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 ?
8752	2^257636-110235	77557	Enzo Doria	05/2014
8753	(23*10^77556+97)/3	77557	Robert Price	02/2017
8751	(2^257639+2630)/2	77557	Stefano Morozzi	01/2020
8754	(2^257625+3354)/2	77553	Stefano Morozzi	01/2020
8755	2^257621-110071	77552	Enzo Doria	04/2014
8756	19580^9129+9129^19580	77546	Hans Havermann	03/2020
8757	2^257567-64875	77536	Lelio R Paula	06/2013
8758	(18098^18211-1)/18097	77532	Serge Batalov	08/2020
8759	(2^257429+2394)/2	77494	Stefano Morozzi	01/2020
8760	(2^257373+1206)/2	77477	Stefano Morozzi	01/2020
8761	2*7^91674+9	77474	Lelio R Paula	10/2014
8762	(2^257248+2442)/2	77440	Stefano Morozzi	01/2020
8763	(17*10^77427-47)/3	77428	Robert Price	05/2017
8764	10^77418+841683	77419	Patrick De Geest	06/2013
8765	10^77418-33	77418	Robert Price	05/2011
8766	19^60539-36	77415	Lelio R Paula	03/2015
8767	(9562^19447-1)/9561	77406	Serge Batalov	08/2020
8768	37401!!-1024	77397	Robert Price	11/2015
8769	(2^257095+1410)/2	77394	Stefano Morozzi	01/2020
8770	11^74313-18750	77390	Enzo Doria	12/2012
8771	2^257044-112883	77378	Enzo Doria	06/2014
8772	8*10^77377+51	77378	Robert Price	05/2017
8773	Phi(258121,2)/719	77375	Jeppe Stig Nielsen	09/2020
8774	2*7^91553+9	77372	Lelio R Paula	10/2014
8775	713^27118+27118^713	77371	Norbert Schneider	12/2016
8776	(22711^17761-1)/22710	77367	Serge Batalov	08/2020
8777	18652^14043+14043^18652	77359	Hans Havermann	03/2020
8778	(11391^19069-1)/11390	77351	Serge Batalov	08/2020
8779	6*10^77346-29	77347	Robert Price	08/2020
8780	2^256920-111155	77341	Enzo Doria	05/2014
8781	2^256896-6555	77334	Lelio R Paula	06/2013
8782	(52*10^77322-7)/9	77323	Robert Price	12/2014
8783	2^256849-112939	77320	Enzo Doria	06/2014
8784	17275^18246+18246^17275	77316	Norbert Schneider	01/2020
8785	(4*10^77309-31)/9	77309	Erik Branger	05/2011
8786	20936^4923+4923^20936	77301	Hans Havermann	04/2020
8787	(25376^17551-1)/25375	77298	Serge Batalov	08/2020
8788	(3^161988+7)/41864	77284	Lelio R Paula	10/2012
8789	(14^67421-1)/13	77272	Paul Bourdelais	09/2008
8790	(2^256679+3554)/2	77268	Stefano Morozzi	01/2020
8792	5*3^161923-4	77258	Lelio R Paula	06/2014
8791	20465^5958+5958^20465	77258	Hans Havermann	02/2020
8793	(2^256591+954)/2	77242	Stefano Morozzi	01/2020
8794	24806^1299+1299^24806	77237	Hans Havermann	05/2020
8795	2^256552-1499	77230	Yves Minet	05/2013
8796	18339^16258+16258^18339	77227	Hans Havermann	04/2020
8797	21243^4316+4316^21243	77221	Hans Havermann	04/2020
8798	(2^256493+3126)/2	77212	Stefano Morozzi	01/2020
8799	2^256460-112757	77203	Enzo Doria	06/2014
8800	(2^256444+2578)/2	77198	Stefano Morozzi	01/2020
8801	2^256398+23299	77184	Yves Minet	02/2011
8802	2^256391-1155*256391	77182	Henri Lifchitz	03/2005
8803	(2^256391-9)/56593	77177	Lelio R Paula	10/2012
8804	(7665^19867-1)/7664	77170	Serge Batalov	08/2020
8805	(2^256338+3834)/2	77166	Stefano Morozzi	01/2020
8806	(2^256339+546)/2	77166	Stefano Morozzi	01/2020
8807	(2^256308+9)/10585	77153	Lelio R Paula	10/2012
8808	21^58348-2	77149	Lelio R Paula	08/2013
8809	(17*2^256291-1)/4785	77149	Lelio R Paula	02/2014
8810	(5*2^256274-1)/2141	77144	Lelio R Paula	02/2014
8811	(2^256244+2326)/2	77137	Stefano Morozzi	01/2020
8812	19^60321+82	77136	Lelio R Paula	03/2015
8813	5*2^256233-3	77135	Lelio R Paula	06/2014
8814	(2^256155+1566)/2	77111	Stefano Morozzi	01/2020
8815	3*2^256149+7	77110	Lelio R Paula	06/2014
8816	(2^256128+1890)/2	77102	Stefano Morozzi	01/2020
8817	3^161594-106	77100	Lelio R Paula	02/2015
8818	2^256114-185	77098	Lelio R Paula	03/2012
8819	8^85349-85349^8	77078	Norbert Schneider	05/2017
8820	2^256043-2786377	77077	Enzo Doria	03/2016
8821	2^255973+1869947	77056	Enzo Doria	05/2016
8822	12^71393-43	77046	Lelio R Paula	02/2015
8823	(2^255882+3630)/2	77028	Stefano Morozzi	01/2020
8824	15^65490+44	77023	Lelio R Paula	02/2015
8825	(3^161411-7)/940	77010	Lelio R Paula	10/2012
8826	lucasU(1107,1,25297)-lucasU(1107,1,25296)	77005	Mike Oakes	05/2009
8828	(570^27943-1)/569	77005	Serge Batalov	12/2016
8827	(570^27943-1)/(570-1)	77005	Michael Stocker	04/2020
8829	2^255750-75	76989	Lelio R Paula	03/2012
8830	3*6^98926-5	76980	Lelio R Paula	10/2014
8831	(2^255708+478)/2	76976	Stefano Morozzi	01/2020
8832	18^61320-1433	76974	Enzo Doria	03/2013
8833	6^98916-17093	76972	Enzo Doria	02/2013
8834	(2^255691+806)/2	76971	Stefano Morozzi	01/2020
8835	2^255659-110131	76962	Enzo Doria	04/2014
8836	69805!4-128	76956	Robert Price	11/2019
8837	12^71303+91	76949	Lelio R Paula	02/2015
8838	18^61298+59	76946	Lelio R Paula	02/2015
8839	(223^32768+1)/131074	76945	Lelio R Paula	02/2009
8840	(2^255613-5)/281517	76942	Lelio R Paula	10/2012
8841	18^61290-11	76936	Lelio R Paula	02/2015
8842	(2^255567+1286)/2	76934	Stefano Morozzi	01/2020
8844	63^42752-2	76926	Lelio R Paula	08/2013
8843	(11*2^255545-1)/117	76926	Lelio R Paula	02/2014
8845	2^255517+56387	76919	Yves Minet	02/2011
8846	(7*10^76916+89)/3	76917	Robert Price	08/2020
8847	18376^15329+15329^18376	76914	Hans Havermann	03/2020
8848	2^255499-112567	76913	Enzo Doria	06/2014
8849	2^255492+345	76911	Lelio R Paula	06/2013
8850	(2^255488+1678)/2	76910	Stefano Morozzi	01/2020
8851	10^76875+217591	76876	Patrick De Geest	05/2013
8853	10^76875-53	76875	Robert Price	05/2011
8852	11^73819-5880	76875	Enzo Doria	01/2013
8854	2^255313+18915	76857	Lelio R Paula	06/2013
8855	(2^255320-1017)/1446667	76853	Lelio R Paula	10/2012
8856	2^255296+5775	76852	Lelio R Paula	06/2013
8857	14^67052-29	76851	Lelio R Paula	02/2015
8858	(8*10^76840+43)/3	76841	Robert Price	10/2017
8859	(2^255246+1642)/2	76837	Stefano Morozzi	01/2020
8860	(2^255243+2250)/2	76836	Stefano Morozzi	01/2020
8861	(2^255240+1218)/2	76835	Stefano Morozzi	01/2020
8862	(7*10^76818-313)/9	76818	Robert Price	11/2016
8863	10^76801+69	76802	Robert Price	03/2011
8864	10^76801-80943	76801	Patrick De Geest	06/2013
8865	2^255105+57	76795	Lelio R Paula	03/2012
8866	(lucasV(1,2,510187)+2)/(3511)	76789	Mike Oakes	04/2017
8867	(2^255097-7)/20020055	76785	Lelio R Paula	10/2012
8868	(2^255063+3098)/2	76782	Stefano Morozzi	01/2020
8869	2^255055+1869353	76780	Enzo Doria	05/2016
8870	17^62396-90	76776	Lelio R Paula	03/2015
8871	18797^12130+12130^18797	76765	Hans Havermann	03/2020
8872	7^90833-60	76763	Lelio R Paula	02/2015
8873	13^68901-56	76752	Lelio R Paula	03/2015
8874	2^254961+1869917	76751	Enzo Doria	05/2016
8875	(2^254950+594)/2	76748	Stefano Morozzi	01/2020
8876	20734^5027+5027^20734	76743	Hans Havermann	03/2020
8877	9*5^109791-8	76742	Lelio R Paula	10/2014
8878	(469^28729-1)/468	76738	Serge Batalov	08/2020
8879	(2^254908+982)/2	76735	Stefano Morozzi	01/2020
8880	(2^254903+2766)/2	76734	Stefano Morozzi	01/2020
8881	(4143^21211-1)/4142	76724	Serge Batalov	08/2020
8882	82^40089+40089^82	76723	Serge Batalov	02/2012
8883	2^254861-2790013	76721	Enzo Doria	03/2016
8884	(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/20459779741	76718	Makoto Kamada	03/2019
8885	10^76705+13	76706	Robert Price	01/2011
8886	10^76705-94077	76705	Patrick De Geest	06/2013
8887	(13709^18541-1)/13708	76701	Serge Batalov	08/2020
8888	(5*2^254785-1)/999	76696	Lelio R Paula	02/2014
8889	2^254758-110405	76690	Enzo Doria	05/2014
8890	(2^254721+470)/2	76679	Stefano Morozzi	01/2020
8891	2^254716-3779	76678	Yves Minet	04/2017
8892	2^254708-110507	76675	Enzo Doria	05/2014
8893	(47*10^76672+133)/9	76673	Robert Price	04/2017
8894	2^254670-112901	76664	Enzo Doria	06/2014
8895	(3^160665+7)/981350	76651	Lelio R Paula	10/2012
8896	2^254598-113183	76642	Enzo Doria	07/2014
8897	19^59932+22	76639	Lelio R Paula	01/2015
8898	77*10^76635+3	76637	Robert Price	06/2020
8899	2^254569-112213	76633	Enzo Doria	06/2014
8900	2*5^109626+9	76626	Lelio R Paula	10/2014
8901	2^254521+1872527	76619	Enzo Doria	05/2016
8902	(2^254515+2570)/2	76617	Stefano Morozzi	01/2020
8903	(76*10^76615+167)/9	76616	Robert Price	08/2016
8904	(2^254495+918)/2	76611	Stefano Morozzi	01/2020
8905	25^54799-24^54799	76606	Robert Price	07/2012
8906	(24737*2^254464+1)/9	76605	Lelio R Paula	06/2014
8907	25863^916+916^25863	76604	Hans Havermann	01/2020
8908	(2^254458+2398)/2	76600	Stefano Morozzi	01/2020
8909	(2^254434+1354)/2	76592	Stefano Morozzi	01/2020
8910	(2^254410+2842)/2	76585	Stefano Morozzi	01/2020
8911	19878^7121+7121^19878	76581	Hans Havermann	01/2020
8912	12^70961-85	76580	Lelio R Paula	02/2015
8913	18867^11452+11452^18867	76579	Hans Havermann	01/2020
8914	(2^254333+1806)/2	76562	Stefano Morozzi	01/2020
8915	7^90590-38	76558	Lelio R Paula	02/2015
8916	2^254304+5227	76554	Lelio R Paula	06/2013
8917	(76*10^76547-211)/9	76548	Robert Price	10/2017
8919	18^60979-5363	76546	Enzo Doria	03/2013
8918	(2^254278+3250)/2	76546	Stefano Morozzi	01/2020
8920	(19098^17881-1)/19097	76545	Serge Batalov	08/2020
8921	(21181*2^254264+1)/55314379	76538	Lelio R Paula	06/2014
8923	(34*10^76547-7)/9/61/94529/214807	76536	Makoto Morimoto	05/2016
8922	(7*10^76536-313)/9	76536	Robert Price	11/2016
8925	2^254239-27	76534	Lelio R Paula	03/2012
8924	2^254238-1841	76534	Yves Minet	03/2013
8926	(2^254235+3978)/2	76533	Stefano Morozzi	01/2020
8928	(10^76537-1)/9/66127969	76529	Jens K. Andersen	04/2009
8927	(2^254223+3938)/2	76529	Stefano Morozzi	01/2020
8929	2^254189-112225	76519	Enzo Doria	06/2014
8930	18^60938-1397	76494	Enzo Doria	03/2013
8932	2^254075-2788417	76485	Enzo Doria	03/2016
8931	18239^15612+15612^18239	76485	Hans Havermann	01/2020
8933	7*10^76483-23	76484	Robert Price	04/2016
8934	18471^13822+13822^18471	76481	Hans Havermann	01/2020
8935	18850^11407+11407^18850	76478	Hans Havermann	01/2020
8936	2^254042-112913	76475	Enzo Doria	06/2014
8937	14^66723-37	76474	Lelio R Paula	02/2015
8938	(2^254040+2970)/2	76474	Stefano Morozzi	01/2020
8939	2^254037-110305	76473	Enzo Doria	05/2014
8940	(2^254008+2290)/2	76464	Stefano Morozzi	01/2020
8941	15927^18196+18196^15927	76463	Norbert Schneider	12/2019
8942	(2^253979+1110)/2	76455	Stefano Morozzi	01/2020
8943	(1575^23911-1)/1574	76447	Serge Batalov	08/2020
8944	2^253931-111109	76441	Enzo Doria	05/2014
8945	2^253926-1167	76440	Lelio R Paula	05/2013
8946	(49*10^76438-13)/9	76439	Robert Price	07/2015
8947	(2^253876+1302)/2	76424	Stefano Morozzi	01/2020
8948	(21*2^253845-1)/143	76415	Lelio R Paula	02/2014
8949	10^76374+31	76375	Robert Price	03/2011
8950	10^76374-222159	76374	Patrick De Geest	05/2013
8951	(6300^20101-1)/6299	76367	Serge Batalov	08/2020
8952	(2^253660+490)/2	76359	Stefano Morozzi	01/2020
8953	19227^9352+9352^19227	76349	Hans Havermann	01/2020
8954	(2^253617+2874)/2	76347	Stefano Morozzi	01/2020
8955	2^253561-110533	76330	Enzo Doria	05/2014
8956	(2^253546+954)/2	76325	Stefano Morozzi	01/2020
8957	gcd(V(917285),5F(183457)(F(183457)+1)+1)	76321	Serge Batalov	04/2015
8958	9*5^109182+2	76316	Lelio R Paula	10/2014
8959	11^73279-3690	76313	Enzo Doria	12/2012
8960	(598*10^76309-31)/9	76311	Robert Price	02/2017
8961	11^73274-24000	76308	Enzo Doria	12/2012
8962	7^90291-6	76305	Theodore Burton	11/2005
8963	(2^253479+3650)/2	76305	Stefano Morozzi	01/2020
8964	(2^253460+2902)/2	76299	Stefano Morozzi	01/2020
8965	6*10^76295-29	76296	Robert Price	08/2020
8966	(21181*2^253432+1)/21437	76291	Lelio R Paula	06/2014
8967	(2^253399+3254)/2	76281	Stefano Morozzi	01/2020
8968	69247!4+4	76280	Robert Price	09/2019
8969	6^98025+145	76279	Lelio R Paula	01/2015
8970	(2^253382+1978)/2	76276	Stefano Morozzi	01/2020
8971	2^253355+1155	76268	Lelio R Paula	05/2013
8972	(73*10^76262+413)/9	76263	Robert Price	10/2017
8973	2^253292-71219	76249	Enzo Doria	04/2016
8974	7^90221-36	76246	Lelio R Paula	02/2015
8975	(2^253273+3486)/2	76243	Stefano Morozzi	01/2020
8976	(2^253238+894)/2	76232	Stefano Morozzi	01/2020
8977	18^60727-3473	76229	Enzo Doria	03/2013
8978	(2^253210+1170)/2	76224	Stefano Morozzi	01/2020
8979	(78557*2^253184+1)/3	76221	Lelio R Paula	06/2014
8980	(8*10^76220-83)/3	76221	Robert Price	10/2017
8981	18568^12717+12717^18568	76211	Hans Havermann	01/2020
8982	(44791^20480+1)/(44791^4096+1)	76206	Serge Batalov	01/2017
8983	(5168^20521-1)/5167	76198	Serge Batalov	08/2020
8984	19443^8294+8294^19443	76193	Hans Havermann	12/2019
8985	11^73163-2010	76192	Enzo Doria	12/2012
8986	19006^10201+10201^19006	76189	Hans Havermann	12/2019
8987	2^253060+54615	76179	Lelio R Paula	05/2013
8988	(2^253049+3966)/2	76176	Stefano Morozzi	01/2020
8989	2^253029+1869761	76170	Enzo Doria	05/2016
8990	(2^253028+1906)/2	76169	Stefano Morozzi	01/2020
8991	(1078^25111-1)/1077	76150	Serge Batalov	08/2020
8992	2^252955-111007	76148	Enzo Doria	05/2014
8993	2*5^108931+7	76140	Lelio R Paula	10/2014
8994	(86*10^76128+121)/9	76129	Robert Price	03/2017
8995	22154*29^52050+9	76123	Curtis Bright	05/2015
8996	18915^10574+10574^18915	76119	Hans Havermann	01/2020
8997	3^159530-112358	76116	Enzo Doria	06/2014
8998	11^73089-48	76115	Lelio R Paula	02/2015
8999	86^39337-85	76098	Norbert Schneider	10/2015
9000	(3^159505-7)/313297316	76095	Lelio R Paula	06/2012

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