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	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
6502	4*10^106914-93	106915	Robert Price	07/2020
6503	4*10^106892-3	106893	Robert Price	10/2015
6504	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
6505	2^354946-3	106850	M. Frind & P. Underwood	08/2002
6506	(2^354945+3134)/2	106849	Stefano Morozzi	09/2020
6507	(46^64384+1)/(46^128+1)	106843	Martin Hopf	12/2023
6508	2^354873-18693	106828	Enzo Doria	05/2013
6509	(2^354831+3186)/2	106815	Stefano Morozzi	09/2020
6511	2^354828+4257	106814	Lelio R Paula	01/2017
6510	25216^17217+17217^25216	106814	Hans Havermann	10/2020
6512	(2^354799+1218)/2	106805	Stefano Morozzi	09/2020
6513	436^40459+40459^436	106791	Norbert Schneider	03/2019
6514	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
6515	(115*10^106772-7)/9	106774	Robert Price	02/2020
6516	2^354640-354640+1	106758	Robert Price	10/2014
6517	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
6518	2^354585+95	106741	Lelio R Paula	10/2011
6519	(206*10^106737+1)/9	106739	Robert Price	04/2022
6520	2^354553+189	106732	Lelio R Paula	10/2011
6522	(2^354546+1338)/2	106729	Stefano Morozzi	02/2021
6521	(8*10^106729-71)/9	106729	Serge Batalov	11/2022
6523	2^354514-109031	106720	Enzo Doria	04/2014
6524	2^354509-109465	106718	Enzo Doria	04/2014
6525	fibonacci(510628)+2	106715	Jon Grantham	08/2023
6526	(15*2^354478-1)/26983	106706	Lelio R Paula	03/2014
6527	Phi(217618,10)/899798636917	106693	Makoto Kamada	06/2019
6528	15^90710+28	106684	Lelio R Paula	04/2017
6529	7^126237+34	106683	Lelio R Paula	03/2017
6530	2^354385-115315	106681	Enzo Doria	06/2015
6531	2^354327-19305	106664	Enzo Doria	06/2013
6532	(35*10^106649+1)/9	106650	Serge Batalov	11/2010
6533	10^106636+97	106637	Lelio R Paula	02/2017
6534	10^106636-22923	106636	Patrick De Geest	03/2017
6535	2^354220-57	106631	Lelio R Paula	10/2011
6536	(68*10^106628-329)/9	106629	Robert Price	03/2021
6537	(29*10^106620-77)/3	106621	Robert Price	02/2020
6538	(746*10^106618+1)/9	106620	Robert Price	03/2020
6539	2*10^106613+29	106614	Robert Price	02/2021
6540	2^354157-17041	106612	Enzo Doria	05/2013
6541	12^98778+73	106600	Lelio R Paula	02/2017
6542	33333^1576+1576^33333	106585	Hans Havermann	11/2020
6543	2^354064+1870651	106584	Enzo Doria	05/2016
6544	24568^21779+21779^24568	106577	Hans Havermann	11/2020
6545	2^353992-57	106563	Lelio R Paula	10/2011
6546	9*10^106559+59	106560	Robert Price	01/2020
6547	7*10^106553+27	106554	Robert Price	11/2020
6548	28847^4938+4938^28847	106548	Hans Havermann	10/2020
6550	NSW(139160)	106535	Robert Price	12/2018
6549	f(278321)	106535	Robert Price	07/2023
6551	(7*10^106516+113)/3	106517	Robert Price	02/2018
6552	2^353832-1853849	106515	Enzo Doria	09/2015
6553	(7^126037-1)/6	106513	Paul Bourdelais	09/2008
6554	2^353794-18453	106503	Enzo Doria	05/2013
6555	(2^353761+2094)/2	106493	Stefano Morozzi	09/2020
6556	2^353728+7695	106483	Lelio R Paula	01/2017
6557	26476^10509+10509^26476	106475	Hans Havermann	10/2020
6558	2^353672-303	106466	Yves Minet	02/2012
6559	6^136811+101	106460	Lelio R Paula	02/2017
6560	2^353641+1871981	106457	Enzo Doria	05/2016
6561	(8*10^106454-29)/3	106455	Robert Price	07/2018
6562	27845^6654+6654^27845	106454	Hans Havermann	11/2020
6563	10^106449-700001	106449	Robert Price	08/2021
6564	25316^16017+16017^25316	106444	Hans Havermann	11/2020
6565	2^353553+54615	106431	Lelio R Paula	01/2017
6566	2^353544-18897	106428	Enzo Doria	05/2013
6567	28894^4823+4823^28894	106426	Hans Havermann	11/2020
6568	(19*10^106422+29)/3	106423	Robert Price	12/2021
6569	(694*10^106418+53)/9	106420	Robert Price	02/2022
6570	6*10^106412-13	106413	Robert Price	07/2022
6571	25696^13829+13829^25696	106402	Hans Havermann	11/2020
6572	6^136729-133	106396	Lelio R Paula	02/2017
6573	2^353418+1605	106390	Lelio R Paula	01/2017
6574	2^353387+65	106381	Lelio R Paula	10/2011
6575	2^353372+74311	106376	Enzo Doria	04/2016
6576	2^353344-3693	106368	Yves Minet	03/2017
6577	(772*10^106365-7)/9	106367	Robert Price	06/2022
6578	(56*10^106351+619)/9	106352	Robert Price	05/2021
6580	2^353277-20089	106347	Enzo Doria	06/2013
6579	2^353275+72173	106347	Enzo Doria	04/2016
6581	2^353268-17705	106345	Enzo Doria	05/2013
6582	2^353267-19857	106344	Enzo Doria	06/2013
6583	(46*10^106343+143)/9	106344	Robert Price	01/2019
6585	(2^353189+3054)/2	106321	Stefano Morozzi	09/2020
6584	35087^1072+1072^35087	106321	Hans Havermann	10/2020
6586	(2^353184+1290)/2	106319	Stefano Morozzi	01/2021
6587	26985^8684+8684^26985	106287	Hans Havermann	10/2020
6588	(2^353051+606)/2	106279	Stefano Morozzi	09/2020
6590	222748^3+3^222748	106278	Anatoly F. Selevich	12/2010
6589	(46*10^106277+107)/9	106278	Robert Price	06/2022
6591	(9179*2^353019-1)/9	106273	Lelio R Paula	05/2015
6592	2^353025+72257	106272	Enzo Doria	04/2016
6595	2^352932-20345	106244	Enzo Doria	06/2013
6593	(2^353011-3)/745325861246794515484535	106244	Lelio R Paula	12/2013
6594	25628^13983+13983^25628	106244	Hans Havermann	10/2020
6596	2^352883-187	106229	Lelio R Paula	10/2011
6597	20^81649-19^81649	106228	Jean-Louis Charton	03/2011
6598	(55*10^106222+377)/9	106223	Robert Price	02/2019
6599	2^352814-131	106208	Lelio R Paula	10/2011
6600	2^352752+73951	106189	Enzo Doria	04/2016
6601	11876*25^75945+357	106171	Eric Chen	10/2023
6602	6^136434+5	106167	Lelio R Paula	11/2014
6603	25296^15737+15737^25296	106166	Hans Havermann	09/2020
6604	8*10^106157-13	106158	Robert Price	08/2019
6605	7*5^151872-8	106155	Lelio R Paula	11/2014
6606	105^52520-2	106153	Lelio R Paula	10/2017
6607	(23*10^106152-29)/3	106153	Robert Price	03/2022
6608	2^352601-1604809	106144	Enzo Doria	05/2015
6609	12^98353-43	106141	Lelio R Paula	02/2017
6610	2^352585-18901	106139	Enzo Doria	05/2013
6611	26363^10614+10614^26363	106135	Hans Havermann	09/2020
6612	(2^352554-3)/193	106128	Lelio R Paula	12/2013
6613	2^352540+15015	106126	Lelio R Paula	01/2017
6614	25068^17119+17119^25068	106125	Hans Havermann	09/2020
6615	2^352524-3149	106121	Yves Minet	10/2014
6616	(7*10^106119-67)/3	106120	Robert Price	10/2021
6617	2^352486-1858781	106109	Enzo Doria	04/2016
6618	2^352444+12705	106097	Lelio R Paula	01/2017
6619	28561^5182+5182^28561	106090	Hans Havermann	10/2020
6620	(182*10^106083+43)/9	106085	Robert Price	02/2020
6621	(266*10^106066+1)/3	106068	Robert Price	04/2020
6622	(7*10^106066-187)/9	106066	Tyler Busby	01/2023
6623	2^352228-18953	106032	Enzo Doria	05/2013
6624	(2^352223+1118)/2	106030	Stefano Morozzi	09/2020
6625	(2^352212+2250)/2	106027	Stefano Morozzi	01/2021
6626	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
6627	2^352107+1872533	105995	Enzo Doria	05/2016
6628	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
6629	2^352066-2591	105983	Yves Minet	07/2014
6630	2^352030+715	105972	Lelio R Paula	10/2011
6631	9*6^136176-5	105967	Lelio R Paula	11/2014
6632	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
6633	28582^5097+5097^28582	105963	Hans Havermann	09/2020
6634	155^48377+2	105962	Lelio R Paula	08/2013
6635	(23*10^105944-119)/3	105945	Robert Price	07/2021
6636	2^351865+1869707	105922	Enzo Doria	05/2016
6637	24974^17427+17427^24974	105921	Hans Havermann	09/2020
6638	25163^16194+16194^25163	105920	Hans Havermann	09/2020
6639	2^351831+23	105912	Lelio R Paula	10/2011
6640	(2^351818+3798)/2	105908	Stefano Morozzi	02/2021
6641	9*2^351784-5	105899	Lelio R Paula	09/2014
6642	(2^351776+2766)/2	105895	Stefano Morozzi	01/2021
6643	(85*10^105881+203)/9	105882	Robert Price	09/2020
6644	2^351671-112387	105864	Enzo Doria	06/2014
6645	2^351669-109501	105863	Enzo Doria	04/2014
6646	2^351644+74731	105856	Enzo Doria	04/2016
6647	13^95025-42	105853	Lelio R Paula	12/2016
6648	2^351599+15015	105842	Lelio R Paula	01/2017
6649	19^82763+90	105834	Lelio R Paula	01/2017
6650	(205*10^105831-1)/3	105833	Robert Price	11/2021
6651	26050^11551+11551^26050	105832	Hans Havermann	09/2020
6652	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
6653	20^81329-51	105812	Lelio R Paula	01/2017
6654	(5*10^105811+211)/9	105811	Robert Price	02/2018
6655	2^351483+28425	105807	Lelio R Paula	01/2017
6656	25231^15610+15610^25231	105804	Hans Havermann	09/2020
6657	15^89960+86	105802	Lelio R Paula	02/2017
6658	2^351460-17289	105801	Enzo Doria	05/2013
6659	19^82735+22	105798	Lelio R Paula	01/2017
6660	2^351435-109077	105793	Enzo Doria	04/2014
6661	2^351393+1089	105780	Lelio R Paula	01/2017
6662	2^351364+72631	105772	Enzo Doria	04/2016
6663	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
6664	26818^8783+8783^26818	105761	Hans Havermann	09/2020
6667	2^351305+1872467	105754	Enzo Doria	05/2016
6666	3^221649+16	105754	Lelio R Paula	11/2016
6665	32511^1790+1790^32511	105754	Hans Havermann	09/2020
6668	8*3^221637-5	105749	Lelio R Paula	09/2014
6669	2^351279-2780449	105746	Enzo Doria	03/2016
6670	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
6671	15^89903-26	105735	Lelio R Paula	02/2017
6673	2^351213-73	105726	Lelio R Paula	10/2011
6672	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
6674	2^351192-4589	105720	Yves Minet	07/2011
6675	20^81250-33	105709	Lelio R Paula	12/2016
6676	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
6677	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
6678	2^351076-113159	105685	Enzo Doria	07/2014
6679	93^53688-2	105684	Lelio R Paula	09/2013
6680	2^351060-4559	105680	Yves Minet	07/2011
6681	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
6682	11^101473-750	105674	Enzo Doria	11/2012
6683	3*5^151181-8	105672	Lelio R Paula	11/2014
6684	15^89831-34	105650	Lelio R Paula	02/2017
6686	11^101448-360	105648	Enzo Doria	08/2012
6685	3*7^125011+4	105648	Lelio R Paula	11/2014
6687	2^350943-113269	105645	Enzo Doria	07/2014
6688	2*10^105636-91	105637	Robert Price	04/2020
6689	24231^22880+22880^24231	105634	Hans Havermann	09/2020
6690	35296^983+983^35296	105626	Hans Havermann	09/2020
6691	2^350868-19725	105622	Enzo Doria	06/2013
6692	2^350858-59291	105619	Enzo Doria	10/2015
6693	2^350851+135	105617	Lelio R Paula	10/2011
6694	2^350841-741	105614	Lelio R Paula	01/2017
6695	3*10^105582+77	105583	Robert Price	09/2018
6696	24915^17284+17284^24915	105581	Hans Havermann	09/2020
6697	(5*10^105576-53)/3	105577	Robert Price	09/2020
6698	8*10^105571+3	105572	Robert Price	08/2015
6699	2^350674-78557	105564	Jorge Menendez	03/2018
6700	2*5^151026-3	105563	Lelio R Paula	11/2014
6701	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
6702	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
6703	3^221211+236	105545	Lelio R Paula	11/2016
6704	(32*10^105530-77)/9	105531	Robert Price	06/2018
6705	10^105515+33	105516	Lelio R Paula	11/2016
6706	24644^19125+19125^24644	105516	Hans Havermann	10/2020
6707	10^105515-41033	105515	Patrick De Geest	12/2016
6708	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
6709	2^350455-430567	105498	Harrison Mesh	06/2022
6710	17^85732-72	105489	Lelio R Paula	01/2017
6711	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
6712	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
6713	2^350356+24241	105468	Enzo Doria	10/2023
6714	25233^15118+15118^25233	105462	Hans Havermann	09/2020
6715	26261^10366+10366^26261	105454	Hans Havermann	09/2020
6716	2^350307-110329	105453	Enzo Doria	05/2014
6717	2^350253-20365	105437	Enzo Doria	06/2013
6718	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
6719	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
6720	4*10^105415-69	105416	Robert Price	01/2022
6721	(22*10^105407+179)/3	105408	Robert Price	02/2022
6722	2^350139-109009	105403	Enzo Doria	04/2014
6723	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
6724	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
6725	3*5^150763+4	105380	Lelio R Paula	11/2014
6726	12^97643+91	105375	Lelio R Paula	02/2017
6727	6*5^150744-7	105367	Lelio R Paula	11/2014
6728	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
6729	4*10^105364-39	105365	Robert Price	09/2020
6731	2^349996-112169	105360	Enzo Doria	06/2014
6730	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
6732	(418*10^105343+23)/9	105345	Robert Price	02/2020
6733	25490^13563+13563^25490	105334	Hans Havermann	10/2020
6734	11^101142-1080	105329	Enzo Doria	12/2012
6735	(68*10^105320-41)/9	105321	Robert Price	10/2013
6736	24800^17649+17649^24800	105319	Hans Havermann	09/2020
6737	3^220712-9934	105307	Enzo Doria	05/2014
6738	7*10^105296+9	105297	Robert Price	09/2015
6739	89*10^105284-7	105286	Robert Price	04/2020
6740	2^349739+1873373	105282	Enzo Doria	06/2016
6741	7^124574+24	105278	Lelio R Paula	11/2016
6742	2^349708-20957	105273	Enzo Doria	06/2013
6743	34115^1218+1218^34115	105267	Hans Havermann	09/2020
6744	2^349649-20469	105255	Enzo Doria	06/2013
6745	2^349607-20109	105243	Enzo Doria	06/2013
6746	(85*10^105242+473)/9	105243	Robert Price	01/2020
6747	2^349594-19085	105239	Enzo Doria	05/2013
6748	2^349530+1874479	105220	Enzo Doria	06/2016
6749	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
6750	(106*10^105199+17)/3	105201	Robert Price	04/2021

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Probable Primes Top 10000

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