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	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
9502	(2^298769+1202)/2	89939	Stefano Morozzi	01/2020
9503	(5941^23827-1)/5940	89916	Serge Batalov	08/2020
9504	17^73067+20	89906	Lelio R Paula	11/2015
9505	2^298637-99	89899	Lelio R Paula	10/2012
9506	25513^3336+3336^25513	89889	Hans Havermann	08/2020
9507	29748^1051+1051^29748	89887	Hans Havermann	08/2020
9508	9*10^89882-91	89883	Robert Price	06/2021
9509	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
9510	2*10^89876+83	89877	Robert Price	12/2021
9511	(2^298558+3654)/2	89875	Stefano Morozzi	01/2020
9512	9*10^89858+19	89859	Robert Price	05/2016
9513	2^298501+1870067	89858	Enzo Doria	05/2016
9514	(286*10^89852-1)/3	89854	Robert Price	11/2020
9515	11^86280-98	89852	Lelio R Paula	11/2015
9516	2^298473-110059	89850	Enzo Doria	04/2014
9517	19^70263-32	89850	Lelio R Paula	12/2015
9518	21208^17221+17221^21208	89839	Hans Havermann	08/2020
9519	(299*10^89836-17)/3	89838	Robert Price	01/2017
9520	3^188286+14	89836	Robert Price	09/2013
9521	(2^298408+450)/2	89830	Stefano Morozzi	01/2020
9522	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
9523	2^298367+58905	89818	Lelio R Paula	11/2013
9524	21966^12269+12269^21966	89815	Hans Havermann	08/2020
9525	(2^298333+3126)/2	89807	Stefano Morozzi	01/2020
9526	2^298319-109657	89803	Enzo Doria	04/2014
9527	7*10^89801+13	89802	Robert Price	03/2021
9528	8*10^89800+81	89801	Robert Price	05/2017
9529	21354^16037+16037^21354	89797	Hans Havermann	08/2020
9530	(2^298249+714)/2	89782	Stefano Morozzi	01/2020
9531	21227^16954+16954^21227	89775	Hans Havermann	08/2020
9532	(733^31333-1)/732	89770	Serge Batalov	08/2020
9535	18^71505-91	89759	Lelio R Paula	12/2015
9533	(2^298171+1586)/2	89759	Stefano Morozzi	01/2020
9534	(4788^24391-1)/4787	89759	Serge Batalov	08/2020
9536	(2^298161+3530)/2	89756	Stefano Morozzi	01/2020
9537	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
9538	2^298079-109531	89731	Enzo Doria	04/2014
9539	(9255^22621-1)/9254	89720	Serge Batalov	08/2020
9540	117^43380+116	89718	Norbert Schneider	08/2018
9541	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
9542	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
9543	2^298003-66945	89708	Lelio R Paula	11/2013
9544	(23*10^89705-83)/3	89706	Robert Price	09/2017
9545	17^72900-54	89700	Lelio R Paula	11/2015
9546	(2^297968+2482)/2	89698	Stefano Morozzi	01/2020
9547	3*2^297956+5	89695	Lelio R Paula	08/2014
9548	(2^297952+3558)/2	89693	Stefano Morozzi	01/2020
9549	(3992^24907-1)/3991	89692	Serge Batalov	08/2020
9550	20^68938-11	89691	Lelio R Paula	01/2016
9551	89*10^89687-7	89689	Robert Price	03/2017
9552	(6882^23371-1)/6881	89688	Serge Batalov	08/2020
9553	(297847^16384+1)/2	89686	Richard Fischer	08/2019
9554	2^297923+77783	89684	Enzo Doria	05/2016
9555	(2^297893+1694)/2	89675	Stefano Morozzi	01/2020
9556	11^86107-24576000	89672	Enzo Doria	02/2013
9557	2^297878-111911	89671	Enzo Doria	05/2014
9558	20823^20236+20236^20823	89667	Hans Havermann	08/2020
9559	25708^3075+3075^25708	89666	Hans Havermann	08/2020
9560	21002^18585+18585^21002	89661	Hans Havermann	08/2020
9561	(2^297830+3670)/2	89656	Stefano Morozzi	01/2020
9562	7^106084+40	89652	Lelio R Paula	10/2015
9563	(2^297815+618)/2	89651	Stefano Morozzi	01/2020
9564	21223^16752+16752^21223	89648	Hans Havermann	08/2020
9566	(86*10^89640-311)/9	89641	Robert Price	10/2017
9565	(2^297781+2094)/2	89641	Stefano Morozzi	01/2020
9567	(2^297741+3326)/2	89629	Stefano Morozzi	01/2020
9568	(2^297724+3606)/2	89624	Stefano Morozzi	01/2020
9569	3*10^89608-59	89609	Robert Price	10/2017
9570	(2^297650+3250)/2	89602	Stefano Morozzi	01/2020
9571	(34*10^89599+191)/9	89600	Robert Price	08/2021
9572	3^187780-11038	89594	Enzo Doria	05/2014
9573	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
9574	5^128141-36	89567	Lelio R Paula	10/2015
9575	4*7^105951+9	89540	Lelio R Paula	10/2014
9576	(7*10^89539-439)/9	89539	Robert Price	09/2017
9577	(9772^22441-1)/9771	89536	Serge Batalov	08/2020
9578	22823^8374+8374^22823	89534	Hans Havermann	08/2020
9579	(2^297401+2954)/2	89527	Stefano Morozzi	01/2020
9580	(2^297403+1670)/2	89527	Stefano Morozzi	01/2020
9581	2^297397+177257	89526	Enzo Doria	05/2016
9582	(77*10^89518+247)/9	89519	Robert Price	03/2021
9583	2^297346-16241	89511	Enzo Doria	04/2013
9584	(5*10^89510+79)/3	89511	Robert Price	11/2017
9586	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
9585	2^297328-869688105	89505	Lelio R Paula	07/2016
9587	2^297325-459043	89504	Enzo Doria	05/2015
9588	2^297310-112391	89500	Enzo Doria	06/2014
9589	2^297296-112157	89496	Enzo Doria	06/2014
9590	57^50966-2	89490	Lelio R Paula	08/2013
9591	(266*10^89482+1)/3	89484	Robert Price	02/2016
9592	(14*10^89480-101)/3	89481	Robert Price	04/2017
9593	2618^26175+26175^2618	89466	Norbert Schneider	01/2020
9594	(2^297150+3922)/2	89451	Stefano Morozzi	01/2020
9595	(2^297141+1842)/2	89449	Stefano Morozzi	01/2020
9596	(2^297140+1458)/2	89448	Stefano Morozzi	01/2020
9597	(2^297129+726)/2	89445	Stefano Morozzi	01/2020
9598	2^297122+99	89443	Lelio R Paula	10/2012
9599	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
9600	(28*10^89425+101)/3	89426	Robert Price	09/2020
9601	(2^297037+3522)/2	89417	Stefano Morozzi	01/2020
9602	(25*10^89413+161)/3	89414	Robert Price	01/2017
9603	(89*10^89411-737)/9	89412	Robert Price	01/2022
9604	29080^1187+1187^29080	89406	Hans Havermann	08/2020
9605	2^296990+1870699	89403	Enzo Doria	05/2016
9606	2^296972-1017	89398	Lelio R Paula	11/2013
9607	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
9608	(85*10^89375-31)/9	89376	Robert Price	11/2015
9609	9*2^296870+7	89368	Lelio R Paula	08/2014
9610	100^44683-99^44683	89366	Robert Price	07/2013
9611	2^296810+76519	89349	Enzo Doria	05/2016
9612	(2747^25981-1)/2746	89342	Serge Batalov	08/2020
9613	8^98928+7^(98928+1)	89341	Robert Price	06/2016
9615	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
9614	21832^12359+12359^21832	89337	Hans Havermann	08/2020
9616	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
9617	2^296736-432149	89327	Paul Bourdelais	05/2013
9618	2^296737-112519	89327	Enzo Doria	06/2014
9619	2^296718-3645	89322	Lelio R Paula	11/2013
9620	(2^296702+2338)/2	89316	Stefano Morozzi	01/2020
9621	2^296681-16221	89310	Enzo Doria	04/2013
9622	2^296669-16513	89307	Enzo Doria	04/2013
9623	(2^296626+1282)/2	89294	Stefano Morozzi	01/2020
9624	2^296619-16357	89292	Enzo Doria	04/2013
9625	2^296614-110051	89290	Enzo Doria	04/2014
9626	(2^296601+1730)/2	89286	Stefano Morozzi	01/2020
9627	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
9628	(2*10^89279+457)/9	89279	Robert Price	01/2017
9629	(2^296568+1222)/2	89276	Stefano Morozzi	01/2020
9630	(133*10^89273+17)/3	89275	Robert Price	11/2021
9631	15^75907-28	89274	Lelio R Paula	11/2015
9632	2^296547-37	89270	Yves Minet	01/2012
9633	2^296485+191	89251	Lelio R Paula	10/2012
9634	2^296467-75	89246	Lelio R Paula	10/2012
9635	(2^296462+1674)/2	89244	Stefano Morozzi	01/2020
9636	2^296416-109535	89231	Enzo Doria	04/2014
9637	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
9638	66^49037-65	89225	Norbert Schneider	11/2014
9639	2^296377-16245	89219	Enzo Doria	04/2013
9640	2^296372-64875	89217	Lelio R Paula	11/2013
9641	5*6^114648-7	89215	Lelio R Paula	10/2014
9642	(2^296361+1262)/2	89214	Stefano Morozzi	01/2020
9643	3*10^89206+13	89207	Robert Price	08/2017
9644	7*3^186960-4	89204	Lelio R Paula	08/2014
9645	(28*10^89203+47)/3	89204	Robert Price	02/2021
9646	2^296290-112133	89193	Enzo Doria	06/2014
9647	6^114620-17003	89192	Enzo Doria	02/2013
9648	(22*10^89190+179)/3	89191	Robert Price	02/2022
9649	(4*10^89189+41)/9	89189	Robert Price	11/2014
9650	2^296261-161181	89184	Enzo Doria	04/2013
9651	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
9652	3^186903-10	89176	Robert Price	09/2013
9653	7*10^89169-3	89170	Dmitry Domanov	11/2010
9654	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
9655	(43*10^89169+47)/9	89170	Robert Price	12/2017
9656	(10^89160+29)/3	89160	Serge Batalov	12/2014
9657	(28*10^89141-97)/3	89142	Robert Price	07/2016
9658	2^296116-734639	89140	Paul Bourdelais	04/2013
9659	(2^296101+1250)/2	89135	Stefano Morozzi	01/2020
9660	22574^8883+8883^22574	89135	Hans Havermann	08/2020
9661	6^114544-133	89133	Lelio R Paula	12/2015
9662	2^296076-113297	89128	Enzo Doria	07/2014
9663	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
9664	5*10^89118+81	89119	Robert Price	08/2017
9665	2^296037-1411	89117	Yves Minet	01/2013
9666	2^296020-2604809	89111	Enzo Doria	05/2015
9667	2^296016+81	89110	Henri Lifchitz	02/2007
9668	2^296010-11	89108	Lelio R Paula	10/2012
9669	2^295998-111911	89105	Enzo Doria	05/2014
9670	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
9671	29529^1040+1040^29529	89090	Hans Havermann	08/2020
9672	2^295939-16621	89087	Enzo Doria	04/2013
9673	2^295934-109691	89086	Enzo Doria	04/2014
9674	(2^295921+2246)/2	89081	Stefano Morozzi	01/2020
9675	(185*10^89070-11)/3	89072	Robert Price	10/2020
9676	(185*10^89063+7)/3	89065	Robert Price	02/2017
9677	(8*10^89055-59)/3	89056	Robert Price	08/2021
9678	2^295831+143	89055	Lelio R Paula	10/2012
9679	31^59713-30	89054	Theodore Burton	02/2007
9680	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
9681	79731!4-32	89049	Robert Price	11/2019
9683	123^42608+2	89047	Lelio R Paula	05/2013
9682	6^114433-114433^6	89047	Norbert Schneider	04/2017
9684	2^295800-459659	89045	Enzo Doria	05/2015
9685	(52*10^89037-1)/3	89039	Robert Price	02/2017
9686	(2^295782+1870)/2	89039	Stefano Morozzi	01/2020
9687	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
9688	11^85470-5850	89008	Enzo Doria	02/2013
9689	(2^295650+522)/2	89000	Stefano Morozzi	01/2020
9690	(35*10^88998+37)/9	88999	Robert Price	05/2022
9691	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
9692	(p(18424)#-4)/2	88985	Robert Price	09/2017
9693	2^295564-189	88974	Lelio R Paula	10/2012
9694	2^295557+73097	88972	Enzo Doria	04/2016
9695	11^85433-5760	88970	Enzo Doria	01/2013
9696	23074^7165+7165^23074	88956	Hans Havermann	08/2020
9697	(2^295479+3050)/2	88948	Stefano Morozzi	01/2020
9698	6*10^88938-91	88939	Robert Price	11/2017
9699	15^75619-88	88935	Lelio R Paula	11/2015
9700	(2^295433+2234)/2	88934	Stefano Morozzi	01/2020
9701	(15589^21211-1)/15588	88930	Serge Batalov	08/2020
9702	23776^5499+5499^23776	88929	Hans Havermann	08/2020
9703	21112^16291+16291^21112	88923	Hans Havermann	08/2020
9704	2^295385-85	88920	Lelio R Paula	10/2012
9705	2^295385-16333	88920	Enzo Doria	04/2013
9706	(89*10^88916-377)/9	88917	Robert Price	07/2021
9707	79617!4+32	88909	Robert Price	09/2019
9708	22077^10640+10640^22077	88903	Hans Havermann	08/2020
9709	2^295309+59	88897	Lelio R Paula	10/2012
9710	2^295288-109799	88891	Enzo Doria	04/2014
9711	10^88888+170373	88889	Stefano Morozzi	07/2018
9712	10^88888+271399	88889	Stefano Morozzi	07/2018
9713	10^88888+375397	88889	Stefano Morozzi	07/2018
9714	10^88888+548823	88889	Stefano Morozzi	07/2018
9715	10^88888+820861	88889	Stefano Morozzi	07/2018
9716	10^88888+1206349	88889	Stefano Morozzi	07/2018
9717	10^88888+1292047	88889	Stefano Morozzi	07/2018
9718	10^88888+1456029	88889	Stefano Morozzi	07/2018
9719	10^88888-490287	88888	Patrick De Geest	09/2018
9720	2^295245+65	88878	Lelio R Paula	10/2012
9721	5*10^88874-37	88875	Robert Price	11/2021
9723	Padovan(727734)	88874	Eric W. Weisstein	04/2011
9722	(2^295231+1554)/2	88874	Stefano Morozzi	01/2020
9724	79585!4-32	88870	Robert Price	11/2019
9725	18^70793-17	88865	Lelio R Paula	11/2015
9726	6^114196-17573	88862	Enzo Doria	02/2013
9727	302^35829+35829^302	88857	Norbert Schneider	12/2014
9728	3^186223+16	88851	Robert Price	10/2013
9729	3*2^295139+7	88847	Lelio R Paula	08/2014
9730	3^186212-113008	88846	Enzo Doria	07/2014
9731	2*10^88844+23	88845	Robert Price	12/2020
9732	23415^6224+6224^23415	88839	Hans Havermann	08/2020
9733	87^45803-86	88836	Norbert Schneider	11/2015
9734	2^295094-110273	88833	Enzo Doria	05/2014
9735	2^295080+1869151	88828	Enzo Doria	05/2016
9736	(2^295061+2174)/2	88822	Stefano Morozzi	01/2020
9737	2^295027-113407	88812	Enzo Doria	07/2014
9738	(2*10^88808-71)/3	88808	Robert Price	01/2017
9739	(2^295009+2102)/2	88807	Stefano Morozzi	01/2020
9740	13^79722-80	88806	Lelio R Paula	11/2015
9741	21112^16077+16077^21112	88802	Hans Havermann	08/2020
9742	3^186103+104	88794	Lelio R Paula	12/2015
9743	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
9744	(4025^24631-1)/4024	88786	Serge Batalov	08/2020
9745	2^294937-115003	88785	Enzo Doria	06/2015
9746	(2^294923+3134)/2	88781	Stefano Morozzi	01/2020
9747	(15326^21211-1)/15325	88773	Serge Batalov	08/2020
9748	2551^26056+26056^2551	88766	Norbert Schneider	01/2020
9749	2^294868-109709	88765	Enzo Doria	04/2014
9750	2^294864-2985	88763	Yves Minet	09/2014

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Probable Primes Top 10000

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