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	8^97731-7^(97731-1)	88260	Robert Price	04/2016
9502	5*10^88254+59	88255	Robert Price	09/2016
9503	4*3^184968-7	88253	Lelio R Paula	08/2014
9504	34*10^88251-9	88253	Robert Price	06/2020
9505	7^104426+88	88251	Lelio R Paula	10/2015
9506	2^293142+99	88245	Lelio R Paula	10/2012
9507	11^84736-2130	88244	Enzo Doria	12/2012
9508	23884^4945+4945^23884	88232	Hans Havermann	08/2020
9509	22080^9907+9907^22080	88231	Hans Havermann	08/2020
9510	(10^110315+1)/(10^22063+1)/5824812682167648578460281641	88225	Makoto Kamada	04/2019
9511	2^293068-89	88223	Lelio R Paula	10/2012
9512	2126^26511+26511^2126	88218	Norbert Schneider	02/2020
9513	2^293014-109655	88207	Enzo Doria	04/2014
9514	8*7^104371-3	88205	Lelio R Paula	10/2014
9515	2^292995-2145	88201	Lelio R Paula	10/2013
9516	28534^1233+1233^28534	88198	Hans Havermann	08/2020
9517	5*10^88182+77	88183	Robert Price	06/2016
9519	2^292929+43877	88181	Donovan Johnson	04/2005
9518	6^113321+131	88181	Lelio R Paula	12/2015
9520	(2^292919+3366)/2	88178	Stefano Morozzi	01/2020
9521	2^292904-583949	88173	Paul Bourdelais	04/2013
9522	2^292894-111851	88170	Enzo Doria	05/2014
9523	2^292872-2797349	88164	Enzo Doria	03/2016
9524	(2^292864+1042)/2	88161	Stefano Morozzi	01/2020
9525	2^292860-109685	88160	Enzo Doria	04/2014
9526	9*6^113288-5	88157	Lelio R Paula	10/2014
9527	(2^292735+2166)/2	88122	Stefano Morozzi	01/2020
9528	(2^292735+2346)/2	88122	Stefano Morozzi	01/2020
9529	(2^292705+1934)/2	88113	Stefano Morozzi	01/2020
9530	(2*10^88112-23)/3	88112	Robert Price	09/2017
9531	29622^943+943^29622	88111	Hans Havermann	08/2020
9532	(73*10^88105+17)/9	88106	Robert Price	10/2015
9533	(2^292673+3026)/2	88104	Stefano Morozzi	01/2020
9534	11^84588+78	88090	Lelio R Paula	11/2015
9535	(265*10^88077+11)/3	88079	Robert Price	03/2017
9536	91^44959-90^44959	88077	Robert Price	07/2015
9537	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
9538	1316^28233+28233^1316	88066	Norbert Schneider	07/2020
9539	(2^292543+2234)/2	88064	Stefano Morozzi	01/2020
9540	(10^88020+101)/3	88020	Robert Price	04/2016
9541	52^51285-51	88006	Norbert Schneider	09/2018
9542	21002^15501+15501^21002	88006	Hans Havermann	08/2020
9543	20466^19951+19951^20466	88004	Hans Havermann	08/2020
9544	(2^292324+2346)/2	87998	Stefano Morozzi	01/2020
9545	21634^11683+11683^21634	87998	Hans Havermann	08/2020
9546	(6340^23143-1)/6339	87988	Serge Batalov	08/2020
9547	20674^18013+18013^20674	87980	Hans Havermann	08/2020
9548	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
9549	(11*10^87960-41)/3	87961	Robert Price	12/2021
9550	(424*10^87930-1)/9	87932	Robert Price	11/2017
9551	(2^292100+3070)/2	87931	Stefano Morozzi	01/2020
9552	p(18225)#/2+128	87929	Robert Price	04/2017
9553	(10607^21841-1)/10606	87919	Serge Batalov	08/2020
9554	(2^292047+1550)/2	87915	Stefano Morozzi	01/2020
9555	4*6^112977+7	87914	Lelio R Paula	10/2014
9556	(2^292016+1062)/2	87906	Stefano Morozzi	01/2020
9557	(11359^21673-1)/11358	87888	Serge Batalov	08/2020
9558	14^76677+69	87882	Lelio R Paula	11/2015
9559	(22*10^87863-1)/3	87864	Robert Price	12/2014
9560	2^291822-2797811	87848	Enzo Doria	04/2016
9561	(22*10^87821-43)/3	87822	Robert Price	10/2021
9562	(2^291730+1614)/2	87820	Stefano Morozzi	01/2020
9563	(277*10^87817-7)/9	87819	Robert Price	02/2022
9564	2^291716-111389	87816	Enzo Doria	05/2014
9565	(782*10^87809-71)/9	87811	Robert Price	06/2017
9566	3^184039+1820	87809	Lelio R Paula	12/2015
9567	12^81356+41	87798	Lelio R Paula	11/2015
9568	21307^13188+13188^21307	87789	Hans Havermann	08/2020
9569	(2527^25801-1)/2526	87788	Serge Batalov	08/2020
9570	(2^291596+1986)/2	87779	Stefano Morozzi	01/2020
9572	6^112792-18983	87770	Enzo Doria	03/2013
9571	(3123^25117-1)/3122	87770	Serge Batalov	08/2020
9573	3*6^112787-5	87766	Lelio R Paula	10/2014
9574	7^103848+82	87762	Lelio R Paula	10/2015
9575	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
9576	(2^291506+918)/2	87752	Stefano Morozzi	01/2020
9577	24411^3932+3932^24411	87749	Hans Havermann	08/2020
9578	(3^183915+5)/128	87748	Lelio R Paula	01/2013
9579	19^68619+24	87747	Lelio R Paula	12/2015
9581	2^291480+1185	87745	Lelio R Paula	10/2013
9580	2^291482+1867369	87745	Enzo Doria	03/2016
9582	2^291467-937	87741	Yves Minet	05/2013
9583	(25*10^87726+161)/3	87727	Robert Price	01/2017
9584	11^84239-2850	87726	Enzo Doria	12/2012
9585	10^87720+215541	87721	Patrick De Geest	01/2011
9586	10^87720-3	87720	Markus Tervooren	07/2010
9587	(2^291383+3078)/2	87715	Stefano Morozzi	01/2020
9589	(5*10^87712-473)/9	87712	Robert Price	12/2017
9588	(2^291373+2946)/2	87712	Stefano Morozzi	01/2020
9590	22591^7630+7630^22591	87711	Hans Havermann	08/2020
9591	22081^9378+9378^22081	87709	Hans Havermann	08/2020
9592	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
9593	(2^291280+462)/2	87684	Stefano Morozzi	01/2020
9594	20749^16816+16816^20749	87680	Hans Havermann	08/2020
9595	93^44541-2	87679	Lelio R Paula	09/2013
9596	2^291261-109561	87679	Enzo Doria	04/2014
9597	(4*10^87669+149)/9	87669	Robert Price	03/2017
9598	2^291217+4257	87666	Lelio R Paula	10/2013
9599	22748^7137+7137^22748	87660	Hans Havermann	08/2020
9600	2*12^81214-5^81214	87645	Mike Oakes	12/2010
9601	(85*10^87637-139)/9	87638	Robert Price	08/2021
9602	(5005^23689-1)/5004	87632	Serge Batalov	08/2020
9603	(5*10^87622-473)/9	87622	Robert Price	12/2017
9604	12^81188+85	87617	Lelio R Paula	11/2015
9605	(2^291030+3462)/2	87609	Stefano Morozzi	01/2020
9606	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
9607	(2^290980+1150)/2	87594	Stefano Morozzi	01/2020
9608	2^290958+127	87588	Lelio R Paula	09/2012
9609	78531!4-8	87580	Robert Price	11/2019
9610	2^290923-67	87577	Lelio R Paula	09/2012
9611	3*10^87573-97	87574	Robert Price	08/2017
9612	(13*10^87565+11)/3	87566	Robert Price	05/2015
9613	(2^290881+1022)/2	87564	Stefano Morozzi	01/2020
9614	(2^290857-7)/55	87555	Lelio R Paula	01/2013
9615	(2^290808+1498)/2	87542	Stefano Morozzi	01/2020
9616	2^290802+82875	87541	Lelio R Paula	10/2013
9617	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
9618	3^183441+236	87524	Lelio R Paula	12/2015
9619	4*10^87513-69	87514	Robert Price	01/2022
9620	2^290618-33	87485	Lelio R Paula	09/2012
9621	(184*10^87473-1)/3	87475	Robert Price	02/2017
9622	2^290534-115151	87460	Enzo Doria	06/2015
9623	2^290512-109757	87453	Enzo Doria	04/2014
9624	(32*10^87448-41)/9	87449	Robert Price	05/2015
9625	(2^290493+3074)/2	87447	Stefano Morozzi	01/2020
9626	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
9627	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
9628	2^290426+82875	87427	Lelio R Paula	11/2013
9629	3*2^290415-7	87425	Lelio R Paula	08/2014
9631	10^87408+57	87409	Robert Price	03/2011
9630	2^290366+74779	87409	Enzo Doria	04/2016
9632	22284^8365+8365^22284	87409	Hans Havermann	08/2020
9633	10^87408-123569	87408	Patrick De Geest	07/2013
9634	21517^11536+11536^21517	87404	Hans Havermann	08/2020
9635	6*10^87396+77	87397	Robert Price	06/2020
9636	(2^290268+3882)/2	87380	Stefano Morozzi	01/2020
9637	2^290265+58905	87379	Lelio R Paula	10/2013
9638	7^103391+16	87376	Lelio R Paula	10/2015
9639	(115*10^87368-7)/9	87370	Robert Price	11/2017
9640	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
9641	8*7^103379+3	87367	Lelio R Paula	10/2014
9642	(2^290226+7)/71	87365	Lelio R Paula	01/2013
9643	(29*10^87355-89)/3	87356	Robert Price	01/2022
9644	(3216^24907-1)/3215	87354	Serge Batalov	08/2020
9645	(2^290160+2686)/2	87347	Stefano Morozzi	01/2020
9646	13^78407-30	87341	Lelio R Paula	11/2015
9647	4*10^87337-99	87338	Robert Price	12/2016
9648	7*10^87319+39	87320	Robert Price	07/2016
9649	3*5^124921+2	87317	Lelio R Paula	10/2014
9650	78315!4-16	87316	Robert Price	11/2019
9651	3^182984+88	87306	Lelio R Paula	12/2015
9652	(10^87323-1)/(9*33909262597306826117)	87303	Alfred Reich	02/2019
9653	(10^87323-1)/305183363375761435053	87303	Anonymous	10/2020
9654	(2^290008+958)/2	87301	Stefano Morozzi	01/2020
9655	(10536^21701-1)/10535	87293	Serge Batalov	08/2020
9656	4*10^87287-99	87288	Robert Price	12/2016
9658	11^83813-1860	87283	Enzo Doria	12/2012
9657	(3068^25033-1)/3067	87283	Serge Batalov	08/2020
9659	734^30453+30453^734	87270	Norbert Schneider	04/2017
9660	12^80855+29	87258	Lelio R Paula	11/2015
9661	22209^8482+8482^22209	87249	Hans Havermann	08/2020
9662	3*6^112119-5	87247	Lelio R Paula	10/2014
9663	12^80806+79	87205	Lelio R Paula	11/2015
9664	91382^9+9^91382	87201	Andrey Kulsha	11/2004
9665	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
9666	6^112054-47	87195	Lelio R Paula	12/2015
9667	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
9668	15^74131-68	87185	Lelio R Paula	11/2015
9669	2^289583-741	87174	Lelio R Paula	10/2013
9670	7^103146+12	87169	Lelio R Paula	10/2015
9671	(2^289562+2182)/2	87167	Stefano Morozzi	01/2020
9672	5*2^289556-3	87166	Lelio R Paula	08/2014
9673	2^289543-112735	87162	Enzo Doria	06/2014
9674	10890^21589-21589^10890	87156	Norbert Schneider	01/2022
9675	20204^20243-20243^20204	87155	Norbert Schneider	04/2020
9676	8*3^182655-7	87150	Lelio R Paula	08/2014
9677	2*10^87144+81	87145	Robert Price	01/2017
9678	20541^17468+17468^20541	87140	Hans Havermann	07/2020
9680	7^103106+2*3^103106	87135	Mike Oakes	08/2010
9679	(65*10^87134-29)/9	87135	Robert Price	01/2021
9681	8*3^182614+7	87130	Lelio R Paula	08/2014
9682	3*10^87121-73	87122	Robert Price	02/2021
9683	(4982^23563-1)/4981	87119	Serge Batalov	08/2020
9684	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
9685	3^182566+14	87107	Robert Price	09/2013
9686	1738^26881+26881^1738	87096	Norbert Schneider	04/2020
9687	24290^3849+3849^24290	87089	Hans Havermann	08/2020
9688	(10^87038+7)/43/53/751	87032	Alfred Reich	06/2021
9689	(3^182385-5)/2	87020	Lelio R Paula	01/2013
9690	11^83534-8	86992	Lelio R Paula	11/2015
9691	4^144479-14267	86986	Mike Oakes	03/2011
9692	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
9693	(151*10^86963-1)/3	86965	Robert Price	04/2017
9694	(2^288892+826)/2	86965	Stefano Morozzi	01/2020
9695	15^73940-58	86961	Lelio R Paula	11/2015
9696	(11*10^86951-71)/3	86952	Robert Price	04/2022
9697	2^288761-113143	86926	Enzo Doria	07/2014
9698	24440^3603+3603^24440	86925	Hans Havermann	08/2020
9700	2^288747+3083	86922	Yves Minet	03/2011
9699	(2^288749+3102)/2	86922	Stefano Morozzi	01/2020
9701	30^58842+29	86917	Norbert Schneider	03/2017
9702	(2^288705+2186)/2	86909	Stefano Morozzi	01/2020
9703	(10^86906-13)/3	86906	Robert Price	02/2017
9704	2^288692-110027	86905	Enzo Doria	04/2014
9705	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
9706	(26*10^86885+79)/3	86886	Robert Price	09/2020
9707	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
9708	3^182089-34	86879	Robert Price	11/2013
9709	(2^288571+1698)/2	86869	Stefano Morozzi	01/2020
9710	2^288543-109801	86861	Enzo Doria	04/2014
9711	60^48847-59	86858	Norbert Schneider	10/2014
9712	(2^288484+3186)/2	86843	Stefano Morozzi	01/2020
9713	2^288470-64875	86839	Lelio R Paula	10/2013
9714	10^86816+32997	86817	Patrick De Geest	07/2013
9715	10^86816-99	86816	Robert Price	05/2011
9716	(89*10^86802-539)/9	86803	Robert Price	11/2017
9717	20272^19123+19123^20272	86796	Hans Havermann	07/2020
9718	(2^288316+1530)/2	86792	Stefano Morozzi	01/2020
9719	(2^288316+2218)/2	86792	Stefano Morozzi	01/2020
9720	41487!2+256	86786	Robert Price	01/2015
9721	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
9722	(2^288278+1750)/2	86781	Stefano Morozzi	01/2020
9723	2^288243+76043	86770	Enzo Doria	04/2016
9724	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
9725	9*6^111495+5	86761	Lelio R Paula	10/2014
9726	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
9727	9*7^102654-2	86754	Lelio R Paula	10/2014
9728	(2^288155+1154)/2	86743	Stefano Morozzi	01/2020
9729	2^288122-112841	86734	Enzo Doria	06/2014
9730	5^124062-68	86716	Lelio R Paula	10/2015
9731	(2^288007-3)/125	86697	Lelio R Paula	01/2013
9732	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
9733	7^102555+48	86670	Lelio R Paula	10/2015
9734	2^287902-4961	86668	Yves Minet	05/2019
9735	77779!4+2	86660	Robert Price	08/2017
9736	(2^287842+3250)/2	86649	Stefano Morozzi	01/2020
9737	2^287809-111355	86640	Enzo Doria	05/2014
9738	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
9739	9*7^102504+8	86627	Lelio R Paula	10/2014
9740	3^181551+32	86622	Robert Price	11/2013
9741	2^287735-521347	86617	Paul Bourdelais	05/2013
9742	21912^8953+8953^21912	86596	Hans Havermann	08/2020
9743	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
9744	(2^287552+1302)/2	86562	Stefano Morozzi	01/2020
9745	2^287540-112967	86559	Enzo Doria	06/2014
9746	3^181407+20	86554	Robert Price	10/2013
9747	(28*10^86550+101)/3	86551	Robert Price	09/2020
9749	(13*10^86546+83)/3	86547	Robert Price	09/2016
9748	(2^287502+2238)/2	86547	Stefano Morozzi	01/2020
9750	2^287482-4715	86541	Yves Minet	05/2019

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