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 ?
8502	2^292929+43877	88181	Donovan Johnson	04/2005
8501	6^113321+131	88181	Lelio R Paula	12/2015
8503	(2^292919+3366)/2	88178	Stefano Morozzi	01/2020
8504	2^292904-583949	88173	Paul Bourdelais	04/2013
8505	2^292894-111851	88170	Enzo Doria	05/2014
8506	2^292872-2797349	88164	Enzo Doria	03/2016
8507	(2^292864+1042)/2	88161	Stefano Morozzi	01/2020
8508	2^292860-109685	88160	Enzo Doria	04/2014
8509	9*6^113288-5	88157	Lelio R Paula	10/2014
8510	(2^292735+2166)/2	88122	Stefano Morozzi	01/2020
8511	(2^292735+2346)/2	88122	Stefano Morozzi	01/2020
8512	(2^292705+1934)/2	88113	Stefano Morozzi	01/2020
8513	(2*10^88112-23)/3	88112	Robert Price	09/2017
8514	29622^943+943^29622	88111	Hans Havermann	08/2020
8515	(73*10^88105+17)/9	88106	Robert Price	10/2015
8516	(2^292673+3026)/2	88104	Stefano Morozzi	01/2020
8517	11^84588+78	88090	Lelio R Paula	11/2015
8518	(265*10^88077+11)/3	88079	Robert Price	03/2017
8519	91^44959-90^44959	88077	Robert Price	07/2015
8520	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
8521	1316^28233+28233^1316	88066	Norbert Schneider	07/2020
8522	(2^292543+2234)/2	88064	Stefano Morozzi	01/2020
8523	(10^88020+101)/3	88020	Robert Price	04/2016
8524	52^51285-51	88006	Norbert Schneider	09/2018
8525	21002^15501+15501^21002	88006	Hans Havermann	08/2020
8526	20466^19951+19951^20466	88004	Hans Havermann	08/2020
8527	(2^292324+2346)/2	87998	Stefano Morozzi	01/2020
8528	21634^11683+11683^21634	87998	Hans Havermann	08/2020
8529	(6340^23143-1)/6339	87988	Serge Batalov	08/2020
8530	20674^18013+18013^20674	87980	Hans Havermann	08/2020
8531	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
8532	(11*10^87960-41)/3	87961	Robert Price	12/2021
8533	(424*10^87930-1)/9	87932	Robert Price	11/2017
8534	(2^292100+3070)/2	87931	Stefano Morozzi	01/2020
8535	p(18225)#/2+128	87929	Robert Price	04/2017
8536	(10607^21841-1)/10606	87919	Serge Batalov	08/2020
8537	(2^292047+1550)/2	87915	Stefano Morozzi	01/2020
8538	4*6^112977+7	87914	Lelio R Paula	10/2014
8539	(2^292016+1062)/2	87906	Stefano Morozzi	01/2020
8540	(11359^21673-1)/11358	87888	Serge Batalov	08/2020
8541	14^76677+69	87882	Lelio R Paula	11/2015
8542	(22*10^87863-1)/3	87864	Robert Price	12/2014
8543	2^291822-2797811	87848	Enzo Doria	04/2016
8544	(22*10^87821-43)/3	87822	Robert Price	10/2021
8545	(2^291730+1614)/2	87820	Stefano Morozzi	01/2020
8546	2^291716-111389	87816	Enzo Doria	05/2014
8547	(782*10^87809-71)/9	87811	Robert Price	06/2017
8548	3^184039+1820	87809	Lelio R Paula	12/2015
8549	12^81356+41	87798	Lelio R Paula	11/2015
8550	21307^13188+13188^21307	87789	Hans Havermann	08/2020
8551	(2527^25801-1)/2526	87788	Serge Batalov	08/2020
8552	(2^291596+1986)/2	87779	Stefano Morozzi	01/2020
8554	6^112792-18983	87770	Enzo Doria	03/2013
8553	(3123^25117-1)/3122	87770	Serge Batalov	08/2020
8555	3*6^112787-5	87766	Lelio R Paula	10/2014
8556	7^103848+82	87762	Lelio R Paula	10/2015
8557	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
8558	(2^291506+918)/2	87752	Stefano Morozzi	01/2020
8559	24411^3932+3932^24411	87749	Hans Havermann	08/2020
8560	(3^183915+5)/128	87748	Lelio R Paula	01/2013
8561	19^68619+24	87747	Lelio R Paula	12/2015
8563	2^291480+1185	87745	Lelio R Paula	10/2013
8562	2^291482+1867369	87745	Enzo Doria	03/2016
8564	2^291467-937	87741	Yves Minet	05/2013
8565	(25*10^87726+161)/3	87727	Robert Price	01/2017
8566	11^84239-2850	87726	Enzo Doria	12/2012
8567	10^87720+215541	87721	Patrick De Geest	01/2011
8568	10^87720-3	87720	Markus Tervooren	07/2010
8569	(2^291383+3078)/2	87715	Stefano Morozzi	01/2020
8571	(5*10^87712-473)/9	87712	Robert Price	12/2017
8570	(2^291373+2946)/2	87712	Stefano Morozzi	01/2020
8572	22591^7630+7630^22591	87711	Hans Havermann	08/2020
8573	22081^9378+9378^22081	87709	Hans Havermann	08/2020
8574	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
8575	(2^291280+462)/2	87684	Stefano Morozzi	01/2020
8576	20749^16816+16816^20749	87680	Hans Havermann	08/2020
8578	93^44541-2	87679	Lelio R Paula	09/2013
8577	2^291261-109561	87679	Enzo Doria	04/2014
8579	(4*10^87669+149)/9	87669	Robert Price	03/2017
8580	2^291217+4257	87666	Lelio R Paula	10/2013
8581	22748^7137+7137^22748	87660	Hans Havermann	08/2020
8582	2*12^81214-5^81214	87645	Mike Oakes	12/2010
8583	(85*10^87637-139)/9	87638	Robert Price	08/2021
8584	(5005^23689-1)/5004	87632	Serge Batalov	08/2020
8585	(5*10^87622-473)/9	87622	Robert Price	12/2017
8586	12^81188+85	87617	Lelio R Paula	11/2015
8587	(2^291030+3462)/2	87609	Stefano Morozzi	01/2020
8588	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
8589	(2^290980+1150)/2	87594	Stefano Morozzi	01/2020
8590	2^290958+127	87588	Lelio R Paula	09/2012
8591	78531!4-8	87580	Robert Price	11/2019
8592	2^290923-67	87577	Lelio R Paula	09/2012
8593	3*10^87573-97	87574	Robert Price	08/2017
8594	(13*10^87565+11)/3	87566	Robert Price	05/2015
8595	(2^290881+1022)/2	87564	Stefano Morozzi	01/2020
8596	(2^290857-7)/55	87555	Lelio R Paula	01/2013
8597	(2^290808+1498)/2	87542	Stefano Morozzi	01/2020
8598	2^290802+82875	87541	Lelio R Paula	10/2013
8599	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
8600	3^183441+236	87524	Lelio R Paula	12/2015
8601	2^290618-33	87485	Lelio R Paula	09/2012
8602	(184*10^87473-1)/3	87475	Robert Price	02/2017
8603	2^290534-115151	87460	Enzo Doria	06/2015
8604	2^290512-109757	87453	Enzo Doria	04/2014
8605	(32*10^87448-41)/9	87449	Robert Price	05/2015
8606	(2^290493+3074)/2	87447	Stefano Morozzi	01/2020
8607	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
8608	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
8609	2^290426+82875	87427	Lelio R Paula	11/2013
8610	3*2^290415-7	87425	Lelio R Paula	08/2014
8613	10^87408+57	87409	Robert Price	03/2011
8611	2^290366+74779	87409	Enzo Doria	04/2016
8612	22284^8365+8365^22284	87409	Hans Havermann	08/2020
8614	10^87408-123569	87408	Patrick De Geest	07/2013
8615	21517^11536+11536^21517	87404	Hans Havermann	08/2020
8616	6*10^87396+77	87397	Robert Price	06/2020
8617	(2^290268+3882)/2	87380	Stefano Morozzi	01/2020
8618	2^290265+58905	87379	Lelio R Paula	10/2013
8619	7^103391+16	87376	Lelio R Paula	10/2015
8620	(115*10^87368-7)/9	87370	Robert Price	11/2017
8621	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
8622	8*7^103379+3	87367	Lelio R Paula	10/2014
8623	(2^290226+7)/71	87365	Lelio R Paula	01/2013
8624	(3216^24907-1)/3215	87354	Serge Batalov	08/2020
8625	(2^290160+2686)/2	87347	Stefano Morozzi	01/2020
8626	13^78407-30	87341	Lelio R Paula	11/2015
8627	4*10^87337-99	87338	Robert Price	12/2016
8628	7*10^87319+39	87320	Robert Price	07/2016
8629	3*5^124921+2	87317	Lelio R Paula	10/2014
8630	78315!4-16	87316	Robert Price	11/2019
8631	3^182984+88	87306	Lelio R Paula	12/2015
8632	(10^87323-1)/(9*33909262597306826117)	87303	Alfred Reich	02/2019
8633	(10^87323-1)/305183363375761435053	87303	Anonymous	10/2020
8634	(2^290008+958)/2	87301	Stefano Morozzi	01/2020
8635	(10536^21701-1)/10535	87293	Serge Batalov	08/2020
8636	4*10^87287-99	87288	Robert Price	12/2016
8638	11^83813-1860	87283	Enzo Doria	12/2012
8637	(3068^25033-1)/3067	87283	Serge Batalov	08/2020
8639	734^30453+30453^734	87270	Norbert Schneider	04/2017
8640	12^80855+29	87258	Lelio R Paula	11/2015
8641	22209^8482+8482^22209	87249	Hans Havermann	08/2020
8642	3*6^112119-5	87247	Lelio R Paula	10/2014
8643	12^80806+79	87205	Lelio R Paula	11/2015
8644	91382^9+9^91382	87201	Andrey Kulsha	11/2004
8645	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
8646	6^112054-47	87195	Lelio R Paula	12/2015
8647	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
8648	15^74131-68	87185	Lelio R Paula	11/2015
8649	2^289583-741	87174	Lelio R Paula	10/2013
8650	7^103146+12	87169	Lelio R Paula	10/2015
8651	(2^289562+2182)/2	87167	Stefano Morozzi	01/2020
8652	5*2^289556-3	87166	Lelio R Paula	08/2014
8653	2^289543-112735	87162	Enzo Doria	06/2014
8654	20204^20243-20243^20204	87155	Norbert Schneider	04/2020
8655	8*3^182655-7	87150	Lelio R Paula	08/2014
8656	2*10^87144+81	87145	Robert Price	01/2017
8657	20541^17468+17468^20541	87140	Hans Havermann	07/2020
8659	7^103106+2*3^103106	87135	Mike Oakes	08/2010
8658	(65*10^87134-29)/9	87135	Robert Price	01/2021
8660	8*3^182614+7	87130	Lelio R Paula	08/2014
8661	3*10^87121-73	87122	Robert Price	02/2021
8662	(4982^23563-1)/4981	87119	Serge Batalov	08/2020
8663	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
8664	3^182566+14	87107	Robert Price	09/2013
8665	1738^26881+26881^1738	87096	Norbert Schneider	04/2020
8666	24290^3849+3849^24290	87089	Hans Havermann	08/2020
8667	(10^87038+7)/43/53/751	87032	Alfred Reich	06/2021
8668	(3^182385-5)/2	87020	Lelio R Paula	01/2013
8669	11^83534-8	86992	Lelio R Paula	11/2015
8670	4^144479-14267	86986	Mike Oakes	03/2011
8671	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
8672	(151*10^86963-1)/3	86965	Robert Price	04/2017
8673	(2^288892+826)/2	86965	Stefano Morozzi	01/2020
8674	15^73940-58	86961	Lelio R Paula	11/2015
8675	2^288761-113143	86926	Enzo Doria	07/2014
8676	24440^3603+3603^24440	86925	Hans Havermann	08/2020
8678	2^288747+3083	86922	Yves Minet	03/2011
8677	(2^288749+3102)/2	86922	Stefano Morozzi	01/2020
8679	30^58842+29	86917	Norbert Schneider	03/2017
8680	(2^288705+2186)/2	86909	Stefano Morozzi	01/2020
8681	(10^86906-13)/3	86906	Robert Price	02/2017
8682	2^288692-110027	86905	Enzo Doria	04/2014
8683	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
8684	(26*10^86885+79)/3	86886	Robert Price	09/2020
8685	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
8686	3^182089-34	86879	Robert Price	11/2013
8687	(2^288571+1698)/2	86869	Stefano Morozzi	01/2020
8688	2^288543-109801	86861	Enzo Doria	04/2014
8689	60^48847-59	86858	Norbert Schneider	10/2014
8690	(2^288484+3186)/2	86843	Stefano Morozzi	01/2020
8691	2^288470-64875	86839	Lelio R Paula	10/2013
8692	10^86816+32997	86817	Patrick De Geest	07/2013
8693	10^86816-99	86816	Robert Price	05/2011
8694	(89*10^86802-539)/9	86803	Robert Price	11/2017
8695	20272^19123+19123^20272	86796	Hans Havermann	07/2020
8696	(2^288316+1530)/2	86792	Stefano Morozzi	01/2020
8697	(2^288316+2218)/2	86792	Stefano Morozzi	01/2020
8698	41487!2+256	86786	Robert Price	01/2015
8699	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
8700	(2^288278+1750)/2	86781	Stefano Morozzi	01/2020
8701	2^288243+76043	86770	Enzo Doria	04/2016
8702	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
8703	9*6^111495+5	86761	Lelio R Paula	10/2014
8704	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
8705	9*7^102654-2	86754	Lelio R Paula	10/2014
8706	(2^288155+1154)/2	86743	Stefano Morozzi	01/2020
8707	2^288122-112841	86734	Enzo Doria	06/2014
8708	5^124062-68	86716	Lelio R Paula	10/2015
8709	(2^288007-3)/125	86697	Lelio R Paula	01/2013
8710	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
8711	7^102555+48	86670	Lelio R Paula	10/2015
8712	2^287902-4961	86668	Yves Minet	05/2019
8713	77779!4+2	86660	Robert Price	08/2017
8714	(2^287842+3250)/2	86649	Stefano Morozzi	01/2020
8715	2^287809-111355	86640	Enzo Doria	05/2014
8716	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
8717	9*7^102504+8	86627	Lelio R Paula	10/2014
8718	3^181551+32	86622	Robert Price	11/2013
8719	2^287735-521347	86617	Paul Bourdelais	05/2013
8720	21912^8953+8953^21912	86596	Hans Havermann	08/2020
8721	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
8722	(2^287552+1302)/2	86562	Stefano Morozzi	01/2020
8723	2^287540-112967	86559	Enzo Doria	06/2014
8724	3^181407+20	86554	Robert Price	10/2013
8725	(28*10^86550+101)/3	86551	Robert Price	09/2020
8727	(13*10^86546+83)/3	86547	Robert Price	09/2016
8726	(2^287502+2238)/2	86547	Stefano Morozzi	01/2020
8728	2^287482-4715	86541	Yves Minet	05/2019
8729	3^181378-2^(181378-1)	86540	Robert Price	01/2016
8730	24588^3305+3305^24588	86530	Hans Havermann	08/2020
8731	83^45080-2	86513	Lelio R Paula	08/2013
8732	(2^287367+2570)/2	86506	Stefano Morozzi	01/2020
8734	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
8733	(2^287360+1006)/2	86504	Stefano Morozzi	01/2020
8735	25*29^59147+20936	86498	Curtis Bright	05/2015
8736	2^287298+1871359	86486	Enzo Doria	05/2016
8737	118^41740-117	86481	Norbert Schneider	08/2018
8738	3*10^86478+89	86479	Robert Price	03/2017
8739	2^287272-79049	86478	Paul Bourdelais	02/2012
8740	(2^287259+2846)/2	86474	Stefano Morozzi	01/2020
8741	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
8742	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
8743	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
8744	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
8745	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
8746	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
8747	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
8748	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
8749	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
8750	(10^86453-1)/9	86453	Lew Baxter	10/2000

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