169	57911	Lelio R Paula	01/2014
9629	2^192339-2515	57900	Yves Minet	07/2014
9630	2^192303+7695	57889	Lelio R Paula	10/2012
9631	2^192273-5955	57880	Lelio R Paula	05/2011
9632	2^192257+16095	57876	Lelio R Paula	05/2011
9633	109^28401-2	57865	Lelio R Paula	10/2017
9634	2^192218-111861	57864	Enzo Doria	05/2014
9635	2^192214-3941	57863	Yves Minet	04/2017
9636	(2^192212+3)/259	57860	Lelio R Paula	02/2012
9637	(3^121270+8)/155939753	57853	Lelio R Paula	03/2012
9638	80^30393-79	57841	Norbert Schneider	03/2015
9639	20^44455-3123	57838	Enzo Doria	03/2013
9640	2^192122-195	57835	Lelio R Paula	04/2011
9641	(29*10^57834+91)/3	57835	Robert Price	03/2016
9642	8*6^74306+5	57823	Lelio R Paula	09/2014
9643	(39^36341-1)/38	57820	Robert Price	04/2012
9644	2^192037-111805	57809	Enzo Doria	05/2014
9645	2^192023-192023^2	57805	Henri Lifchitz	05/2005
9646	21^43717+2	57804	Ray Chandler	08/2011
9647	8*5^82687+7	57797	Lelio R Paula	09/2014
9648	16459^3246+3246^16459	57794	Hans Havermann	04/2019
9649	5^82680-24	57791	Lelio R Paula	10/2012
9651	(2^191915+47)/95	57771	Lelio R Paula	02/2012
9650	12019^14160-14160^12019	57771	Norbert Schneider	02/2019
9652	(74*10^57763+133)/9	57764	Robert Price	10/2017
9653	6^74227-95	57760	Lelio R Paula	10/2012
9654	2^191861+29835	57756	Lelio R Paula	10/2012
9656	1908^17605+17605^1908	57755	Serge Batalov	05/2014
9655	5*10^57754+59	57755	Robert Price	09/2016
9657	10418^14373-14373^10418	57748	Norbert Schneider	06/2019
9658	(5*2^191821-1)/8924067	57738	Lelio R Paula	01/2014
9659	14100^12431+12431^14100	57733	Hans Havermann	04/2019
9660	38^63917+5^63917-34^63917+3*2^63917	57724	Mike Oakes	11/2010
9661	41399!3-6561	57723	Robert Price	11/2015
9662	(44*10^57721-233)/9	57722	Robert Price	10/2017
9663	2^191745+17	57721	Lelio R Paula	04/2011
9664	2^191730-761	57717	Yves Minet	01/2012
9665	(2^191733-3)/2251	57715	Lelio R Paula	02/2012
9666	2^191698-111	57707	Lelio R Paula	04/2011
9667	(13*10^57691+23)/9	57692	Robert Price	02/2015
9668	2^191640-4475	57690	Yves Minet	03/2019
9669	20^44340-5423	57688	Enzo Doria	03/2013
9670	(27*2^191629+1)/125	57686	Lelio R Paula	07/2012
9671	410^57684+37^57684	57685	Mike Oakes	11/2010
9673	2*3^120898+5	57684	Lelio R Paula	04/2014
9672	10650^14323-14323^10650	57684	Norbert Schneider	05/2019
9674	(6883*2^191610-1)/7347	57681	Lelio R Paula	04/2015
9675	6^74117-49	57675	Lelio R Paula	10/2012
9676	2^191586-113201	57674	Enzo Doria	07/2014
9677	2^191580+193	57672	Lelio R Paula	04/2011
9678	(103*29^39433+10401)/4	57669	Curtis Bright	05/2015
9679	2^191560+255255	57666	Lelio R Paula	05/2011
9680	2^191515-85	57652	Lelio R Paula	04/2011
9681	2^191502-1127	57648	Yves Minet	05/2013
9682	2*5^82473-3^82473	57647	Mike Oakes	08/2010
9683	(13*10^57634-61)/3	57635	Robert Price	08/2017
9684	10635^14312-14312^10635	57631	Norbert Schneider	05/2019
9685	85^29868-29868^85	57628	Norbert Schneider	11/2017
9686	2^191430+103	57627	Lelio R Paula	04/2011
9687	3*2^191408+5	57621	Lelio R Paula	03/2014
9688	2^191382-1858931	57612	Enzo Doria	04/2016
9689	6*7^68163+5	57606	Lelio R Paula	09/2014
9690	91^29403-2	57602	Lelio R Paula	08/2013
9691	11^55308-7950	57598	Enzo Doria	02/2013
9692	2^191329+65	57596	Lelio R Paula	04/2011
9693	11^55302-240	57592	Enzo Doria	07/2012
9694	2^191299-1031467	57587	Paul Bourdelais	11/2012
9695	2^191295-111991	57586	Enzo Doria	05/2014
9696	10824^14273-14273^10824	57583	Norbert Schneider	04/2019
9697	2^191279-1297	57581	Yves Minet	08/2012
9698	14827^7630+7630^14827	57567	Hans Havermann	04/2019
9699	10047^14384-14384^10047	57566	Norbert Schneider	06/2019
9700	3*6^73961+5	57554	Lelio R Paula	09/2014
9701	16177^3610+3610^16177	57550	Hans Havermann	04/2019
9702	(3^120623+5)/52144	57548	Lelio R Paula	04/2012
9703	(17*10^57543-29)/3	57544	Robert Price	09/2017
9704	42^35445-41	57537	Norbert Schneider	06/2014
9705	(71^31079-1)/70	57534	Paul Bourdelais	08/2017
9706	2^191069-723403	57518	Paul Bourdelais	11/2012
9707	4*10^57506-3	57507	Serge Batalov	11/2010
9708	10^57501+67359	57502	Patrick De Geest	06/2016
9709	10^57501-1000000001	57501	Robert Price	05/2016
9710	10^57501-249861	57501	Patrick De Geest	06/2016
9711	10090^14361-14361^10090	57500	Norbert Schneider	06/2019
9712	(9^60251+4^60251)/13	57493	Robert Price	02/2013
9713	20^44184-6003	57485	Enzo Doria	03/2013
9714	2^190948+12705	57482	Lelio R Paula	10/2012
9715	2^190945+29	57481	Henri Lifchitz	06/2005
9716	2^190922-401	57474	Yves Minet	01/2012
9717	15^48860+46	57464	Lelio R Paula	02/2013
9718	3^120434+20	57462	Lelio R Paula	10/2012
9719	7^67964-38	57437	Lelio R Paula	10/2012
9720	2^190799-113065	57437	Enzo Doria	07/2014
9721	9*5^82159+2	57428	Lelio R Paula	09/2014
9723	(F(22898)^13-F(22897)^13)/F(22896)	57422	Wayne Halsdorf	03/2012
9722	15362^5469+5469^15362	57422	Hans Havermann	04/2019
9724	14005^12586+12586^14005	57419	Hans Havermann	04/2019
9725	10159^14330-14330^10159	57419	Norbert Schneider	05/2019
9728	lucasU(432,25,21787)-5*lucasU(432,25,21786)	57416	Mike Oakes	05/2009
9726	(103*10^57414-1)/3	57416	Serge Batalov	12/2014
9727	(1654*30^38869-1)/29	57416	Karsten Bonath	05/2017
9729	2*10^57410+9^57410	57411	Mike Oakes	04/2011
9730	2^190704-1595	57408	Lelio R Paula	05/2011
9731	11^55121-1740	57403	Enzo Doria	11/2012
9732	2^190644-185	57390	Lelio R Paula	04/2011
9733	41182!3-3^41182	57389	Robert Price	08/2015
9734	2^190629-112255	57386	Enzo Doria	06/2014
9735	(2*10^57384-71)/3	57384	Robert Price	01/2017
9737	2*6^73735+5^73735	57378	Mike Oakes	11/2009
9736	2^190605+59	57378	Lelio R Paula	04/2011
9738	6^73727-7	57371	Lelio R Paula	10/2012
9739	2^190561-112225	57365	Enzo Doria	06/2014
9740	10^57358+170899	57359	Patrick De Geest	06/2016
9741	10^57358-8001	57358	Robert Price	03/2016
9742	18^45687-11	57350	Lelio R Paula	02/2013
9743	11^55069-210	57349	Enzo Doria	07/2012
9744	11^55068-12	57348	Lelio R Paula	02/2013
9745	19^44839+54	57339	Lelio R Paula	02/2013
9746	(7*2^190468-1)/8511	57334	Lelio R Paula	01/2014
9747	(23*10^57333-59)/9	57334	Robert Price	03/2017
9748	2^190455-1155*190455	57333	Henri Lifchitz	02/2005
9749	14376^9721+9721^14376	57328	Hans Havermann	04/2019
9750	65^31620+28	57325	Lelio R Paula	01/2016

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Probable Primes Top 10000

(253476 PRPs in the top)