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	22971^21692+21692^22971	99610	Hans Havermann	03/2018
9502	2^330845+71687	99595	Enzo Doria	04/2016
9503	(26667^22501-1)/26666	99585	Serge Batalov	06/2022
9504	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
9505	24494^11613+11613^24494	99567	Hans Havermann	03/2018
9506	2^330735+8415	99562	Lelio R Paula	09/2016
9507	2^330720+74071	99557	Enzo Doria	04/2016
9508	(10405^24781-1)/10404	99548	Serge Batalov	06/2022
9510	31^66738-2	99531	Lelio R Paula	09/2013
9509	(9002^25171-1)/9001	99531	Serge Batalov	06/2022
9511	(5023^26893-1)/5022	99527	Serge Batalov	06/2022
9512	7*3^208567+4	99513	Lelio R Paula	08/2014
9513	(15881^23689-1)/15880	99511	Serge Batalov	06/2022
9514	(13*10^99508+47)/3	99509	Robert Price	01/2017
9515	2^330553+779	99507	Lelio R Paula	01/2013
9516	15^84606-94	99505	Lelio R Paula	08/2016
9517	(10^99497+173)/3	99497	Robert Price	05/2021
9518	9*10^99493-43	99494	Robert Price	09/2021
9519	6^127858+47	99493	Lelio R Paula	08/2016
9520	5^142337+48	99490	Lelio R Paula	08/2016
9521	7^117724-20	99489	Lelio R Paula	08/2016
9522	(559^36209-1)/558	99479	Serge Batalov	06/2022
9523	(13470^24091-1)/13469	99477	Serge Batalov	06/2022
9524	(29*10^99474-17)/3	99475	Erik Branger	09/2014
9525	(185*10^99466-11)/3	99468	Robert Price	10/2020
9526	(2^330410+2038)/2	99464	Stefano Morozzi	09/2020
9527	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
9528	(516*32^66077-175)/31	99458	Eric Chen	04/2023
9529	(2863^28771-1)/2862	99453	Serge Batalov	06/2022
9530	(2^330373+2114)/2	99452	Stefano Morozzi	09/2020
9531	(68*10^99441+7)/3	99443	Robert Price	03/2016
9532	10^99434+155571	99435	Patrick De Geest	04/2020
9533	10^99434-123456789	99434	Robert Price	02/2020
9534	10^99434-191237	99434	Patrick De Geest	04/2020
9535	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
9536	23839^14802+14802^23839	99417	Hans Havermann	02/2018
9537	(2*10^99408+529)/9	99408	Robert Price	01/2017
9538	(2^330216+3510)/2	99405	Stefano Morozzi	09/2020
9539	53^57646-2	99398	Lelio R Paula	09/2013
9540	2^330165+1870025	99390	Enzo Doria	05/2016
9541	7*10^99383+97	99384	Robert Price	09/2021
9542	2^330142-155	99383	Lelio R Paula	12/2012
9543	2^330088-115259	99367	Enzo Doria	06/2015
9544	24216^12671+12671^24216	99354	Hans Havermann	01/2018
9545	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
9546	(746*10^99303+1)/9	99305	Robert Price	02/2017
9547	3^208107+40	99293	Lelio R Paula	08/2016
9548	2^329843+211343	99293	Enzo Doria	08/2023
9549	(3939^27617-1)/3938	99291	Serge Batalov	06/2022
9550	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
9551	8*3^208093+5	99287	Lelio R Paula	08/2014
9552	5^142043+56	99284	Lelio R Paula	08/2016
9553	(13*10^99282-157)/9	99283	Robert Price	05/2021
9554	(10^99284+7)/53/67	99281	Alfred Reich	06/2021
9555	22*10^99275+7	99277	Robert Price	04/2016
9556	2^329778+1876189	99274	Enzo Doria	07/2016
9557	(149557^19321-1)/(149557^139-1)	99264	Ryan Propper	11/2023
9558	(6580^25997-1)/6579	99259	Serge Batalov	06/2022
9559	(2249^29611-1)/2248	99253	Serge Batalov	06/2022
9560	(10^99239-13)/3	99239	Robert Price	02/2017
9561	(1199^32233-1)/1198	99237	Serge Batalov	06/2022
9563	3^207987+62	99236	Lelio R Paula	08/2016
9562	(62*10^99235+91)/9	99236	Robert Price	07/2021
9564	2^329638+49	99231	Lelio R Paula	12/2012
9565	7^117413-18	99226	Lelio R Paula	08/2016
9566	2^329586-458903	99216	Enzo Doria	04/2015
9567	(6290^26119-1)/6289	99214	Serge Batalov	06/2022
9569	2^329553+101	99206	Lelio R Paula	12/2012
9568	(21297^22921-1)/21296	99206	Serge Batalov	06/2022
9570	2^329551-112897	99205	Enzo Doria	06/2014
9571	(3^207925+7)/50	99204	Lelio R Paula	09/2013
9572	6^127458-17993	99182	Enzo Doria	03/2013
9573	27197^4428+4428^27197	99166	Hans Havermann	10/2017
9574	(46*10^99143-1)/9	99144	Robert Price	12/2014
9575	(64*10^99135+161)/9	99136	Robert Price	08/2022
9576	7*10^99133+69	99134	Robert Price	10/2017
9577	(21701^22861-1)/21700	99132	Serge Batalov	06/2022
9578	18^78968-3065	99127	Enzo Doria	03/2013
9579	25927^6654+6654^25927	99122	Hans Havermann	10/2017
9580	87915!4+16	99122	Robert Price	09/2019
9581	2^329259+189	99117	Lelio R Paula	12/2012
9582	8*10^99113+39	99114	Robert Price	01/2017
9583	6^127364+77	99109	Lelio R Paula	08/2016
9584	(82*10^99103+143)/9	99104	Robert Price	06/2021
9585	(11414^24421-1)/11413	99083	Serge Batalov	06/2022
9586	(2^329135+1110)/2	99080	Stefano Morozzi	09/2020
9587	(22089^22807-1)/22088	99074	Serge Batalov	06/2022
9588	(59*10^99069+391)/9	99070	Robert Price	03/2021
9589	(797*10^99061-41)/9	99063	Robert Price	04/2022
9590	2^329058-287681	99057	Harrison Mesh	06/2022
9591	6^127285+13	99047	Lelio R Paula	08/2016
9592	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
9593	2^329007+73283	99041	Enzo Doria	04/2016
9594	(145413^19321-1)/(145413^139-1)	99030	Ryan Propper	11/2023
9595	5*3^207543-8	99024	Lelio R Paula	08/2014
9596	(2^328930+570)/2	99018	Stefano Morozzi	09/2020
9597	2^328885+149	99005	Lelio R Paula	12/2012
9598	23392^17075+17075^23392	99004	Hans Havermann	09/2017
9599	(7424^25579-1)/7423	99004	Serge Batalov	06/2022
9600	(2^328879-9)/119	99001	Lelio R Paula	10/2013
9601	5^141618+54	98987	Lelio R Paula	08/2016
9602	2^328824+24391	98986	Enzo Doria	10/2023
9603	8*10^98982+51	98983	Robert Price	05/2017
9604	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
9605	2^328794-2797601	98977	Enzo Doria	04/2016
9606	(88331^20011-1)/88330	98972	Serge Batalov	06/2022
9607	6^127176+5	98963	Lelio R Paula	11/2014
9608	2*10^98961-21	98962	Robert Price	09/2020
9609	24262^11989+11989^24262	98960	Hans Havermann	09/2017
9610	(60138^20707-1)/60137	98958	Serge Batalov	06/2022
9611	2^328700-109709	98949	Enzo Doria	04/2014
9612	(2^328698+1810)/2	98948	Stefano Morozzi	01/2021
9613	(1014^32917-1)/1013	98947	Serge Batalov	06/2022
9614	87771!4-128	98944	Robert Price	11/2019
9615	(4576^27031-1)/4575	98943	Serge Batalov	06/2022
9616	(2^328658+3042)/2	98936	Stefano Morozzi	09/2020
9617	(1933^30103-1)/1932	98923	Serge Batalov	06/2022
9618	46711!2-2^46711	98916	Robert Price	09/2015
9619	9*7^117037+4	98909	Lelio R Paula	11/2014
9620	127^47012+126	98905	Norbert Schneider	01/2019
9621	(93826^19891-1)/93825	98900	Serge Batalov	06/2022
9622	(2^328525+1250)/2	98896	Stefano Morozzi	09/2020
9623	(10^98890+149)/3	98890	Serge Batalov	12/2014
9624	22775^21978+21978^22775	98889	Hans Havermann	08/2017
9625	2^328497-216933	98888	Enzo Doria	05/2014
9626	2^328487+32769	98885	Lelio R Paula	08/2016
9627	3^207250-112358	98884	Enzo Doria	06/2014
9628	13^88754-90	98867	Lelio R Paula	08/2016
9630	2^328406+709	98861	Lelio R Paula	02/2013
9629	2*10^98860-21	98861	Robert Price	09/2020
9631	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
9632	7^116976+76	98857	Lelio R Paula	08/2016
9633	(2^328378+2710)/2	98852	Stefano Morozzi	09/2020
9634	(25411^22441-1)/25410	98849	Serge Batalov	06/2022
9635	(18668^23143-1)/18667	98842	Serge Batalov	06/2022
9637	2^328335+1155	98839	Lelio R Paula	08/2016
9636	2^328333-349003	98839	Harrison Mesh	06/2022
9639	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
9638	287^40210+40210^287	98832	Norbert Schneider	11/2014
9640	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
9641	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
9642	(28623^22171-1)/28622	98806	Serge Batalov	06/2022
9643	24746^9825+9825^24746	98795	Hans Havermann	07/2020
9644	26620^5143+5143^26620	98793	Hans Havermann	07/2020
9645	65^54491+48	98788	Lelio R Paula	04/2016
9646	3^207042+98	98785	Lelio R Paula	08/2016
9647	(2^328121+3110)/2	98774	Stefano Morozzi	09/2020
9648	10^98754+73383	98755	Patrick De Geest	02/2021
9651	3^206977-112756	98754	Enzo Doria	07/2014
9650	10^98754-40000000001	98754	Robert Price	09/2020
9649	10^98754-169343	98754	Patrick De Geest	02/2021
9652	7^116846-50	98747	Lelio R Paula	08/2016
9653	(19152^23059-1)/19151	98740	Serge Batalov	06/2022
9654	23267^17512+17512^23267	98730	Hans Havermann	04/2020
9655	2^327967-28635	98728	Lelio R Paula	08/2016
9656	707^34642+34642^707	98710	Norbert Schneider	12/2017
9657	(10771^24481-1)/10770	98710	Serge Batalov	06/2022
9658	6^126850-47	98709	Lelio R Paula	08/2016
9659	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
9660	(22*10^98697+47)/3	98698	Robert Price	06/2021
9661	(139706^19321-1)/(139706^139-1)	98696	Ryan Propper	11/2023
9662	8*6^126830-7	98694	Lelio R Paula	11/2014
9663	11^94770-270	98693	Enzo Doria	08/2012
9664	(2^327846+3250)/2	98692	Stefano Morozzi	01/2021
9665	2^327832+43	98688	Lelio R Paula	12/2012
9666	2^327795+761	98677	Lelio R Paula	02/2013
9667	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
9668	10^98669+147411	98670	Patrick De Geest	11/2016
9670	10^98669-9^(98669-1)	98669	Robert Price	05/2016
9669	10^98669-105249	98669	Patrick De Geest	11/2016
9671	(7911^25309-1)/7910	98657	Serge Batalov	06/2022
9672	2^327671-109801	98639	Enzo Doria	04/2014
9673	24398^11037+11037^24398	98638	Hans Havermann	10/2019
9674	5^141090-14	98618	Lelio R Paula	08/2016
9675	20^75799+47	98617	Lelio R Paula	08/2016
9676	(5452^26393-1)/5451	98616	Serge Batalov	06/2022
9677	28101^3226+3226^28101	98597	Hans Havermann	07/2020
9678	2^327515-1017	98592	Lelio R Paula	08/2016
9679	6^126692+97681	98586	Mike Oakes	04/2011
9680	2^327467-741	98578	Lelio R Paula	08/2016
9681	(2947^28411-1)/2946	98566	Serge Batalov	06/2022
9682	22713^21800+21800^22713	98540	Hans Havermann	05/2020
9683	(2^327329+9)/19	98535	Lelio R Paula	10/2013
9684	7^116577-66	98519	Lelio R Paula	08/2016
9686	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
9685	23220^17479+17479^23220	98512	Hans Havermann	03/2020
9687	(2^327240+3798)/2	98509	Stefano Morozzi	02/2021
9688	(28514^22111-1)/28513	98502	Serge Batalov	06/2022
9689	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
9690	2^327162-66945	98486	Lelio R Paula	08/2016
9691	30139^1852+1852^30139	98484	Hans Havermann	02/2020
9692	23182^17703+17703^23182	98479	Hans Havermann	01/2020
9693	4*10^98472-3	98473	Erik Branger	11/2013
9694	26167^5794+5794^26167	98466	Hans Havermann	01/2020
9695	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
9696	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
9697	(2009^29803-1)/2008	98436	Serge Batalov	06/2022
9698	13^88363+94	98432	Lelio R Paula	08/2016
9699	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
9700	6^126481+41	98422	Lelio R Paula	08/2016
9701	78*10^98413-7	98415	Robert Price	05/2017
9702	22634^22263+22263^22634	98404	Hans Havermann	07/2020
9703	(47*10^98386+241)/9	98387	Robert Price	06/2022
9704	7^116416+46	98383	Lelio R Paula	08/2016
9705	7^116407-24	98376	Lelio R Paula	07/2016
9706	439^37228+37228^439	98374	Norbert Schneider	08/2018
9707	2^326782-1860671	98372	Enzo Doria	03/2016
9708	17^79948+58	98372	Lelio R Paula	08/2016
9709	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
9710	3^206143-98	98356	Lelio R Paula	08/2016
9711	8*5^140705+7	98350	Lelio R Paula	11/2014
9712	(2^326632+1662)/2	98326	Stefano Morozzi	09/2020
9713	(638^35053-1)/637	98315	Serge Batalov	06/2022
9714	2^326585+11	98312	Lelio R Paula	12/2012
9715	2^326582-459161	98311	Enzo Doria	05/2015
9716	(1266^31687-1)/1265	98304	Serge Batalov	06/2022
9718	(2^326548+9)/5	98301	Lelio R Paula	10/2013
9717	(2^326549+18)/10	98301	Stefano Morozzi	03/2020
9719	2^326538+71659	98298	Enzo Doria	04/2016
9720	(2^326520+2082)/2	98293	Stefano Morozzi	09/2020
9721	(2^326521+1002)/2	98293	Stefano Morozzi	09/2020
9722	15^83575-58	98292	Lelio R Paula	08/2016
9723	10^98288+3	98289	Robert Price	03/2011
9724	10^98288-117017	98288	Patrick De Geest	11/2011
9725	(44*10^98284-719)/9	98285	Robert Price	12/2017
9726	(5985^26021-1)/5984	98280	Serge Batalov	06/2022
9727	23466^15419+15419^23466	98277	Hans Havermann	02/2020
9728	2^326421-2797573	98263	Enzo Doria	04/2016
9729	2^326401+16095	98257	Lelio R Paula	07/2016
9730	(6494^25771-1)/6493	98249	Serge Batalov	06/2022
9731	7^116240-116240^7	98235	Norbert Schneider	05/2017
9732	17^79826-78	98222	Lelio R Paula	08/2016
9733	2^326268-809	98217	Yves Minet	04/2011
9734	22659^21590+21590^22659	98210	Hans Havermann	10/2019
9735	22268^22587-22587^22268	98202	Norbert Schneider	08/2020
9736	(418*10^98199+23)/9	98201	Robert Price	08/2017
9737	12*10^98198-7	98200	Robert Price	11/2017
9738	15^83496-76	98199	Lelio R Paula	08/2016
9739	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
9740	9*5^140471-4	98186	Lelio R Paula	11/2014
9741	(35103^21601-1)/35102	98180	Serge Batalov	06/2022
9743	22774^20455+20455^22774	98175	Hans Havermann	07/2020
9742	(4516^26863-1)/4515	98175	Serge Batalov	06/2022
9744	2^326069-2383	98157	Yves Minet	10/2013
9745	(9661^24631-1)/9660	98152	Serge Batalov	06/2022
9746	(4175^27109-1)/4174	98149	Serge Batalov	06/2022
9747	(57801^20611-1)/57800	98144	Serge Batalov	06/2022
9748	2^325973+1185	98128	Lelio R Paula	07/2016
9749	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
9750	2^325945-1847269	98120	Enzo Doria	07/2015

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Probable Primes Top 10000

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