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*10^81985+107)/3	81986	Robert Price	02/2017
9502	(3*2^272356+1)/177163	81983	Lelio R Paula	12/2012
9503	2^272296-111149	81970	Enzo Doria	05/2014
9504	(2^272293+2810)/2	81969	Stefano Morozzi	01/2020
9505	(2^272278+2118)/2	81964	Stefano Morozzi	01/2020
9506	(9*2^272243-1)/7	81954	Lelio R Paula	02/2014
9507	2^272177-111223	81934	Enzo Doria	05/2014
9508	(2^272127+3878)/2	81919	Stefano Morozzi	01/2020
9510	(151009^15817+1)/151010	81912	Faysal YAtim	06/2017
9509	(2^272104+1950)/2	81912	Stefano Morozzi	01/2020
9511	23160^3437+3437^23160	81898	Hans Havermann	05/2020
9512	(16*10^81896-19)/3	81897	Robert Price	03/2016
9513	(16*10^81872-73)/3	81873	Robert Price	07/2020
9514	(2^271922+78557)/63	81855	Lelio R Paula	12/2012
9515	(10^81848+77)/3	81848	Robert Price	01/2017
9516	(24737*2^271883+1)/3757	81846	Lelio R Paula	06/2014
9517	(2^271885+1670)/2	81846	Stefano Morozzi	01/2020
9518	18813^19144-19144^18813	81831	Norbert Schneider	02/2020
9519	(14*10^81818-89)/3	81819	Robert Price	05/2020
9520	19492^15731+15731^19492	81804	Hans Havermann	07/2020
9521	20420^10137+10137^20420	81801	Hans Havermann	06/2020
9522	(2^271734+3942)/2	81800	Stefano Morozzi	01/2020
9523	(15429^19531-1)/15428	81799	Serge Batalov	08/2020
9524	10^81778+39	81779	Robert Price	03/2011
9525	10^81778-171999	81778	Patrick De Geest	07/2013
9526	(2^271652+2886)/2	81776	Stefano Morozzi	01/2020
9527	(14*10^81767-11)/3	81768	Erik Branger	09/2014
9528	(2^271546+610)/2	81744	Stefano Morozzi	01/2020
9529	2^271541+1868417	81742	Enzo Doria	04/2016
9530	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
9531	19339^16836+16836^19339	81732	Hans Havermann	06/2020
9532	2^271484-167	81725	Lelio R Paula	06/2012
9534	(8*10^81709-611)/9	81709	Robert Price	11/2017
9533	(2^271431+1790)/2	81709	Stefano Morozzi	01/2020
9535	19648^14399+14399^19648	81703	Hans Havermann	05/2020
9536	2^271382+12909	81695	Lelio R Paula	07/2013
9537	49^48334+48	81694	Norbert Schneider	07/2014
9538	7^96668+48	81694	Lelio R Paula	10/2015
9539	11^78435-1410	81682	Enzo Doria	12/2012
9540	19575^14882+14882^19575	81680	Hans Havermann	04/2020
9541	5*10^81653+9	81654	Dmitry Domanov	11/2010
9542	(2^271224+1230)/2	81647	Stefano Morozzi	01/2020
9543	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
9544	(2^271168+1806)/2	81630	Stefano Morozzi	01/2020
9545	3^171068+52	81621	Lelio R Paula	12/2015
9546	2^271115-110407	81614	Enzo Doria	05/2014
9547	2^271111-110635	81613	Enzo Doria	05/2014
9548	2^271098-111	81609	Lelio R Paula	06/2012
9549	(77*10^81606+13)/9	81607	Robert Price	10/2015
9550	2^271064-2790209	81599	Enzo Doria	03/2016
9551	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
9552	2^271040-57	81592	Lelio R Paula	06/2012
9553	(14*10^81585+73)/3	81586	Robert Price	04/2016
9554	127^38779+126	81584	Norbert Schneider	02/2015
9555	18^64966-43	81551	Lelio R Paula	11/2015
9556	19406^15909+15909^19406	81538	Hans Havermann	06/2020
9557	(17*10^81535-161)/9	81536	Robert Price	02/2021
9558	(2^270843+1074)/2	81532	Stefano Morozzi	01/2020
9559	(2^270840+47)/591	81529	Lelio R Paula	12/2012
9560	20^62654+87	81515	Lelio R Paula	01/2016
9561	20120^11241+11241^20120	81503	Hans Havermann	05/2020
9562	(19*10^81488+191)/3	81489	Robert Price	01/2017
9563	8*10^81487+21	81488	Robert Price	02/2017
9564	(73*10^81485+107)/9	81486	Robert Price	08/2016
9565	536^29847+29847^536	81458	Norbert Schneider	03/2017
9566	8*7^96378+9	81450	Lelio R Paula	10/2014
9567	(2^270560+3862)/2	81447	Stefano Morozzi	01/2020
9568	(5728^21673-1)/5727	81444	Serge Batalov	08/2020
9569	2^270546-110345	81443	Enzo Doria	05/2014
9570	13^73105-60	81435	Lelio R Paula	11/2015
9571	(2^270502+1518)/2	81429	Stefano Morozzi	01/2020
9572	(2^270479+2114)/2	81422	Stefano Morozzi	01/2020
9573	(2^270384+1218)/2	81394	Stefano Morozzi	01/2020
9574	44^49524+43	81391	Norbert Schneider	06/2014
9575	(3*2^270368-1)/13	81389	Lelio R Paula	02/2014
9576	96*10^81387-7	81389	Robert Price	03/2021
9577	19548^14563+14563^19548	81384	Hans Havermann	05/2020
9578	(2^270337+1130)/2	81380	Stefano Morozzi	01/2020
9579	27405^932+932^27405	81377	Hans Havermann	05/2020
9580	19396^15683+15683^19396	81375	Hans Havermann	05/2020
9582	(10^81363+719)/9	81363	Serge Batalov	12/2014
9581	(734^28393-1)/733	81363	Serge Batalov	08/2020
9583	(10^81353+449)/9	81353	Serge Batalov	12/2014
9584	14^70978-89	81350	Lelio R Paula	11/2015
9585	11^78108-2040	81342	Enzo Doria	12/2012
9586	7*10^81327-57	81328	Robert Price	06/2020
9587	(7*10^81328-79)/9	81328	Robert Price	01/2021
9588	19102^18065+18065^19102	81315	Hans Havermann	07/2020
9589	3^170400-58	81302	Lelio R Paula	12/2015
9590	(17*10^81300-131)/3	81301	Robert Price	12/2017
9591	10^81297+36991	81298	Patrick De Geest	06/2013
9592	10^81297-57	81297	Robert Price	05/2011
9593	(2^270063+3206)/2	81297	Stefano Morozzi	01/2020
9594	19359^15826+15826^19359	81296	Hans Havermann	06/2020
9595	2^270055-113047	81295	Enzo Doria	07/2014
9596	18^64759-55	81291	Lelio R Paula	11/2015
9597	3*10^81290-17	81291	Robert Price	03/2021
9598	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
9599	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
9600	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014
9601	(194^35521-1)/193	81263	Serge Batalov	08/2020
9602	20722^8343+8343^20722	81258	Hans Havermann	07/2020
9603	(2^269922+3574)/2	81255	Stefano Morozzi	01/2020
9604	21310^6497+6497^21310	81249	Hans Havermann	07/2020
9605	(16392^19273-1)/16391	81225	Serge Batalov	08/2020
9606	2^269819-4597	81224	Yves Minet	03/2019
9607	(2^269816+7)/424901	81218	Lelio R Paula	12/2012
9608	23470^2887+2887^23470	81217	Hans Havermann	05/2020
9609	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
9610	(2^269720+3778)/2	81194	Stefano Morozzi	01/2020
9611	(17*2^269720+1)/303	81193	Lelio R Paula	07/2012
9612	56^46441-55^46441	81188	Robert Price	10/2013
9613	2^269664+177	81177	Lelio R Paula	06/2012
9614	(13*2^269665-1)/185	81177	Lelio R Paula	02/2014
9615	21642^5615+5615^21642	81144	Hans Havermann	07/2020
9616	2^269539-112249	81140	Enzo Doria	06/2014
9617	((2170026-3)3^(170026-1)+1)/4	81128	Robert Price	01/2015
9619	(2^269495-5)/9	81126	Lelio R Paula	12/2012
9618	1239^26228+26228^1239	81126	Norbert Schneider	10/2019
9620	2^269490-3623	81125	Yves Minet	10/2009
9621	(55459*2^269444+1)/35	81114	Lelio R Paula	06/2014
9622	19554^14065+14065^19554	81113	Hans Havermann	06/2020
9623	(2^269417+78557)/5257	81099	Lelio R Paula	12/2012
9624	4*5^116011-7	81089	Lelio R Paula	10/2014
9625	(2^269349+2366)/2	81082	Stefano Morozzi	01/2020
9626	(2^269303+2946)/2	81068	Stefano Morozzi	01/2020
9627	6*10^81060+53	81061	Robert Price	05/2020
9628	7*10^81058+79	81059	Robert Price	02/2017
9629	2^269236-109907	81049	Enzo Doria	04/2014
9630	(2^269182+1870)/2	81032	Stefano Morozzi	01/2020
9631	(2^269179+3006)/2	81031	Stefano Morozzi	01/2020
9632	(8*10^81029-11)/3	81030	Erik Branger	03/2014
9633	19749^12668+12668^19749	81025	Hans Havermann	05/2020
9634	3*10^81021+7	81022	Erik Branger	11/2013
9635	6^104115+103	81018	Lelio R Paula	12/2015
9636	2^269120+1869151	81014	Enzo Doria	05/2016
9637	5^115901+12	81012	Lelio R Paula	10/2015
9638	(622*10^80999-1)/9	81001	Robert Price	11/2021
9639	(2^269072+3610)/2	80999	Stefano Morozzi	01/2020
9640	(2^269083-9)/320369	80997	Lelio R Paula	12/2012
9641	(5*10^80992-179)/3	80993	Robert Price	10/2020
9642	2*10^80981-49	80982	Robert Price	09/2020
9643	(2^269002+1614)/2	80978	Stefano Morozzi	01/2020
9644	17^65810-20	80976	Lelio R Paula	11/2015
9645	20^62236-23	80971	Lelio R Paula	01/2016
9646	2^268974-112181	80970	Enzo Doria	06/2014
9648	L(387433)	80969	Renaud Lifchitz	11/2003
9647	V(387433)	80969	Serge Batalov	03/2015
9649	22732^3645+3645^22732	80965	Hans Havermann	06/2020
9650	(2^268957+602)/2	80964	Stefano Morozzi	01/2020
9651	(2^268955-509203)/5	80963	Lelio R Paula	12/2012
9652	19485^14284+14284^19485	80958	Hans Havermann	05/2020
9653	(87398^16384+1)/65537	80957	Lelio R Paula	11/2011
9654	329^32160+32160^329	80954	Norbert Schneider	11/2014
9655	19678^12973+12973^19678	80937	Hans Havermann	02/2020
9656	(2^268864+3558)/2	80936	Stefano Morozzi	01/2020
9657	2^268859-159	80935	Lelio R Paula	05/2012
9658	(2^268841-lucasV(1,2,268841)+1)/2	80929	Mike Oakes	11/2016
9660	2^268827+5775	80925	Lelio R Paula	07/2013
9659	2^268824-110255	80925	Enzo Doria	05/2014
9661	(2^268824+1902)/2	80924	Stefano Morozzi	01/2020
9662	2^268798-1868321	80917	Enzo Doria	04/2016
9663	20613^8420+8420^20613	80913	Hans Havermann	03/2020
9664	2^268753-114621	80903	Enzo Doria	05/2015
9665	2^268743+1605	80900	Lelio R Paula	07/2013
9666	6^103954-139	80892	Lelio R Paula	12/2015
9667	10^80883+49	80884	Robert Price	03/2011
9668	10^80883-80327	80883	Patrick De Geest	07/2013
9669	6^103937+121	80879	Lelio R Paula	12/2015
9670	148^37266+147	80877	Norbert Schneider	12/2018
9671	(26*10^80875-119)/3	80876	Robert Price	07/2016
9672	(22699*2^268657+1)/6351	80875	Lelio R Paula	06/2014
9673	(2^268612+2530)/2	80860	Stefano Morozzi	01/2020
9674	2^268581-869688105	80851	Lelio R Paula	05/2016
9675	10^80849-70001	80849	Robert Price	12/2021
9676	(11*2^268521-1)/3	80834	Lelio R Paula	02/2014
9677	2^268516-249	80832	Yves Minet	02/2012
9678	22259^4278+4278^22259	80828	Hans Havermann	03/2020
9679	2^268500+16095	80827	Lelio R Paula	07/2013
9680	3^169402+100	80826	Lelio R Paula	12/2015
9681	(2^268495+566)/2	80825	Stefano Morozzi	01/2020
9682	9^84698+8^(84698-1)	80823	Robert Price	03/2016
9683	2^268472-109739	80819	Enzo Doria	04/2014
9684	(9*2^268454+1)/37	80813	Lelio R Paula	12/2012
9685	(3*2^268502+1)/377902188435353647	80811	Lelio R Paula	12/2012
9686	(2^268441+3962)/2	80809	Stefano Morozzi	01/2020
9687	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
9688	15^68702-76	80800	Lelio R Paula	11/2015
9689	2^268408+7	80799	Lelio R Paula	05/2012
9690	(16095^19207-1)/16094	80794	Serge Batalov	08/2020
9691	2^268375+141	80789	Lelio R Paula	05/2012
9692	12^74856-47	80784	Lelio R Paula	11/2015
9693	2^268346+524287	80781	Paul Underwood	08/2018
9694	9*10^80777-41	80778	Robert Price	08/2020
9695	(10868^20011-1)/10867	80764	Serge Batalov	08/2020
9696	6^103770-107	80749	Lelio R Paula	12/2015
9697	(751^28081-1)/750	80748	Serge Batalov	08/2020
9698	3^169224-62	80741	Lelio R Paula	12/2015
9699	p(16866)#/2+64	80741	Robert Price	03/2017
9700	5^115502-72	80733	Lelio R Paula	10/2015
9701	(2^268154+2262)/2	80723	Stefano Morozzi	01/2020
9702	(2^268156+1290)/2	80723	Stefano Morozzi	01/2020
9704	2^268079-1927	80700	Yves Minet	10/2009
9703	(2^268078+2514)/2	80700	Stefano Morozzi	01/2020
9705	(13*10^80685+71)/3	80686	Robert Price	06/2021
9706	2^268028+117	80685	Lelio R Paula	05/2012
9707	121^38738+120	80683	Norbert Schneider	01/2015
9708	(3^169097-8)/835	80677	Lelio R Paula	12/2012
9709	(2^267956+1810)/2	80663	Stefano Morozzi	01/2020
9710	19359^14666+14666^19359	80656	Hans Havermann	12/2019
9711	2^267918+67	80652	Lelio R Paula	05/2012
9712	(89*10^80650-179)/9	80651	Robert Price	11/2017
9713	(2^267914+2094)/2	80650	Stefano Morozzi	01/2020
9714	(2^267894+2202)/2	80644	Stefano Morozzi	01/2020
9715	(302*10^80638+13)/9	80640	Robert Price	01/2017
9716	3^169004+2660	80636	Lelio R Paula	12/2015
9717	2^267860-112859	80634	Enzo Doria	06/2014
9718	96*10^80624-7	80626	Robert Price	03/2021
9719	2^267828-110705	80625	Enzo Doria	05/2014
9720	(2956^23227-1)/2955	80611	Serge Batalov	08/2020
9721	(2^267752+2602)/2	80602	Stefano Morozzi	01/2020
9722	2^267743+12705	80599	Lelio R Paula	07/2013
9723	(22*10^80595+23)/9	80596	Robert Price	03/2015
9724	(2^267712+2358)/2	80590	Stefano Morozzi	01/2020
9725	(2^267685+854)/2	80581	Stefano Morozzi	01/2020
9726	2^267674-51	80578	Lelio R Paula	05/2012
9727	(86*10^80571-41)/9	80572	Robert Price	11/2015
9728	(2^267637+2454)/2	80567	Stefano Morozzi	01/2020
9729	20452^8693+8693^20452	80564	Hans Havermann	02/2020
9730	2^267612-1965	80560	Lelio R Paula	07/2013
9731	2^267553+4097	80542	Lelio R Paula	07/2013
9732	7^95276-8	80518	Robert Price	01/2014
9733	(15185*2^267457-1)/47829	80513	Lelio R Paula	04/2015
9734	6^103467+163	80513	Lelio R Paula	12/2015
9735	20283^9314+9314^20283	80506	Hans Havermann	02/2020
9736	(2^267387+2294)/2	80492	Stefano Morozzi	01/2020
9737	(7*10^80490+143)/3	80491	Robert Price	04/2016
9738	19887^11152+11152^19887	80490	Hans Havermann	01/2020
9739	(2^267348+3810)/2	80480	Stefano Morozzi	01/2020
9740	86^41597-85^41597	80470	Robert Price	04/2015
9741	13^72237+30	80468	Lelio R Paula	11/2015
9742	17^65389+14	80458	Lelio R Paula	11/2015
9743	423^30634+30634^423	80456	Norbert Schneider	05/2017
9744	(2^267257+470)/2	80453	Stefano Morozzi	01/2020
9745	2^267232+105	80445	Lelio R Paula	05/2012
9747	(298*10^80442+11)/3	80444	Robert Price	11/2020
9746	(55*10^80443+629)/9	80444	Robert Price	01/2022
9748	22101^4360+4360^22101	80437	Hans Havermann	02/2020
9749	11^77237-3072000	80435	Enzo Doria	01/2013
9750	20696^7689+7689^20696	80422	Hans Havermann	01/2020

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Probable Primes Top 10000

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