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 ?
9751	(3^112297-2)/7627	53576	Lelio R Paula	03/2012
9752	3*2^177948-7	53569	Lelio R Paula	03/2014
9753	10^53558+18543	53559	Patrick De Geest	12/2012
9754	10^53558-21	53558	Robert Price	03/2011
9755	2^177792-95	53521	Lelio R Paula	02/2011
9756	13392^9919+9919^13392	53521	Hans Havermann	07/2016
9757	13105^12132+12132^13105	53520	Hans Havermann	07/2016
9758	13^48042+82	53517	Lelio R Paula	01/2013
9759	2^177768+39121	53514	Yves Minet	10/2010
9760	13835^7366+7366^13835	53504	Hans Havermann	07/2016
9761	17^43477+84	53497	Lelio R Paula	01/2013
9762	5*10^53492+9	53493	Dmitry Domanov	11/2010
9763	2^177683+95	53488	Lelio R Paula	01/2011
9764	11057^13226-13226^11057	53482	Norbert Schneider	12/2017
9765	(2^177678+3)/514627	53481	Lelio R Paula	02/2012
9766	2^177641-255463	53476	Gary Barnes	08/2009
9767	p(11608)#/2+16	53469	Robert Price	12/2016
9768	(14*10^53465+211)/9	53466	Robert Price	11/2017
9769	37302#*10^(37302+52)+p(37302+1)	53457	Jason Earls	08/2008
9770	12001^13104-13104^12001	53455	Norbert Schneider	10/2017
9771	1829^16384+1828^16384	53449	Henri Lifchitz	01/2007
9772	10^53442+12621	53443	Patrick De Geest	06/2018
9773	10^53442-2007	53442	Patrick De Geest	06/2018
9774	35^34608-9602	53438	Enzo Doria	03/2013
9775	(3^111992+8)/14867	53430	Lelio R Paula	03/2012
9777	2^177480+1869661	53427	Enzo Doria	05/2016
9776	11791^13122-13122^11791	53427	Norbert Schneider	10/2017
9778	(8*10^53411+1)/9	53411	Serge Batalov	12/2008
9779	4*5^76410-3	53409	Lelio R Paula	09/2014
9780	2^177380-113045	53397	Enzo Doria	07/2014
9782	5^76362-2*3^76362	53375	Mike Oakes	11/2009
9781	72365!6-24	53375	Robert Price	08/2018
9783	4159^14747-140	53370	Enzo Doria	07/2012
9784	(lucasV(1,2,354503)-2)/3	53358	Mike Oakes	03/2017
9785	p(11586)#/2+32	53357	Robert Price	12/2016
9786	15^45362-46	53350	Lelio R Paula	01/2013
9787	14147^5892+5892^14147	53338	Hans Havermann	07/2016
9788	7^63109+46	53334	Lelio R Paula	10/2012
9789	20^40986-1343	53325	Enzo Doria	03/2013
9790	4*10^53324-89	53325	Robert Price	08/2017
9791	20^40977-8883	53313	Enzo Doria	03/2013
9792	3^111711+2660	53300	Lelio R Paula	10/2012
9793	2^177040-11865	53295	Enzo Doria	10/2012
9794	(7*10^53287+17)/3	53288	Erik Branger	03/2014
9795	35^34506-10758	53280	Enzo Doria	03/2013
9796	(11*10^53274-17)/3	53275	Erik Branger	03/2014
9797	(1017*2^176971-1)/335	53275	Lelio R Paula	03/2015
9798	5821^14150-14150^5821	53275	Norbert Schneider	01/2019
9799	2^176961-2833	53271	Yves Minet	09/2014
9800	3^111642+110	53267	Lelio R Paula	10/2012
9801	17^43290-98	53267	Lelio R Paula	01/2013
9802	7^63028+36	53265	Lelio R Paula	10/2012
9803	(22*10^53264+71)/3	53265	Robert Price	05/2017
9804	7^63023-36	53261	Lelio R Paula	10/2012
9805	19783^492+492^19783	53256	Anatoly F. Selevich	02/2007
9806	13350^9739+9739^13350	53247	Hans Havermann	10/2015
9807	14394^4993+4993^14394	53235	Hans Havermann	10/2015
9808	2^176823-112807	53230	Enzo Doria	06/2014
9809	1684^16495+16495^1684	53219	Serge Batalov	05/2014
9810	15277^3042+3042^15277	53213	Hans Havermann	06/2016
9811	(50322^11317-1)/50321	53206	Serge Batalov	04/2015
9812	2^176742-1595	53205	Lelio R Paula	10/2009
9813	(27*2^176767-1)/20455056355	53204	Lelio R Paula	01/2014
9814	72149!6-12	53200	Robert Price	08/2018
9815	(-lucasV(1,2,353460)-2)/(3^2*5^2)	53199	Mike Oakes	03/2017
9816	(3*2^176696-1)/299	53189	Lelio R Paula	01/2014
9817	(7*10^53185-1)/3	53186	Erik Branger	03/2014
9818	2^176629+465	53171	Lelio R Paula	07/2012
9819	(3*2^176604-1)/359	53162	Lelio R Paula	01/2014
9820	10955^13158-13158^10955	53154	Norbert Schneider	11/2017
9821	5^76038-14366	53149	Enzo Doria	02/2013
9822	15156^3209+3209^15156	53143	Hans Havermann	06/2016
9823	2^176532-2837	53142	Yves Minet	09/2014
9824	52^30967-51	53140	Norbert Schneider	08/2014
9825	9*5^76023-2	53139	Lelio R Paula	09/2014
9826	(14283!+1)/464216177	53135	Michael Porter	03/2016
9827	2^176461-165	53121	Lelio R Paula	02/2011
9828	(62*10^53111+1)/9	53112	Serge Batalov	05/2010
9829	2^176403-139	53103	Lelio R Paula	02/2011
9830	55^30508-2	53095	Lelio R Paula	08/2013
9831	(48591^11329-1)/48590	53090	Serge Batalov	04/2015
9832	3^111254-88	53082	Lelio R Paula	10/2012
9833	15^45129-56	53076	Lelio R Paula	01/2013
9834	(640^18913-1)/639	53071	Eric Chen	09/2018
9835	2^176293-73	53070	Lelio R Paula	01/2011
9837	(67*10^53068+41)/9	53069	Robert Price	09/2015
9836	15271^2986+2986^15271	53069	Hans Havermann	06/2016
9838	2^176255-667	53059	Yves Minet	01/2012
9839	36471*2^176221+8647	53053	Paul Vanderveen	04/2016
9840	(19*10^53049-1)/9	53050	Serge Batalov	03/2009
9841	9*2^176203-5	53044	Lelio R Paula	03/2014
9842	2^176205-94395	53043	Lelio R Paula	08/2011
9843	(19*2^176224-1)/217916913	53042	Lelio R Paula	01/2014
9844	8600^13481-13481^8600	53041	Norbert Schneider	05/2018
9845	17^43103+14	53037	Lelio R Paula	01/2013
9846	(31*2^176188-1)/3555	53036	Lelio R Paula	01/2014
9847	2^176177+60947	53035	David Broadhurst	05/2002
9848	(22*10^53033-7)/3	53034	Erik Branger	09/2014
9849	13810^6909+6909^13810	53023	Hans Havermann	06/2016
9851	2^176108+16095	53014	Lelio R Paula	10/2009
9850	2^176107+18915	53014	Lelio R Paula	07/2012
9852	3^111080-9628	52999	Enzo Doria	02/2013
9853	2^176047-1551	52996	Yves Minet	08/2012
9854	2^176042+73519	52994	Enzo Doria	04/2016
9855	lucasV(1715,1,2^14)/65537	52986	Mike Oakes	04/2009
9856	2^175984-112259	52977	Enzo Doria	06/2014
9857	11^50870+10	52976	Lelio R Paula	01/2013
9858	(11*10^52956+19)/3	52957	Robert Price	03/2016
9859	6773^13820-13820^6773	52942	Norbert Schneider	11/2018
9860	gcd(V(949965),5F(189993)(F(189993)+1)+1)	52941	Serge Batalov	04/2015
9861	(-lucasV(1,2,351735)+2)/(37263)	52938	Mike Oakes	03/2017
9862	(98*10^52931-89)/99	52931	Ray Chandler	11/2010
9863	13774^6963+6963^13774	52931	Hans Havermann	06/2016
9864	2^175812-1367	52925	Yves Minet	05/2013
9865	2^175801+1155*175801	52922	Henri Lifchitz	01/2005
9866	11^50801-9090	52904	Enzo Doria	02/2013
9867	7803^13592-13592^7803	52904	Norbert Schneider	07/2018
9868	43^32374+12	52882	Robert Price	11/2013
9869	155^24138+154	52871	Norbert Schneider	12/2018
9870	2^175628+13	52870	Lelio R Paula	01/2011
9871	2^175615-1747	52866	Yves Minet	09/2012
9872	(13*10^52861+107)/3	52862	Robert Price	11/2017
9873	9*2^175586-7	52858	Lelio R Paula	03/2014
9874	12174^12937+12937^12174	52854	Norbert Schneider	04/2016
9875	(15*2^175565+1)/8359	52848	Lelio R Paula	07/2012
9876	(2^175631-1)/330463093135534238072561/92733169	52839	Robert Kinser	03/2017
9877	14256^5077+5077^14256	52828	Hans Havermann	06/2016
9878	2^175467+82875	52821	Lelio R Paula	07/2012
9879	(7*10^52819+167)/3	52820	Robert Kinser	10/2017
9881	(67607*2^175426+1)/3	52813	Lelio R Paula	05/2014
9880	71671!6-32	52813	Robert Price	08/2018
9882	13^47400-60	52801	Lelio R Paula	01/2013
9883	4*10^52792+63	52793	Robert Price	06/2016
9885	(78557*2^175360+1)/3087	52791	Lelio R Paula	06/2014
9884	18^42055-2929	52791	Enzo Doria	03/2013
9886	9*5^75521+2	52788	Lelio R Paula	09/2014
9887	6^67814+31	52770	Lelio R Paula	10/2012
9888	70^28600+69	52770	Norbert Schneider	10/2012
9889	14^46038+97	52766	Lelio R Paula	01/2013
9890	(61*10^52763-7)/9	52764	Serge Batalov	02/2009
9891	2*5^75474+9	52755	Lelio R Paula	09/2014
9892	10^52753+2826430609	52754	Robert Price	05/2015
9893	10^52753+183997	52754	Patrick De Geest	01/2016
9894	10^52753-50153	52753	Patrick De Geest	03/2016
9895	19846^455+455^19846	52751	Anatoly F. Selevich	02/2007
9896	2^175217+72977	52746	Enzo Doria	04/2016
9897	p(11466)#/2-256	52746	Robert Price	05/2017
9898	(4*10^52740+41)/9	52740	Robert Price	11/2014
9899	2^175189+5385	52738	Lelio R Paula	08/2009
9900	2^175160+9385	52729	Lelio R Paula	07/2008
9901	12356^12885+12885^12356	52724	Norbert Schneider	03/2016
9902	2^175137+11	52722	Lelio R Paula	01/2011
9903	65^29077-64^29077	52715	Robert Price	08/2013
9904	2*10^52713-87	52714	Robert Price	06/2016
9905	2^175106-465	52713	Lelio R Paula	08/2009
9906	2^175089-58695	52708	Lelio R Paula	08/2009
9908	2^175045+195	52694	Lelio R Paula	02/2011
9907	195^23010-2	52694	Lelio R Paula	10/2017
9909	2^175025+149	52688	Lelio R Paula	02/2011
9910	(19^41201+1)/20	52685	Paul Bourdelais	03/2010
9911	(436*10^52683-13)/9	52685	Robert Price	10/2017
9912	2*12^48815-5^48815	52681	Mike Oakes	10/2010
9913	335^20862-20862^335	52678	Norbert Schneider	09/2015
9914	2^174983-7605	52676	Lelio R Paula	07/2009
9915	4*10^52667+19	52668	Robert Price	04/2016
9916	(10^52667+77)/3	52667	Robert Price	01/2017
9917	11434^12977+12977^11434	52664	Norbert Schneider	04/2016
9918	2^174941-1203	52663	Lelio R Paula	07/2009
9919	8501^13400-13400^8501	52655	Norbert Schneider	03/2018
9920	2^174910+12705	52654	Lelio R Paula	07/2012
9921	3^110338+74	52645	Lelio R Paula	10/2012
9922	5^75303+12	52635	Lelio R Paula	10/2012
9923	2^174836+255255	52631	Lelio R Paula	07/2009
9924	(66^28921+1)/67	52622	Paul Bourdelais	08/2017
9925	20^40443+9	52618	Lelio R Paula	01/2013
9926	(11*2^174788+1)/9	52617	Lelio R Paula	01/2012
9927	(11*2^174786-1)/703	52615	Lelio R Paula	01/2014
9928	11^50520-1290	52612	Enzo Doria	11/2012
9929	(670^18617-1)/669	52611	Eric Chen	09/2018
9930	(10^52608-19)/9	52608	Robert Price	10/2017
9931	(9913*2^174736-1)/333	52603	Lelio R Paula	03/2015
9932	13145^10024+10024^13145	52594	Hans Havermann	05/2016
9933	5003^14217-150	52592	Enzo Doria	07/2012
9934	2^174698-4055	52590	Yves Minet	02/2018
9935	19^41123+10	52587	Lelio R Paula	01/2013
9936	2^174683+12909	52585	Lelio R Paula	01/2011
9937	2^174643+59	52573	Lelio R Paula	01/2011
9938	(1017*2^174640-1)/773	52572	Lelio R Paula	03/2015
9939	13529^7662+7662^13529	52552	Hans Havermann	06/2016
9940	121421#+188767	52548	Makoto Morimoto	02/2016
9941	20^40375-5923	52530	Enzo Doria	03/2013
9942	(67607*2^174503+1)/90948079	52528	Lelio R Paula	05/2014
9943	(-lucasV(1,2,349014)+2)/(7508731047043)	52521	Mike Oakes	03/2017
9944	2^174462+345	52519	Lelio R Paula	07/2009
9945	t(178863)	52509	Robert Price	10/2014
9946	2^174416+855	52505	Lelio R Paula	07/2009
9947	6^67467-103	52500	Lelio R Paula	10/2012
9948	(2^174533-1)/(193594572654550537*91917886778031629891960890057)	52494	Dario Alpern	06/2017
9949	7888^13467-13467^7888	52481	Norbert Schneider	05/2018
9950	2^174329-11265	52479	Enzo Doria	06/2014
9951	2^174314-1241	52474	Yves Minet	05/2009
9952	52^30577-51	52471	Norbert Schneider	08/2014
9953	9403^13206-13206^9403	52471	Norbert Schneider	12/2017
9954	15692^2205+2205^15692	52465	Hans Havermann	06/2016
9955	(2^174281-7)/628817029615	52453	Lelio R Paula	02/2012
9956	(2^174240+5)/3	52451	Lelio R Paula	02/2012
9957	(86*10^52450-221)/9	52451	Robert Price	06/2017
9958	(62*10^52448-197)/9	52449	Robert Price	10/2017
9959	(15*2^174221+1)/403	52445	Lelio R Paula	07/2012
9960	26313!2-32	52443	Robert Price	10/2015
9961	(3*2^174214-1)/3748729	52438	Lelio R Paula	01/2014
9962	2*3^109900-5	52436	Lelio R Paula	03/2014
9964	4159^14488-150	52432	Enzo Doria	07/2012
9963	(89*10^52431-71)/9	52432	Robert Price	11/2015
9965	2^174170-3941	52431	Yves Minet	04/2017
9966	(7*2^174171-1)/685	52429	Lelio R Paula	01/2014
9967	5375^14052-14052^5375	52420	Norbert Schneider	10/2018
9968	(260137^9679+1)/260138	52409	Faysal YAtim	03/2008
9969	2^174098+79	52409	Lelio R Paula	01/2011
9970	35^33940-2214	52406	Enzo Doria	03/2013
9971	15^44557+2	52404	Ray Chandler	07/2011
9972	2^174049-439	52394	Yves Minet	01/2012
9973	6^67329+115	52393	Lelio R Paula	10/2012
9975	2^174041+262145	52392	Lelio R Paula	07/2009
9974	141^24377+2	52392	Lelio R Paula	05/2013
9976	lucasU(285,1,21339)-lucasU(285,1,21338)	52382	Mike Oakes	05/2009
9977	2^174001-5955	52380	Lelio R Paula	07/2009
9978	lucasV(-1,2,347969)	52375	Mike Oakes	02/2017
9979	3^109764-140	52371	Lelio R Paula	10/2012
9981	2*3^109761+7	52370	Lelio R Paula	03/2014
9980	9863^13112-13112^9863	52370	Norbert Schneider	10/2017
9983	(145^24229+1)/146	52366	Richard Fischer	02/2018
9982	8094^13399-13399^8094	52366	Norbert Schneider	03/2018
9984	2^173944-112253	52363	Enzo Doria	06/2014
9986	2^173940+1111	52362	Lelio R Paula	01/2011
9985	(3126^14983-1)/3125	52362	Richard Fischer	03/2015
9987	15214^2763+2763^15214	52358	Hans Havermann	05/2016
9988	13200^9247+9247^13200	52352	Hans Havermann	05/2016
9989	(1017*2^173867-1)/7175	52339	Lelio R Paula	03/2015
9990	13732^6465+6465^13732	52327	Hans Havermann	05/2016
9991	(2^173867-1)/52536637502689	52326	Donovan Johnson	06/2005
9992	2^173811-684877	52323	Paul Bourdelais	11/2012
9993	2^173807-5955	52322	Lelio R Paula	06/2009
9994	2^173796-1044689	52318	Paul Bourdelais	11/2012
9995	10^52317+64497	52318	Patrick De Geest	12/2012
9996	10^52317+64743	52318	Patrick De Geest	12/2012
9998	10^52317-71	52317	Robert Price	05/2011
9997	10821^12968+12968^10821	52317	Norbert Schneider	04/2016
9999	(298*10^52308-7)/3	52310	Robert Price	06/2017
10000	(2^173778-3)/57959	52308	Lelio R Paula	02/2012

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PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)