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	2^306153+11	92162	Lelio R Paula	11/2012
6502	(2^306141-7)/5	92157	Lelio R Paula	06/2013
6503	21725^17454+17454^21725	92156	Hans Havermann	09/2020
6504	(26*10^92152-23)/3	92153	Robert Price	08/2016
6505	(2*10^92152+67)/3	92152	Robert Price	04/2017
6506	21368^20457+20457^21368	92115	Hans Havermann	08/2020
6507	(2^305996+3018)/2	92114	Stefano Morozzi	09/2020
6508	410^92099+37^92099	92100	Mike Oakes	12/2010
6509	30504^1045+1045^30504	92096	Hans Havermann	08/2020
6510	24334^6085+6085^24334	92087	Hans Havermann	08/2020
6511	(2^305898+2262)/2	92085	Stefano Morozzi	01/2021
6512	(4591^25147-1)/4590	92083	Serge Batalov	08/2020
6513	115^44684+114	92081	Norbert Schneider	07/2018
6514	(416771^16384+1)/2	92077	Richard Fischer	08/2020
6515	(2^305867-2^152934+1)/5	92075		11/2006
6516	2^305851-109495	92071	Enzo Doria	04/2014
6517	(416213^16384+1)/2	92067	Richard Fischer	08/2020
6519	12^85300+35	92055	Lelio R Paula	06/2016
6518	((10^46026-1)1000/9+739)10^46026+(10^46026-1)/9	92055	Hans Havermann	05/2019
6520	21732^17201+17201^21732	92048	Hans Havermann	08/2020
6521	7*10^92043-39	92044	Robert Price	07/2020
6522	3^192911+92	92042	Lelio R Paula	04/2016
6523	2^305723-276271	92032	Enzo Doria	07/2015
6524	(2^305714+3738)/2	92029	Stefano Morozzi	09/2020
6525	(2^305707+798)/2	92027	Stefano Morozzi	01/2021
6526	(2^305682+3202)/2	92020	Stefano Morozzi	09/2020
6527	2^305676+93	92018	Donovan Johnson	06/2008
6528	3^192819+4	91999	Lelio R Paula	04/2013
6529	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
6530	2^305539+72911	91977	Enzo Doria	04/2016
6531	Phi(212014,10)	91960	Makoto Kamada	04/2019
6532	(2^305423+2666)/2	91942	Stefano Morozzi	09/2020
6533	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
6534	82077!4-128	91928	Robert Price	11/2019
6535	85^47642+84	91922	Norbert Schneider	10/2015
6536	10^91920+187651	91921	Patrick De Geest	07/2013
6537	10^91920-39	91920	Robert Price	05/2011
6538	(3975^25537-1)/3974	91913	Serge Batalov	08/2020
6539	(22*10^91903+41)/9	91904	Robert Price	02/2015
6541	2^305275-27	91897	Lelio R Paula	11/2012
6540	3^192607-7726	91897	Enzo Doria	05/2014
6542	(2^305243+2274)/2	91887	Stefano Morozzi	02/2021
6543	(2^305220+1278)/2	91881	Stefano Morozzi	01/2021
6544	(6958^23911-1)/6957	91874	Serge Batalov	08/2020
6545	(7*10^91856-61)/9	91856	Erik Branger	12/2009
6546	(2^305107+1274)/2	91847	Stefano Morozzi	01/2021
6547	(89*10^91839-53)/9	91840	Robert Price	11/2015
6548	1678^28479+28479^1678	91839	Norbert Schneider	08/2020
6549	(2^304996+406)/2	91813	Stefano Morozzi	02/2021
6550	8*5^131351+7	91812	Lelio R Paula	10/2014
6551	3^192426-68	91811	Lelio R Paula	04/2016
6553	2^304973+117	91807	Lelio R Paula	11/2012
6552	(2^304974+234)/2	91807	Stefano Morozzi	09/2020
6554	2^304939-1863727	91796	Enzo Doria	03/2016
6555	2^304902+8415	91785	Lelio R Paula	02/2016
6556	18^73119+61	91785	Lelio R Paula	06/2016
6557	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
6558	2^304747+71355	91738	Lelio R Paula	02/2016
6559	(2^304738+2262)/2	91735	Stefano Morozzi	01/2021
6560	8*3^192251+5	91728	Lelio R Paula	08/2014
6561	(2^304693+3746)/2	91722	Stefano Morozzi	01/2021
6562	2^304674-87	91717	Lelio R Paula	11/2012
6563	(28*10^91715+701)/9	91716	Robert Price	11/2017
6565	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
6564	(2^304671+1046)/2	91715	Stefano Morozzi	09/2020
6566	(2^304667+3614)/2	91714	Stefano Morozzi	09/2020
6567	(5*10^91707-119)/3	91708	Robert Price	04/2016
6568	2^304633-112771	91704	Enzo Doria	06/2014
6569	(395347^16384+1)/2	91701	Richard Fischer	06/2020
6570	9*10^91693+23	91694	Robert Price	11/2017
6571	2^304578-16713	91688	Enzo Doria	05/2013
6572	6^117824-18713	91685	Enzo Doria	03/2013
6573	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
6574	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
6575	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
6576	2^304507-16645	91666	Enzo Doria	04/2013
6577	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
6578	21221^20860+20860^21221	91661	Hans Havermann	08/2020
6579	2^304471-1836127	91655	Enzo Doria	04/2015
6580	2^304433+32769	91644	Lelio R Paula	02/2016
6581	2^304410-16625	91637	Enzo Doria	04/2013
6582	183^40500-2	91630	Lelio R Paula	10/2017
6583	(2^304373+1850)/2	91626	Stefano Morozzi	02/2021
6584	(203*10^91613+1)/3	91615	Robert Price	09/2017
6585	4*5^131052+7	91603	Lelio R Paula	10/2014
6587	21725^16458+16458^21725	91601	Hans Havermann	08/2020
6586	(2^304290+3270)/2	91601	Stefano Morozzi	02/2021
6588	2^304278-4001	91597	Yves Minet	04/2017
6589	2^304272-1866377	91595	Enzo Doria	03/2016
6590	2^304268+19683	91594	Lelio R Paula	02/2016
6591	21718^16497+16497^21718	91594	Hans Havermann	08/2020
6592	22759^10576+10576^22759	91590	Hans Havermann	08/2020
6593	2^304162-161	91562	Lelio R Paula	11/2012
6594	5*7^108331+6	91552	Lelio R Paula	10/2014
6595	2^304082-2787821	91538	Enzo Doria	03/2016
6596	2^304015+64133	91518	David Broadhurst	06/2002
6597	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
6598	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
6599	(384007^16384+1)/2	91494	Richard Fischer	05/2020
6600	2^303930+1880527	91493	Enzo Doria	10/2016
6601	24810^4859+4859^24810	91464	Hans Havermann	08/2020
6602	2*10^91457+29	91458	Robert Price	02/2021
6603	3^191684-68	91457	Lelio R Paula	04/2016
6604	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
6605	(298*10^91446+11)/3	91448	Robert Price	11/2020
6606	11^87797-120	91432	Enzo Doria	07/2012
6607	2^303698-1847231	91423	Enzo Doria	07/2015
6608	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
6609	25660^3643+3643^25660	91388	Hans Havermann	08/2020
6610	2^303554+77299	91379	Enzo Doria	05/2016
6611	2^303542+12705	91376	Lelio R Paula	02/2016
6612	31^61269-2	91375	Lelio R Paula	09/2013
6613	(2^303525+2774)/2	91370	Stefano Morozzi	01/2021
6614	2^303516-64875	91368	Lelio R Paula	02/2016
6615	(2^303497+1266)/2	91362	Stefano Morozzi	09/2020
6616	(2^303497+3710)/2	91362	Stefano Morozzi	09/2020
6617	21856^15121+15121^21856	91349	Hans Havermann	09/2020
6618	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
6619	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
6620	23081^9046+9046^23081	91319	Hans Havermann	09/2020
6621	2^303344-2786969	91316	Enzo Doria	03/2016
6622	6^117346+65	91313	Lelio R Paula	05/2016
6623	2^303321+855	91309	Lelio R Paula	02/2016
6624	(2^303315+3746)/2	91307	Stefano Morozzi	01/2021
6625	12^84606+47	91306	Lelio R Paula	06/2016
6626	2^303288+1874311	91299	Enzo Doria	06/2016
6627	197^39788-2	91293	Lelio R Paula	10/2017
6628	11^87663-1710	91292	Enzo Doria	12/2012
6629	2^303224+2533	91280	Henri Lifchitz	05/2005
6630	(2^303226+1830)/2	91280	Stefano Morozzi	02/2021
6631	6^117302+143	91279	Lelio R Paula	05/2016
6632	3^191306-112880	91277	Enzo Doria	07/2014
6633	(10052^22807-1)/10051	91276	Serge Batalov	08/2020
6634	2^303207+12915	91275	Lelio R Paula	02/2016
6635	2^303191-111259	91270	Enzo Doria	05/2014
6636	81539!4+32	91267	Robert Price	09/2019
6637	(2^303116+3570)/2	91247	Stefano Morozzi	09/2020
6639	10^91230+9^(91230+1)	91231	Robert Price	08/2016
6638	10^91230+7921	91231	Patrick De Geest	11/2016
6641	10^91230-911141	91230	Patrick De Geest	11/2016
6640	10^91229+348793	91230	Patrick De Geest	07/2019
6642	10^91229-2471	91229	Patrick De Geest	01/2019
6643	2996^26241+26241^2996	91228	Norbert Schneider	01/2020
6645	10^91225+5271	91226	Patrick De Geest	01/2019
6644	2816^26445+26445^2816	91226	Norbert Schneider	02/2020
6647	6^117232-17423	91225	Enzo Doria	02/2013
6646	10^91225-147219	91225	Patrick De Geest	07/2019
6648	7*10^91215+3	91216	Erik Branger	11/2009
6649	10^91215+230611	91216	Patrick De Geest	07/2019
6650	10^91215-4539	91215	Patrick De Geest	01/2019
6651	(2^303007+606)/2	91214	Stefano Morozzi	09/2020
6652	(2^302998+3102)/2	91212	Stefano Morozzi	09/2020
6653	10^91210+2421	91211	Patrick De Geest	01/2019
6654	10^91210-1737	91210	Patrick De Geest	01/2019
6655	97*10^91205-3	91207	Robert Price	01/2017
6656	2^302979-161181	91206	Enzo Doria	04/2013
6657	(166*10^91199-7)/3	91201	Robert Price	11/2020
6658	2^302949+81	91197	Henri Lifchitz	02/2007
6659	10^91194+200361	91195	Patrick De Geest	07/2019
6661	4*6^117192-5	91194	Lelio R Paula	10/2014
6660	10^91194-8663	91194	Patrick De Geest	01/2019
6662	2^302918+99	91188	Lelio R Paula	11/2012
6663	10^91186+268111	91187	Patrick De Geest	07/2019
6664	10^91186-7763	91186	Patrick De Geest	01/2019
6665	10^91181+550471	91182	Patrick De Geest	07/2019
6666	10^91181-1367	91181	Patrick De Geest	01/2019
6667	10^91178+71883	91179	Patrick De Geest	07/2019
6668	10^91178-4719	91178	Patrick De Geest	01/2019
6669	24686^4935+4935^24686	91173	Hans Havermann	08/2020
6670	10^91165+3043	91166	Patrick De Geest	01/2019
6671	10^91165-399413	91165	Patrick De Geest	07/2019
6672	10^91156+3861	91157	Patrick De Geest	01/2019
6673	10^91156-231497	91156	Patrick De Geest	07/2019
6674	2^302797+1869587	91151	Enzo Doria	05/2016
6675	265^37614+37614^265	91148	Norbert Schneider	01/2015
6676	7^107852+82	91146	Lelio R Paula	04/2016
6677	(38*10^91144-11)/9	91145	Robert Price	05/2015
6678	(55*10^91142+377)/9	91143	Robert Price	10/2017
6679	10^91128+9961	91129	Patrick De Geest	01/2019
6681	249^38030+38030^249	91128	Norbert Schneider	01/2015
6680	10^91128-189153	91128	Patrick De Geest	07/2019
6682	(2^302718+2814)/2	91127	Stefano Morozzi	02/2021
6683	6^117094-211049	91117	Mike Oakes	05/2011
6684	21353^18472+18472^21353	91103	Hans Havermann	05/2020
6686	2^302602-1867181	91093	Enzo Doria	03/2016
6685	10^91092+56127	91093	Patrick De Geest	07/2019
6687	10^91092-9107	91092	Patrick De Geest	01/2019
6688	(1017*2^302592-1)/53	91091	Lelio R Paula	04/2015
6689	15^77445-16	91083	Lelio R Paula	07/2016
6690	21656^16053+16053^21656	91076	Hans Havermann	05/2020
6691	2^302505+81	91064	Henri Lifchitz	02/2007
6692	2^302496-112349	91061	Enzo Doria	06/2014
6693	(2^302475+1790)/2	91054	Stefano Morozzi	01/2021
6694	17^73999-72	91052	Lelio R Paula	07/2016
6695	10^91047+9331	91048	Patrick De Geest	01/2019
6696	10^91047-671169	91047	Patrick De Geest	07/2019
6697	10^91044+2077	91045	Patrick De Geest	01/2019
6698	10^91044-136359	91044	Patrick De Geest	07/2019
6699	10^91041+9349	91042	Patrick De Geest	01/2019
6700	10^91041-7823	91041	Patrick De Geest	01/2019
6701	10^91040+4077	91041	Patrick De Geest	01/2019
6702	10^91040-119421	91040	Patrick De Geest	07/2019
6703	10^91037+2769	91038	Patrick De Geest	01/2019
6704	10^91037-22649	91037	Patrick De Geest	07/2019
6705	(16*10^91032+41)/3	91033	Robert Price	10/2017
6706	10^91023+58039	91024	Patrick De Geest	07/2019
6707	10^91023-6471	91023	Patrick De Geest	01/2019
6708	10^91018+7873	91019	Patrick De Geest	01/2019
6709	10^91018-333177	91018	Patrick De Geest	07/2019
6710	10^91017+68767	91018	Patrick De Geest	07/2019
6711	10^91017-428327	91017	Patrick De Geest	07/2019
6712	10^91016+73111	91017	Patrick De Geest	07/2019
6713	10^91016-7973	91016	Patrick De Geest	01/2019
6714	1949^27666+27666^1949	91016	Norbert Schneider	04/2020
6715	2^302332+577294575	91012	Lelio R Paula	08/2016
6716	10^91004+9073	91005	Patrick De Geest	01/2019
6717	10^91004-491519	91004	Patrick De Geest	07/2019
6718	10^91003+74269	91004	Patrick De Geest	07/2019
6719	10^91003-3903	91003	Patrick De Geest	01/2019
6720	2^302274+74209	90994	Enzo Doria	04/2016
6721	10^90991+81147	90992	Patrick De Geest	07/2019
6722	10^90991-6279	90991	Patrick De Geest	01/2019
6723	10^90983+1393	90984	Patrick De Geest	01/2019
6724	11*10^90982+9	90984	Robert Price	08/2020
6725	10^90983-562383	90983	Patrick De Geest	07/2019
6726	(311^36497-1)/310	90976	Eric Chen	09/2017
6727	(2^302210+1014)/2	90974	Stefano Morozzi	09/2020
6728	(3^190668+2)/89	90970	Lelio R Paula	04/2013
6729	2^302188+90195	90968	Lelio R Paula	02/2016
6731	(53*10^90965-71)/9	90966	Robert Price	09/2015
6730	10^90965+573987	90966	Patrick De Geest	07/2019
6732	10^90965-6833	90965	Patrick De Geest	01/2019
6733	10^90964+48789	90965	Patrick De Geest	07/2019
6734	10^90964-52103	90964	Patrick De Geest	07/2019
6735	10^90963+191889	90964	Patrick De Geest	07/2019
6736	10^90963-3659	90963	Patrick De Geest	01/2019
6737	10^90962+7657	90963	Patrick De Geest	01/2019
6738	10^90962-215633	90962	Patrick De Geest	07/2019
6739	10^90961+67471	90962	Patrick De Geest	07/2019
6740	10^90961-211043	90961	Patrick De Geest	07/2019
6741	10^90960+1072117	90961	Patrick De Geest	07/2019
6742	10^90959+8791	90960	Patrick De Geest	01/2019
6743	10^90960-610659	90960	Patrick De Geest	07/2019
6744	10^90959-275213	90959	Patrick De Geest	07/2019
6745	(2^302129+3110)/2	90950	Stefano Morozzi	09/2020
6747	10^90948+9867	90949	Patrick De Geest	01/2019
6746	21665^15774+15774^21665	90949	Hans Havermann	04/2020
6748	10^90948-109239	90948	Patrick De Geest	07/2019
6749	2^302113+74105	90946	Enzo Doria	04/2016
6750	2^302102-6555	90942	Lelio R Paula	02/2016

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Probable Primes Top 10000

(280932 PRPs in the top)