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 ?
8501	21713^17914+17914^21713	92350	Hans Havermann	09/2020
8502	2^306672-109059	92318	Enzo Doria	04/2014
8503	(430463^16384+1)/2	92307	Richard Fischer	09/2020
8504	6^118604-17063	92292	Enzo Doria	02/2013
8505	21969^15878+15878^21969	92288	Hans Havermann	08/2020
8506	21690^17959+17959^21690	92276	Hans Havermann	08/2020
8507	(7613^23773-1)/7612	92273	Serge Batalov	08/2020
8508	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
8509	2^306467-1835611	92256	Enzo Doria	04/2015
8510	2^306433+76427	92246	Enzo Doria	05/2016
8511	2^306430-113313	92245	Enzo Doria	07/2014
8512	(23*10^92244-59)/9	92245	Robert Price	03/2017
8513	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
8514	21436^20043+20043^21436	92217	Hans Havermann	09/2020
8515	(25*10^92186+59)/3	92187	Robert Price	05/2016
8516	2^306213-286183	92180	Enzo Doria	06/2015
8517	10^92178+61	92179	Robert Price	04/2011
8518	10^92178-175509	92178	Patrick De Geest	07/2013
8519	2^306200+1185	92176	Lelio R Paula	02/2016
8520	(2^306171+1514)/2	92167	Stefano Morozzi	09/2020
8521	2^306153+11	92162	Lelio R Paula	11/2012
8522	(2^306141-7)/5	92157	Lelio R Paula	06/2013
8523	21725^17454+17454^21725	92156	Hans Havermann	09/2020
8524	(26*10^92152-23)/3	92153	Robert Price	08/2016
8525	(2*10^92152+67)/3	92152	Robert Price	04/2017
8526	21368^20457+20457^21368	92115	Hans Havermann	08/2020
8527	(2^305996+3018)/2	92114	Stefano Morozzi	09/2020
8528	410^92099+37^92099	92100	Mike Oakes	12/2010
8529	30504^1045+1045^30504	92096	Hans Havermann	08/2020
8530	24334^6085+6085^24334	92087	Hans Havermann	08/2020
8531	(2^305898+2262)/2	92085	Stefano Morozzi	01/2021
8532	(4591^25147-1)/4590	92083	Serge Batalov	08/2020
8533	115^44684+114	92081	Norbert Schneider	07/2018
8534	(416771^16384+1)/2	92077	Richard Fischer	08/2020
8535	(2^305867-2^152934+1)/5	92075		11/2006
8536	2^305851-109495	92071	Enzo Doria	04/2014
8537	(416213^16384+1)/2	92067	Richard Fischer	08/2020
8539	12^85300+35	92055	Lelio R Paula	06/2016
8538	((10^46026-1)1000/9+739)10^46026+(10^46026-1)/9	92055	Hans Havermann	05/2019
8540	21732^17201+17201^21732	92048	Hans Havermann	08/2020
8541	7*10^92043-39	92044	Robert Price	07/2020
8542	3^192911+92	92042	Lelio R Paula	04/2016
8543	2^305723-276271	92032	Enzo Doria	07/2015
8544	(2^305714+3738)/2	92029	Stefano Morozzi	09/2020
8545	(2^305707+798)/2	92027	Stefano Morozzi	01/2021
8546	(2^305682+3202)/2	92020	Stefano Morozzi	09/2020
8547	2^305676+93	92018	Donovan Johnson	06/2008
8548	3^192819+4	91999	Lelio R Paula	04/2013
8549	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
8550	2^305539+72911	91977	Enzo Doria	04/2016
8551	Phi(212014,10)	91960	Makoto Kamada	04/2019
8552	(2^305423+2666)/2	91942	Stefano Morozzi	09/2020
8553	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
8554	82077!4-128	91928	Robert Price	11/2019
8555	85^47642+84	91922	Norbert Schneider	10/2015
8556	10^91920+187651	91921	Patrick De Geest	07/2013
8557	10^91920-39	91920	Robert Price	05/2011
8558	(3975^25537-1)/3974	91913	Serge Batalov	08/2020
8559	(22*10^91903+41)/9	91904	Robert Price	02/2015
8561	2^305275-27	91897	Lelio R Paula	11/2012
8560	3^192607-7726	91897	Enzo Doria	05/2014
8562	(2^305243+2274)/2	91887	Stefano Morozzi	02/2021
8563	(2^305220+1278)/2	91881	Stefano Morozzi	01/2021
8565	(6958^23911-1)/6957	91874	Serge Batalov	08/2020
8564	9*10^91873-91	91874	Robert Price	06/2021
8566	(7*10^91856-61)/9	91856	Erik Branger	12/2009
8567	(2^305107+1274)/2	91847	Stefano Morozzi	01/2021
8568	(89*10^91839-53)/9	91840	Robert Price	11/2015
8569	1678^28479+28479^1678	91839	Norbert Schneider	08/2020
8570	(2^304996+406)/2	91813	Stefano Morozzi	02/2021
8571	8*5^131351+7	91812	Lelio R Paula	10/2014
8572	3^192426-68	91811	Lelio R Paula	04/2016
8573	2^304979-375607	91808	Harrison Mesh	06/2022
8575	2^304973+117	91807	Lelio R Paula	11/2012
8574	(2^304974+234)/2	91807	Stefano Morozzi	09/2020
8576	2^304939-1863727	91796	Enzo Doria	03/2016
8577	2^304902+8415	91785	Lelio R Paula	02/2016
8578	18^73119+61	91785	Lelio R Paula	06/2016
8579	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
8580	2^304747+71355	91738	Lelio R Paula	02/2016
8581	(2^304738+2262)/2	91735	Stefano Morozzi	01/2021
8582	8*3^192251+5	91728	Lelio R Paula	08/2014
8583	(2^304693+3746)/2	91722	Stefano Morozzi	01/2021
8584	2^304674-87	91717	Lelio R Paula	11/2012
8585	(28*10^91715+701)/9	91716	Robert Price	11/2017
8586	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
8587	(2^304671+1046)/2	91715	Stefano Morozzi	09/2020
8588	(2^304667+3614)/2	91714	Stefano Morozzi	09/2020
8589	(5*10^91707-119)/3	91708	Robert Price	04/2016
8590	2^304633-112771	91704	Enzo Doria	06/2014
8591	(395347^16384+1)/2	91701	Richard Fischer	06/2020
8592	9*10^91693+23	91694	Robert Price	11/2017
8593	2^304578-16713	91688	Enzo Doria	05/2013
8594	6^117824-18713	91685	Enzo Doria	03/2013
8595	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
8596	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
8597	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
8598	2^304507-16645	91666	Enzo Doria	04/2013
8599	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
8600	21221^20860+20860^21221	91661	Hans Havermann	08/2020
8601	2^304471-1836127	91655	Enzo Doria	04/2015
8602	2^304433+32769	91644	Lelio R Paula	02/2016
8603	2^304410-16625	91637	Enzo Doria	04/2013
8604	183^40500-2	91630	Lelio R Paula	10/2017
8605	(2^304373+1850)/2	91626	Stefano Morozzi	02/2021
8606	(203*10^91613+1)/3	91615	Robert Price	09/2017
8607	4*5^131052+7	91603	Lelio R Paula	10/2014
8609	21725^16458+16458^21725	91601	Hans Havermann	08/2020
8608	(2^304290+3270)/2	91601	Stefano Morozzi	02/2021
8610	2^304278-4001	91597	Yves Minet	04/2017
8611	2^304272-1866377	91595	Enzo Doria	03/2016
8612	2^304268+19683	91594	Lelio R Paula	02/2016
8613	21718^16497+16497^21718	91594	Hans Havermann	08/2020
8614	22759^10576+10576^22759	91590	Hans Havermann	08/2020
8615	(29*10^91584-119)/9	91585	Robert Price	12/2021
8616	2^304162-161	91562	Lelio R Paula	11/2012
8617	5*7^108331+6	91552	Lelio R Paula	10/2014
8618	2^304082-2787821	91538	Enzo Doria	03/2016
8619	2^304015+64133	91518	David Broadhurst	06/2002
8620	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
8621	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
8622	(384007^16384+1)/2	91494	Richard Fischer	05/2020
8623	2^303930+1880527	91493	Enzo Doria	10/2016
8624	24810^4859+4859^24810	91464	Hans Havermann	08/2020
8625	2*10^91457+29	91458	Robert Price	02/2021
8626	3^191684-68	91457	Lelio R Paula	04/2016
8627	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
8628	(298*10^91446+11)/3	91448	Robert Price	11/2020
8629	11^87797-120	91432	Enzo Doria	07/2012
8630	2^303698-1847231	91423	Enzo Doria	07/2015
8631	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
8632	25660^3643+3643^25660	91388	Hans Havermann	08/2020
8633	2^303554+77299	91379	Enzo Doria	05/2016
8634	2^303542+12705	91376	Lelio R Paula	02/2016
8635	31^61269-2	91375	Lelio R Paula	09/2013
8636	(2^303525+2774)/2	91370	Stefano Morozzi	01/2021
8637	2^303516-64875	91368	Lelio R Paula	02/2016
8638	(2^303497+1266)/2	91362	Stefano Morozzi	09/2020
8639	(2^303497+3710)/2	91362	Stefano Morozzi	09/2020
8640	(31*10^91352+257)/9	91353	Robert Price	12/2021
8641	21856^15121+15121^21856	91349	Hans Havermann	09/2020
8642	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
8643	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
8644	23081^9046+9046^23081	91319	Hans Havermann	09/2020
8645	2^303344-2786969	91316	Enzo Doria	03/2016
8646	6^117346+65	91313	Lelio R Paula	05/2016
8647	2^303321+855	91309	Lelio R Paula	02/2016
8648	(2^303315+3746)/2	91307	Stefano Morozzi	01/2021
8649	12^84606+47	91306	Lelio R Paula	06/2016
8650	2^303288+1874311	91299	Enzo Doria	06/2016
8651	197^39788-2	91293	Lelio R Paula	10/2017
8652	11^87663-1710	91292	Enzo Doria	12/2012
8653	(4*10^91284-61)/3	91285	Robert Price	12/2021
8655	2^303224+2533	91280	Henri Lifchitz	05/2005
8654	(2^303226+1830)/2	91280	Stefano Morozzi	02/2021
8656	6^117302+143	91279	Lelio R Paula	05/2016
8657	3^191306-112880	91277	Enzo Doria	07/2014
8658	(10052^22807-1)/10051	91276	Serge Batalov	08/2020
8659	2^303207+12915	91275	Lelio R Paula	02/2016
8660	2^303191-111259	91270	Enzo Doria	05/2014
8661	81539!4+32	91267	Robert Price	09/2019
8662	(2^303116+3570)/2	91247	Stefano Morozzi	09/2020
8663	10^91230+9^(91230+1)	91231	Robert Price	08/2016
8664	10^91230+7921	91231	Patrick De Geest	11/2016
8665	10^91230-911141	91230	Patrick De Geest	11/2016
8666	10^91229+348793	91230	Patrick De Geest	07/2019
8667	10^91229-2471	91229	Patrick De Geest	01/2019
8668	2996^26241+26241^2996	91228	Norbert Schneider	01/2020
8669	2^303249-494953	91228	Harrison Mesh	06/2022
8671	10^91225+5271	91226	Patrick De Geest	01/2019
8670	2816^26445+26445^2816	91226	Norbert Schneider	02/2020
8673	6^117232-17423	91225	Enzo Doria	02/2013
8672	10^91225-147219	91225	Patrick De Geest	07/2019
8674	7*10^91215+3	91216	Erik Branger	11/2009
8675	10^91215+230611	91216	Patrick De Geest	07/2019
8676	10^91215-4539	91215	Patrick De Geest	01/2019
8677	(2^303007+606)/2	91214	Stefano Morozzi	09/2020
8678	9*10^91212-47	91213	Robert Price	11/2021
8679	(2^302998+3102)/2	91212	Stefano Morozzi	09/2020
8680	10^91210+2421	91211	Patrick De Geest	01/2019
8681	10^91210-1737	91210	Patrick De Geest	01/2019
8682	97*10^91205-3	91207	Robert Price	01/2017
8683	2^302979-161181	91206	Enzo Doria	04/2013
8684	(166*10^91199-7)/3	91201	Robert Price	11/2020
8685	2^302949+81	91197	Henri Lifchitz	02/2007
8686	10^91194+200361	91195	Patrick De Geest	07/2019
8688	4*6^117192-5	91194	Lelio R Paula	10/2014
8687	10^91194-8663	91194	Patrick De Geest	01/2019
8689	2^302918+99	91188	Lelio R Paula	11/2012
8690	10^91186+268111	91187	Patrick De Geest	07/2019
8691	10^91186-7763	91186	Patrick De Geest	01/2019
8692	10^91181+550471	91182	Patrick De Geest	07/2019
8693	(26*10^91181-83)/3	91182	Robert Price	12/2021
8694	10^91181-1367	91181	Patrick De Geest	01/2019
8695	10^91178+71883	91179	Patrick De Geest	07/2019
8696	10^91178-4719	91178	Patrick De Geest	01/2019
8697	24686^4935+4935^24686	91173	Hans Havermann	08/2020
8698	10^91165+3043	91166	Patrick De Geest	01/2019
8699	10^91165-399413	91165	Patrick De Geest	07/2019
8700	10^91156+3861	91157	Patrick De Geest	01/2019
8701	10^91156-231497	91156	Patrick De Geest	07/2019
8702	2^302797+1869587	91151	Enzo Doria	05/2016
8703	265^37614+37614^265	91148	Norbert Schneider	01/2015
8704	7^107852+82	91146	Lelio R Paula	04/2016
8705	(38*10^91144-11)/9	91145	Robert Price	05/2015
8706	(55*10^91142+377)/9	91143	Robert Price	10/2017
8707	10^91128+9961	91129	Patrick De Geest	01/2019
8709	249^38030+38030^249	91128	Norbert Schneider	01/2015
8708	10^91128-189153	91128	Patrick De Geest	07/2019
8710	(2^302718+2814)/2	91127	Stefano Morozzi	02/2021
8711	6^117094-211049	91117	Mike Oakes	05/2011
8712	21353^18472+18472^21353	91103	Hans Havermann	05/2020
8714	2^302602-1867181	91093	Enzo Doria	03/2016
8713	10^91092+56127	91093	Patrick De Geest	07/2019
8715	10^91092-9107	91092	Patrick De Geest	01/2019
8716	(1017*2^302592-1)/53	91091	Lelio R Paula	04/2015
8717	15^77445-16	91083	Lelio R Paula	07/2016
8718	21656^16053+16053^21656	91076	Hans Havermann	05/2020
8719	2^302505+81	91064	Henri Lifchitz	02/2007
8720	2^302496-112349	91061	Enzo Doria	06/2014
8721	(2^302475+1790)/2	91054	Stefano Morozzi	01/2021
8722	17^73999-72	91052	Lelio R Paula	07/2016
8723	10^91047+9331	91048	Patrick De Geest	01/2019
8724	10^91047-671169	91047	Patrick De Geest	07/2019
8725	10^91044+2077	91045	Patrick De Geest	01/2019
8726	10^91044-136359	91044	Patrick De Geest	07/2019
8727	10^91041+9349	91042	Patrick De Geest	01/2019
8728	10^91041-7823	91041	Patrick De Geest	01/2019
8729	10^91040+4077	91041	Patrick De Geest	01/2019
8730	10^91040-119421	91040	Patrick De Geest	07/2019
8731	10^91037+2769	91038	Patrick De Geest	01/2019
8732	10^91037-22649	91037	Patrick De Geest	07/2019
8733	(16*10^91032+41)/3	91033	Robert Price	10/2017
8734	10^91023+58039	91024	Patrick De Geest	07/2019
8735	10^91023-6471	91023	Patrick De Geest	01/2019
8736	10^91018+7873	91019	Patrick De Geest	01/2019
8737	10^91018-333177	91018	Patrick De Geest	07/2019
8738	10^91017+68767	91018	Patrick De Geest	07/2019
8739	10^91017-428327	91017	Patrick De Geest	07/2019
8740	10^91016+73111	91017	Patrick De Geest	07/2019
8741	10^91016-7973	91016	Patrick De Geest	01/2019
8742	1949^27666+27666^1949	91016	Norbert Schneider	04/2020
8743	2^302332+577294575	91012	Lelio R Paula	08/2016
8744	10^91004+9073	91005	Patrick De Geest	01/2019
8745	10^91004-491519	91004	Patrick De Geest	07/2019
8746	10^91003+74269	91004	Patrick De Geest	07/2019
8747	10^91003-3903	91003	Patrick De Geest	01/2019
8748	2^302274+74209	90994	Enzo Doria	04/2016
8749	10^90991+81147	90992	Patrick De Geest	07/2019
8750	10^90991-6279	90991	Patrick De Geest	01/2019

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