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 ?
6501	10^90209-724797	90209	Patrick De Geest	07/2019
6502	10^90208+189531	90209	Patrick De Geest	07/2019
6503	10^90208-2247	90208	Patrick De Geest	09/2018
6504	(629^32233-1)/628	90207	Michael Stocker	05/2020
6505	116^43693-115	90203	Norbert Schneider	08/2018
6506	10^90202+3553	90203	Patrick De Geest	09/2018
6508	3^189053+280	90202	Lelio R Paula	04/2016
6507	10^90202-67793	90202	Patrick De Geest	07/2019
6509	2^299639-187	90201	Lelio R Paula	10/2012
6510	10^90199+254031	90200	Patrick De Geest	07/2019
6511	10^90199-2891	90199	Patrick De Geest	09/2018
6513	2^299631+183	90198	Lelio R Paula	10/2012
6512	21567^15212+15212^21567	90198	Hans Havermann	08/2020
6514	10^90196+187539	90197	Patrick De Geest	07/2019
6516	10^90196-9683	90196	Patrick De Geest	09/2018
6515	21708^14287+14287^21708	90196	Hans Havermann	08/2020
6517	10^90193+104973	90194	Patrick De Geest	07/2019
6518	10^90193-9809	90193	Patrick De Geest	09/2018
6519	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
6520	(2277^26863-1)/2276	90186	Serge Batalov	08/2020
6521	2^299567+113	90179	Lelio R Paula	10/2012
6522	2^299550+189	90174	Lelio R Paula	10/2012
6523	10^90170+376063	90171	Patrick De Geest	07/2019
6524	10^90170-6749	90170	Patrick De Geest	09/2018
6525	(2^299535+3)/29	90168	Lelio R Paula	01/2013
6526	(2^299521+13)/15	90164	Stefano Morozzi	03/2020
6527	22316^10971+10971^22316	90163	Hans Havermann	08/2020
6528	10^90160+271947	90161	Patrick De Geest	07/2019
6529	10^90160-5613	90160	Patrick De Geest	09/2018
6530	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
6532	3^188938+8680	90147	Lelio R Paula	04/2016
6531	10^90146+160209	90147	Patrick De Geest	07/2019
6533	10^90146-2027	90146	Patrick De Geest	09/2018
6534	6^115840-55	90142	Lelio R Paula	05/2016
6535	(5*10^90142-473)/9	90142	Robert Price	12/2017
6536	8*7^106659+5	90139	Lelio R Paula	10/2014
6539	2^299406-16653	90131	Enzo Doria	05/2013
6537	(317057^16384+1)/2	90131	Richard Fischer	10/2019
6538	(2^299409+834)/2	90131	Stefano Morozzi	01/2020
6540	10^90128+288673	90129	Patrick De Geest	07/2019
6542	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
6541	10^90128-8387	90128	Patrick De Geest	09/2018
6543	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
6544	6^115819-53	90125	Lelio R Paula	05/2016
6545	10^90123+6313	90124	Patrick De Geest	09/2018
6547	6^115816-16853	90123	Enzo Doria	02/2013
6546	10^90123-22617	90123	Patrick De Geest	07/2019
6548	6^115813-23	90121	Lelio R Paula	05/2016
6549	(22*10^90110+161)/3	90111	Robert Price	02/2017
6551	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
6550	10^90105+915759	90106	Patrick De Geest	07/2019
6553	10^90105-767	90105	Patrick De Geest	09/2018
6552	10^90104+48189	90105	Patrick De Geest	07/2019
6554	(6050^23827-1)/6049	90105	Serge Batalov	08/2020
6555	10^90104-7703	90104	Patrick De Geest	09/2018
6556	10^90103+9159	90104	Patrick De Geest	09/2018
6557	10^90103-208457	90103	Patrick De Geest	07/2019
6558	10^90102+73011	90103	Patrick De Geest	07/2019
6559	10^90102-602433	90102	Patrick De Geest	07/2019
6560	10^90101+1225537	90102	Patrick De Geest	07/2019
6561	10^90101-3207	90101	Patrick De Geest	09/2018
6562	21730^14007+14007^21730	90101	Hans Havermann	08/2020
6563	(29*10^90096-17)/3	90097	Erik Branger	09/2014
6564	10^90089+143181	90090	Patrick De Geest	07/2019
6565	10^90089-3573	90089	Patrick De Geest	09/2018
6566	2^299247+1870529	90083	Enzo Doria	05/2016
6567	10^90079+1609	90080	Patrick De Geest	09/2018
6568	10^90079-230043	90079	Patrick De Geest	07/2019
6569	2^299229-2797783	90077	Enzo Doria	04/2016
6570	2^299220-16317	90075	Enzo Doria	04/2013
6571	11^86491-1350	90072	Enzo Doria	12/2012
6572	10^90071+52333	90072	Patrick De Geest	07/2019
6574	10^90071-1233	90071	Patrick De Geest	09/2018
6573	(314401^16384+1)/2	90071	Richard Fischer	10/2019
6575	10^90069+158527	90070	Patrick De Geest	07/2019
6576	10^90069-7841	90069	Patrick De Geest	09/2018
6577	(31*10^90064-1)/3	90066	Robert Price	03/2017
6578	10^90060+149431	90061	Patrick De Geest	07/2019
6579	10^90060-839	90060	Patrick De Geest	09/2018
6580	10^90052+2361	90053	Patrick De Geest	09/2018
6581	10^90052-90929	90052	Patrick De Geest	07/2019
6582	10^90047+619	90048	Patrick De Geest	09/2018
6583	10^90047-151071	90047	Patrick De Geest	07/2019
6584	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
6585	22996^8233+8233^22996	90043	Hans Havermann	08/2020
6586	2^299112+73951	90042	Enzo Doria	04/2016
6587	8^99702+7^(99702-1)	90040	Robert Price	02/2016
6588	10^90038+157803	90039	Patrick De Geest	07/2019
6589	10^90038-9687	90038	Patrick De Geest	09/2018
6591	5*10^90033+3	90034	Dmitry Domanov	11/2010
6590	(17574^21211-1)/17573	90034	Serge Batalov	08/2020
6592	10^90030+225813	90031	Patrick De Geest	07/2019
6593	10^90030-1461	90030	Patrick De Geest	09/2018
6594	243^37738+37738^243	90029	Norbert Schneider	01/2015
6595	10^90025+70569	90026	Patrick De Geest	07/2019
6596	10^90025-8703	90025	Patrick De Geest	09/2018
6597	2^299048-113297	90023	Enzo Doria	07/2014
6598	10^90015+849	90016	Patrick De Geest	09/2018
6599	10^90015-228387	90015	Patrick De Geest	07/2019
6600	10^90010+6811	90011	Patrick De Geest	09/2018
6601	10^90010-183597	90010	Patrick De Geest	11/2018
6602	10^90009+58321	90010	Patrick De Geest	11/2018
6603	10^90008+847	90009	Patrick De Geest	09/2018
6604	10^90009-356013	90009	Patrick De Geest	11/2018
6605	25696^3183+3183^25696	90009	Hans Havermann	08/2020
6607	3^188648+92	90008	Lelio R Paula	12/2015
6606	10^90008-706049	90008	Patrick De Geest	11/2018
6608	5*2^298991+7	90006	Lelio R Paula	08/2014
6609	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
6610	10^90000+8869	90001	Patrick De Geest	12/2009
6612	10^89999+82939	90000	Dirk Augustin	04/2007
6611	10^90000-140343	90000	Patrick De Geest	12/2009
6613	10^89999-194891	89999	Patrick De Geest	11/2009
6614	(2^298918+1798)/2	89983	Stefano Morozzi	01/2020
6615	19^70365-78	89980	Lelio R Paula	12/2015
6616	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
6617	2^298852-64875	89964	Lelio R Paula	11/2013
6618	(2^298825+1010)/2	89955	Stefano Morozzi	01/2020
6619	18^71659+37	89952	Lelio R Paula	12/2015
6620	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
6621	(2^298769+1202)/2	89939	Stefano Morozzi	01/2020
6622	(5941^23827-1)/5940	89916	Serge Batalov	08/2020
6623	17^73067+20	89906	Lelio R Paula	11/2015
6624	2^298637-99	89899	Lelio R Paula	10/2012
6625	25513^3336+3336^25513	89889	Hans Havermann	08/2020
6626	29748^1051+1051^29748	89887	Hans Havermann	08/2020
6627	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
6628	(2^298558+3654)/2	89875	Stefano Morozzi	01/2020
6629	9*10^89858+19	89859	Robert Price	05/2016
6630	2^298501+1870067	89858	Enzo Doria	05/2016
6631	(286*10^89852-1)/3	89854	Robert Price	11/2020
6632	11^86280-98	89852	Lelio R Paula	11/2015
6633	2^298473-110059	89850	Enzo Doria	04/2014
6634	19^70263-32	89850	Lelio R Paula	12/2015
6635	21208^17221+17221^21208	89839	Hans Havermann	08/2020
6636	(299*10^89836-17)/3	89838	Robert Price	01/2017
6637	3^188286+14	89836	Robert Price	09/2013
6638	(2^298408+450)/2	89830	Stefano Morozzi	01/2020
6639	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
6640	2^298367+58905	89818	Lelio R Paula	11/2013
6641	21966^12269+12269^21966	89815	Hans Havermann	08/2020
6642	(2^298333+3126)/2	89807	Stefano Morozzi	01/2020
6643	2^298319-109657	89803	Enzo Doria	04/2014
6644	8*10^89800+81	89801	Robert Price	05/2017
6645	21354^16037+16037^21354	89797	Hans Havermann	08/2020
6646	(2^298249+714)/2	89782	Stefano Morozzi	01/2020
6647	21227^16954+16954^21227	89775	Hans Havermann	08/2020
6648	(733^31333-1)/732	89770	Serge Batalov	08/2020
6651	18^71505-91	89759	Lelio R Paula	12/2015
6649	(2^298171+1586)/2	89759	Stefano Morozzi	01/2020
6650	(4788^24391-1)/4787	89759	Serge Batalov	08/2020
6652	(2^298161+3530)/2	89756	Stefano Morozzi	01/2020
6653	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
6654	2^298079-109531	89731	Enzo Doria	04/2014
6655	(9255^22621-1)/9254	89720	Serge Batalov	08/2020
6656	117^43380+116	89718	Norbert Schneider	08/2018
6657	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
6658	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
6659	2^298003-66945	89708	Lelio R Paula	11/2013
6660	(23*10^89705-83)/3	89706	Robert Price	09/2017
6661	17^72900-54	89700	Lelio R Paula	11/2015
6662	(2^297968+2482)/2	89698	Stefano Morozzi	01/2020
6663	3*2^297956+5	89695	Lelio R Paula	08/2014
6664	(2^297952+3558)/2	89693	Stefano Morozzi	01/2020
6665	(3992^24907-1)/3991	89692	Serge Batalov	08/2020
6666	20^68938-11	89691	Lelio R Paula	01/2016
6667	89*10^89687-7	89689	Robert Price	03/2017
6668	(6882^23371-1)/6881	89688	Serge Batalov	08/2020
6669	(297847^16384+1)/2	89686	Richard Fischer	08/2019
6670	2^297923+77783	89684	Enzo Doria	05/2016
6671	(2^297893+1694)/2	89675	Stefano Morozzi	01/2020
6672	11^86107-24576000	89672	Enzo Doria	02/2013
6673	2^297878-111911	89671	Enzo Doria	05/2014
6674	20823^20236+20236^20823	89667	Hans Havermann	08/2020
6675	25708^3075+3075^25708	89666	Hans Havermann	08/2020
6676	21002^18585+18585^21002	89661	Hans Havermann	08/2020
6677	(2^297830+3670)/2	89656	Stefano Morozzi	01/2020
6678	7^106084+40	89652	Lelio R Paula	10/2015
6679	(2^297815+618)/2	89651	Stefano Morozzi	01/2020
6680	21223^16752+16752^21223	89648	Hans Havermann	08/2020
6682	(86*10^89640-311)/9	89641	Robert Price	10/2017
6681	(2^297781+2094)/2	89641	Stefano Morozzi	01/2020
6683	(2^297741+3326)/2	89629	Stefano Morozzi	01/2020
6684	(2^297724+3606)/2	89624	Stefano Morozzi	01/2020
6685	3*10^89608-59	89609	Robert Price	10/2017
6686	(2^297650+3250)/2	89602	Stefano Morozzi	01/2020
6687	3^187780-11038	89594	Enzo Doria	05/2014
6688	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
6689	5^128141-36	89567	Lelio R Paula	10/2015
6690	4*7^105951+9	89540	Lelio R Paula	10/2014
6691	(7*10^89539-439)/9	89539	Robert Price	09/2017
6692	(9772^22441-1)/9771	89536	Serge Batalov	08/2020
6693	22823^8374+8374^22823	89534	Hans Havermann	08/2020
6694	(2^297401+2954)/2	89527	Stefano Morozzi	01/2020
6695	(2^297403+1670)/2	89527	Stefano Morozzi	01/2020
6696	2^297397+177257	89526	Enzo Doria	05/2016
6698	2^297346-16241	89511	Enzo Doria	04/2013
6697	(5*10^89510+79)/3	89511	Robert Price	11/2017
6699	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
6700	2^297328-869688105	89505	Lelio R Paula	07/2016
6701	2^297325-459043	89504	Enzo Doria	05/2015
6702	2^297310-112391	89500	Enzo Doria	06/2014
6703	2^297296-112157	89496	Enzo Doria	06/2014
6704	57^50966-2	89490	Lelio R Paula	08/2013
6705	(266*10^89482+1)/3	89484	Robert Price	02/2016
6706	(14*10^89480-101)/3	89481	Robert Price	04/2017
6707	2618^26175+26175^2618	89466	Norbert Schneider	01/2020
6708	(2^297150+3922)/2	89451	Stefano Morozzi	01/2020
6709	(2^297141+1842)/2	89449	Stefano Morozzi	01/2020
6710	(2^297140+1458)/2	89448	Stefano Morozzi	01/2020
6711	(2^297129+726)/2	89445	Stefano Morozzi	01/2020
6712	2^297122+99	89443	Lelio R Paula	10/2012
6713	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
6714	(28*10^89425+101)/3	89426	Robert Price	09/2020
6715	(2^297037+3522)/2	89417	Stefano Morozzi	01/2020
6716	(25*10^89413+161)/3	89414	Robert Price	01/2017
6717	29080^1187+1187^29080	89406	Hans Havermann	08/2020
6718	2^296990+1870699	89403	Enzo Doria	05/2016
6719	2^296972-1017	89398	Lelio R Paula	11/2013
6720	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
6721	(85*10^89375-31)/9	89376	Robert Price	11/2015
6722	9*2^296870+7	89368	Lelio R Paula	08/2014
6723	100^44683-99^44683	89366	Robert Price	07/2013
6724	2^296810+76519	89349	Enzo Doria	05/2016
6725	(2747^25981-1)/2746	89342	Serge Batalov	08/2020
6726	8^98928+7^(98928+1)	89341	Robert Price	06/2016
6728	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
6727	21832^12359+12359^21832	89337	Hans Havermann	08/2020
6729	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
6730	2^296736-432149	89327	Paul Bourdelais	05/2013
6731	2^296737-112519	89327	Enzo Doria	06/2014
6732	2^296718-3645	89322	Lelio R Paula	11/2013
6733	(2^296702+2338)/2	89316	Stefano Morozzi	01/2020
6734	2^296681-16221	89310	Enzo Doria	04/2013
6735	2^296669-16513	89307	Enzo Doria	04/2013
6736	(2^296626+1282)/2	89294	Stefano Morozzi	01/2020
6737	2^296619-16357	89292	Enzo Doria	04/2013
6738	2^296614-110051	89290	Enzo Doria	04/2014
6739	(2^296601+1730)/2	89286	Stefano Morozzi	01/2020
6740	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
6741	(2*10^89279+457)/9	89279	Robert Price	01/2017
6742	(2^296568+1222)/2	89276	Stefano Morozzi	01/2020
6743	15^75907-28	89274	Lelio R Paula	11/2015
6744	2^296547-37	89270	Yves Minet	01/2012
6745	2^296485+191	89251	Lelio R Paula	10/2012
6746	2^296467-75	89246	Lelio R Paula	10/2012
6747	(2^296462+1674)/2	89244	Stefano Morozzi	01/2020
6748	2^296416-109535	89231	Enzo Doria	04/2014
6749	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
6750	66^49037-65	89225	Norbert Schneider	11/2014

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Probable Primes Top 10000

(277054 PRPs in the top)