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 ?
8751	(2^309138+1794)/2	93060	Stefano Morozzi	01/2021
8752	2^309131+1869383	93058	Enzo Doria	05/2016
8753	(2^309114+3610)/2	93053	Stefano Morozzi	09/2020
8754	2^309066-93	93039	Lelio R Paula	11/2012
8755	2^309063-113269	93038	Enzo Doria	07/2014
8756	3^194965+16	93022	Robert Price	10/2013
8757	(89*10^93019-737)/9	93020	Robert Price	01/2022
8758	2^308979+1869143	93012	Enzo Doria	05/2016
8759	5^133064+54	93008	Lelio R Paula	04/2016
8760	(2^308947+2750)/2	93003	Stefano Morozzi	01/2021
8761	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
8762	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
8763	(2*10^92976-17)/3	92976	Robert Price	08/2014
8764	24783^5642+5642^24783	92972	Hans Havermann	08/2020
8765	(472489^16384+1)/2	92969	Richard Fischer	01/2021
8766	2^308809+37967	92961	Phil Moore	03/2008
8767	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
8768	norm(Mod(x,x^3-x-1)^760951-1)	92930	Paul Vanderveen	08/2022
8769	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
8770	2^308650+513	92913	Lelio R Paula	02/2016
8771	5*7^109936+6	92908	Lelio R Paula	10/2014
8772	2*10^92897+89	92898	Robert Price	07/2016
8773	(2^308585+3182)/2	92894	Stefano Morozzi	09/2020
8774	(467307^16384+1)/2	92891	Richard Fischer	01/2021
8775	12^86073-29	92889	Lelio R Paula	06/2016
8776	2^308566-117	92888	Lelio R Paula	11/2012
8777	11594^22851-22851^11594	92872	Norbert Schneider	03/2022
8778	(17*10^92869-11)/3	92870	Robert Price	07/2015
8779	2^308459+75431	92856	Enzo Doria	04/2016
8780	2^308426-1866377	92846	Enzo Doria	03/2016
8781	24810^5521+5521^24810	92840	Hans Havermann	09/2020
8782	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
8783	2^308349-112111	92823	Enzo Doria	06/2014
8784	9*10^92821+19	92822	Robert Price	05/2016
8785	2^308337-75	92819	Lelio R Paula	11/2012
8786	4*3^194508+7	92805	Lelio R Paula	08/2014
8787	22*25^66379-113	92796	Curtis Bright	05/2015
8788	24538^6047+6047^24538	92792	Hans Havermann	09/2020
8789	11^89101-1080	92790	Enzo Doria	12/2012
8790	2^308236-1867859	92789	Enzo Doria	04/2016
8791	12^85963+25	92770	Lelio R Paula	06/2016
8792	23692^8221+8221^23692	92753	Hans Havermann	08/2020
8793	7^109750-66	92750	Lelio R Paula	04/2016
8794	9*10^92742+11	92743	Robert Kinser	01/2017
8795	(2^308054+778)/2	92734	Stefano Morozzi	09/2020
8796	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
8797	2^307997-110655	92717	Enzo Doria	05/2014
8798	L(443609)	92709	Renaud Lifchitz	11/2003
8799	10^92691+9	92692	Robert Price	03/2011
8800	10^92691-252291	92691	Patrick De Geest	08/2013
8801	(2^307883+3506)/2	92682	Stefano Morozzi	09/2020
8802	2^307879-2521	92681	Yves Minet	07/2014
8803	21269^21412+21412^21269	92666	Norbert Schneider	04/2020
8804	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
8805	14^80831+47	92643	Lelio R Paula	06/2016
8806	15^78744+92	92611	Lelio R Paula	07/2016
8807	65^51083-64	92610	Norbert Schneider	11/2014
8808	(2^307639+506)/2	92609	Stefano Morozzi	09/2020
8809	131^43737-130	92604	Norbert Schneider	02/2019
8810	6^118996-16943	92597	Enzo Doria	02/2013
8811	(16*10^92591+41)/3	92592	Robert Price	10/2017
8812	(2^307566+3094)/2	92587	Stefano Morozzi	09/2020
8813	(2^307528+1578)/2	92575	Stefano Morozzi	09/2020
8814	9*10^92573+83	92574	Robert Price	11/2020
8815	(3^194014-7)/2	92568	Lelio R Paula	04/2013
8816	(2^307498+570)/2	92566	Stefano Morozzi	09/2020
8817	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
8818	(26*10^92546-77)/3	92547	Robert Price	02/2017
8819	3^193954+340	92540	Lelio R Paula	04/2016
8820	2^307407-307407^2	92539	Henri Lifchitz	05/2005
8821	24299^6430+6430^24299	92536	Hans Havermann	08/2020
8823	(17*10^92513-11)/3	92514	Robert Price	07/2015
8822	2^307322-399071	92514	Harrison Mesh	06/2022
8824	2^307318-4211	92512	Yves Minet	06/2011
8825	2^307280+193	92501	Lelio R Paula	11/2012
8826	20^71075-33	92471	Lelio R Paula	05/2016
8827	2^307126-78795	92455	Lelio R Paula	02/2016
8828	2^307125-49789	92454	Henri Lifchitz	08/2005
8829	2^307099+23	92447	Lelio R Paula	11/2012
8830	129^43798+128	92440	Norbert Schneider	01/2019
8831	21826^17181+17181^21826	92435	Hans Havermann	09/2020
8832	Phi(277314,10)/3327769	92430	Makoto Kamada	05/2019
8833	(2^307022+1038)/2	92423	Stefano Morozzi	09/2020
8834	7*10^92414-69	92415	Robert Price	01/2017
8835	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
8836	22280^14037+14037^22280	92402	Hans Havermann	09/2020
8837	2^306915+1873373	92391	Enzo Doria	06/2016
8838	2^306908+12915	92389	Lelio R Paula	02/2016
8839	21620^18759+18759^21620	92387	Hans Havermann	09/2020
8840	(2^306897+1142)/2	92385	Stefano Morozzi	09/2020
8841	19^72244-80	92383	Lelio R Paula	06/2016
8843	2^306849+75	92371	Lelio R Paula	11/2012
8842	(397*10^92369+53)/9	92371	Robert Price	11/2017
8844	2^306813-869688105	92360	Lelio R Paula	08/2016
8845	(2^306797+2694)/2	92355	Stefano Morozzi	09/2020
8846	21713^17914+17914^21713	92350	Hans Havermann	09/2020
8847	2^306672-109059	92318	Enzo Doria	04/2014
8848	(430463^16384+1)/2	92307	Richard Fischer	09/2020
8849	6^118604-17063	92292	Enzo Doria	02/2013
8850	21969^15878+15878^21969	92288	Hans Havermann	08/2020
8851	21690^17959+17959^21690	92276	Hans Havermann	08/2020
8852	(7613^23773-1)/7612	92273	Serge Batalov	08/2020
8853	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
8854	2^306467-1835611	92256	Enzo Doria	04/2015
8855	2^306433+76427	92246	Enzo Doria	05/2016
8856	2^306430-113313	92245	Enzo Doria	07/2014
8857	(23*10^92244-59)/9	92245	Robert Price	03/2017
8858	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
8859	21436^20043+20043^21436	92217	Hans Havermann	09/2020
8860	(25*10^92186+59)/3	92187	Robert Price	05/2016
8861	2^306213-286183	92180	Enzo Doria	06/2015
8862	10^92178+61	92179	Robert Price	04/2011
8863	10^92178-175509	92178	Patrick De Geest	07/2013
8864	2^306200+1185	92176	Lelio R Paula	02/2016
8865	(2^306171+1514)/2	92167	Stefano Morozzi	09/2020
8866	2^306153+11	92162	Lelio R Paula	11/2012
8867	(2^306141-7)/5	92157	Lelio R Paula	06/2013
8868	21725^17454+17454^21725	92156	Hans Havermann	09/2020
8869	(26*10^92152-23)/3	92153	Robert Price	08/2016
8870	(2*10^92152+67)/3	92152	Robert Price	04/2017
8871	21368^20457+20457^21368	92115	Hans Havermann	08/2020
8872	(2^305996+3018)/2	92114	Stefano Morozzi	09/2020
8873	410^92099+37^92099	92100	Mike Oakes	12/2010
8874	30504^1045+1045^30504	92096	Hans Havermann	08/2020
8875	24334^6085+6085^24334	92087	Hans Havermann	08/2020
8876	(2^305898+2262)/2	92085	Stefano Morozzi	01/2021
8877	(4591^25147-1)/4590	92083	Serge Batalov	08/2020
8878	115^44684+114	92081	Norbert Schneider	07/2018
8879	(416771^16384+1)/2	92077	Richard Fischer	08/2020
8880	(2^305867-2^152934+1)/5	92075		11/2006
8881	2^305851-109495	92071	Enzo Doria	04/2014
8882	(416213^16384+1)/2	92067	Richard Fischer	08/2020
8884	12^85300+35	92055	Lelio R Paula	06/2016
8883	((10^46026-1)1000/9+739)10^46026+(10^46026-1)/9	92055	Hans Havermann	05/2019
8885	21732^17201+17201^21732	92048	Hans Havermann	08/2020
8886	7*10^92043-39	92044	Robert Price	07/2020
8887	3^192911+92	92042	Lelio R Paula	04/2016
8888	2^305723-276271	92032	Enzo Doria	07/2015
8889	(2^305714+3738)/2	92029	Stefano Morozzi	09/2020
8890	(2^305707+798)/2	92027	Stefano Morozzi	01/2021
8891	(2^305682+3202)/2	92020	Stefano Morozzi	09/2020
8892	2^305676+93	92018	Donovan Johnson	06/2008
8893	3^192819+4	91999	Lelio R Paula	04/2013
8894	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
8895	2^305539+72911	91977	Enzo Doria	04/2016
8896	Phi(212014,10)	91960	Makoto Kamada	04/2019
8897	(2^305423+2666)/2	91942	Stefano Morozzi	09/2020
8898	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
8899	82077!4-128	91928	Robert Price	11/2019
8900	85^47642+84	91922	Norbert Schneider	10/2015
8901	10^91920+187651	91921	Patrick De Geest	07/2013
8902	10^91920-39	91920	Robert Price	05/2011
8903	(3975^25537-1)/3974	91913	Serge Batalov	08/2020
8904	(22*10^91903+41)/9	91904	Robert Price	02/2015
8906	2^305275-27	91897	Lelio R Paula	11/2012
8905	3^192607-7726	91897	Enzo Doria	05/2014
8907	(2^305243+2274)/2	91887	Stefano Morozzi	02/2021
8908	(2^305220+1278)/2	91881	Stefano Morozzi	01/2021
8910	(6958^23911-1)/6957	91874	Serge Batalov	08/2020
8909	9*10^91873-91	91874	Robert Price	06/2021
8911	(7*10^91856-61)/9	91856	Erik Branger	12/2009
8912	(2^305107+1274)/2	91847	Stefano Morozzi	01/2021
8913	(89*10^91839-53)/9	91840	Robert Price	11/2015
8914	1678^28479+28479^1678	91839	Norbert Schneider	08/2020
8915	(2^304996+406)/2	91813	Stefano Morozzi	02/2021
8916	8*5^131351+7	91812	Lelio R Paula	10/2014
8917	3^192426-68	91811	Lelio R Paula	04/2016
8918	2^304979-375607	91808	Harrison Mesh	06/2022
8920	2^304973+117	91807	Lelio R Paula	11/2012
8919	(2^304974+234)/2	91807	Stefano Morozzi	09/2020
8921	2^304939-1863727	91796	Enzo Doria	03/2016
8922	2^304902+8415	91785	Lelio R Paula	02/2016
8923	18^73119+61	91785	Lelio R Paula	06/2016
8924	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
8925	2^304747+71355	91738	Lelio R Paula	02/2016
8926	(2^304738+2262)/2	91735	Stefano Morozzi	01/2021
8927	8*3^192251+5	91728	Lelio R Paula	08/2014
8928	(2^304693+3746)/2	91722	Stefano Morozzi	01/2021
8929	2^304674-87	91717	Lelio R Paula	11/2012
8930	(28*10^91715+701)/9	91716	Robert Price	11/2017
8931	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
8932	(2^304671+1046)/2	91715	Stefano Morozzi	09/2020
8933	(2^304667+3614)/2	91714	Stefano Morozzi	09/2020
8934	(5*10^91707-119)/3	91708	Robert Price	04/2016
8935	2^304633-112771	91704	Enzo Doria	06/2014
8936	(5*10^91702+19)/3	91703	Robert Price	07/2022
8937	(395347^16384+1)/2	91701	Richard Fischer	06/2020
8938	9*10^91693+23	91694	Robert Price	11/2017
8939	2^304578-16713	91688	Enzo Doria	05/2013
8940	6^117824-18713	91685	Enzo Doria	03/2013
8941	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
8942	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
8943	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
8944	2^304507-16645	91666	Enzo Doria	04/2013
8945	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
8946	21221^20860+20860^21221	91661	Hans Havermann	08/2020
8947	2^304471-1836127	91655	Enzo Doria	04/2015
8948	2^304433+32769	91644	Lelio R Paula	02/2016
8949	2^304410-16625	91637	Enzo Doria	04/2013
8950	183^40500-2	91630	Lelio R Paula	10/2017
8951	(2^304373+1850)/2	91626	Stefano Morozzi	02/2021
8952	(203*10^91613+1)/3	91615	Robert Price	09/2017
8953	4*5^131052+7	91603	Lelio R Paula	10/2014
8955	21725^16458+16458^21725	91601	Hans Havermann	08/2020
8954	(2^304290+3270)/2	91601	Stefano Morozzi	02/2021
8956	2^304278-4001	91597	Yves Minet	04/2017
8957	2^304272-1866377	91595	Enzo Doria	03/2016
8958	2^304268+19683	91594	Lelio R Paula	02/2016
8959	21718^16497+16497^21718	91594	Hans Havermann	08/2020
8960	22759^10576+10576^22759	91590	Hans Havermann	08/2020
8961	(29*10^91584-119)/9	91585	Robert Price	12/2021
8962	2^304162-161	91562	Lelio R Paula	11/2012
8963	5*7^108331+6	91552	Lelio R Paula	10/2014
8964	2^304082-2787821	91538	Enzo Doria	03/2016
8965	2^304015+64133	91518	David Broadhurst	06/2002
8966	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
8967	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
8968	(384007^16384+1)/2	91494	Richard Fischer	05/2020
8969	2^303930+1880527	91493	Enzo Doria	10/2016
8970	24810^4859+4859^24810	91464	Hans Havermann	08/2020
8971	2*10^91457+29	91458	Robert Price	02/2021
8972	3^191684-68	91457	Lelio R Paula	04/2016
8973	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
8974	(298*10^91446+11)/3	91448	Robert Price	11/2020
8975	11^87797-120	91432	Enzo Doria	07/2012
8976	2^303698-1847231	91423	Enzo Doria	07/2015
8977	(38^28933-1)^2-2	91416	Norbert Schneider	06/2016
8978	25660^3643+3643^25660	91388	Hans Havermann	08/2020
8979	2^303554+77299	91379	Enzo Doria	05/2016
8980	2^303542+12705	91376	Lelio R Paula	02/2016
8981	31^61269-2	91375	Lelio R Paula	09/2013
8982	(2^303525+2774)/2	91370	Stefano Morozzi	01/2021
8983	2^303516-64875	91368	Lelio R Paula	02/2016
8984	(2^303497+1266)/2	91362	Stefano Morozzi	09/2020
8985	(2^303497+3710)/2	91362	Stefano Morozzi	09/2020
8986	(31*10^91352+257)/9	91353	Robert Price	12/2021
8987	21856^15121+15121^21856	91349	Hans Havermann	09/2020
8988	(24737*2^303428+1)/3	91345	Lelio R Paula	06/2014
8989	(21181*2^303357+1)/32361	91320	Lelio R Paula	06/2014
8990	23081^9046+9046^23081	91319	Hans Havermann	09/2020
8991	2^303344-2786969	91316	Enzo Doria	03/2016
8992	6^117346+65	91313	Lelio R Paula	05/2016
8993	2^303321+855	91309	Lelio R Paula	02/2016
8994	(2^303315+3746)/2	91307	Stefano Morozzi	01/2021
8995	12^84606+47	91306	Lelio R Paula	06/2016
8996	2^303288+1874311	91299	Enzo Doria	06/2016
8997	197^39788-2	91293	Lelio R Paula	10/2017
8998	11^87663-1710	91292	Enzo Doria	12/2012
8999	(4*10^91284-61)/3	91285	Robert Price	12/2021
9000	(2^303226+1830)/2	91280	Stefano Morozzi	02/2021

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