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 (> 30000)	Who ?	When ?
9001	2^180000+130153	54186	Jim Fougeron	09/2002
9002	3^113565-74	54185	Lelio R Paula	10/2012
9003	50^31891-49	54182	Norbert Schneider	07/2014
9004	(5*2^179991-1)/11427	54180	Lelio R Paula	01/2014
9005	3^113548+26	54177	Lelio R Paula	10/2012
9006	(lucasV(1,2,360029)-2)/(3^3522251725981)	54177	Mike Oakes	04/2017
9007	181^23996-2	54176	Lelio R Paula	10/2017
9008	4159^14969-138	54173	Enzo Doria	07/2012
9010	2^179955+5775	54172	Lelio R Paula	10/2009
9009	2^179953-231313	54172	Enzo Doria	05/2014
9011	5^77485+6	54160	Lelio R Paula	10/2012
9012	18^43141+85	54154	Lelio R Paula	02/2013
9013	10^54149+187647	54150	Patrick De Geest	07/2017
9016	3^113489-340	54149	Lelio R Paula	10/2012
9014	10^54149-800001	54149	Robert Price	06/2017
9015	10^54149-36501	54149	Patrick De Geest	07/2017
9017	7^64070+90	54146	Lelio R Paula	10/2012
9018	12549^13210-13210^12549	54143	Norbert Schneider	12/2017
9019	18^43131+71	54142	Lelio R Paula	02/2013
9020	2^179826-131	54134	Lelio R Paula	02/2011
9021	2^179815-112735	54130	Enzo Doria	06/2014
9022	2^179806+73849	54127	Enzo Doria	04/2016
9023	2^179790+33	54123	Donovan Johnson	02/2006
9024	14287^6138+6138^14287	54120	Hans Havermann	06/2016
9025	(17*10^54117+1)/9	54118	Serge Batalov	05/2010
9026	2^179763-189	54115	Lelio R Paula	02/2011
9027	(21181*2^179770+1)/3029105	54115	Lelio R Paula	05/2014
9028	1828^16589+16589^1828	54113	Serge Batalov	05/2014
9030	20^41588-5883	54108	Enzo Doria	03/2013
9029	50^31847-49	54108	Norbert Schneider	07/2014
9031	2^179733-6855	54106	Lelio R Paula	10/2009
9032	20^41584-5583	54103	Enzo Doria	03/2013
9033	10^54084+3*3^54084	54085	Mike Oakes	05/2010
9034	2^179613-1795	54069	Lelio R Paula	10/2009
9035	2^179589-1011523	54062	Paul Bourdelais	11/2012
9036	2^179574-2531	54058	Yves Minet	07/2014
9037	(41*10^54051-23)/9	54052	Robert Price	05/2015
9038	117^26131-116	54044	Norbert Schneider	10/2013
9039	(10^54038-31)/3	54038	Serge Batalov	12/2014
9040	11^51885-84	54033	Lelio R Paula	01/2013
9041	14990^4011+4011^14990	54013	Hans Havermann	07/2016
9042	(19*2^179414+1)/7	54010	Lelio R Paula	07/2012
9043	3^113182-10408	54002	Enzo Doria	02/2013
9044	35^34970-8786	53997	Enzo Doria	03/2013
9045	2^179371-1637587	53997	Enzo Doria	05/2015
9046	19^42225-92	53996	Lelio R Paula	01/2013
9047	(3^113188+7)/73917675784	53994	Lelio R Paula	03/2012
9048	7*3^113162+8	53993	Lelio R Paula	03/2014
9049	(10^53991+179)/9	53991	Serge Batalov	12/2014
9050	2^179350-2145	53990	Lelio R Paula	10/2009
9051	(-lucasV(1,2,358718)-2)/(51719)	53990	Mike Oakes	04/2017
9052	8^59782-6^59782-3^59782	53989	Mike Oakes	11/2009
9053	3*7^63861+8	53970	Lelio R Paula	09/2014
9054	2^179274+71389	53967	Enzo Doria	04/2016
9055	2^179259-58695	53963	Lelio R Paula	10/2009
9056	6^69345+61	53961	Lelio R Paula	10/2012
9057	(-lucasV(1,2,358635)+2)/(71793172321719602511716271)	53957	Mike Oakes	04/2017
9058	(40216^11719-1)/40215	53955	Serge Batalov	04/2015
9059	89*10^53951-9	53953	Robert Price	05/2017
9060	14^47067-3	53945	Lelio R Paula	01/2013
9061	p(11700)#/2-512	53937	Robert Price	07/2017
9062	(2^179168-5)/59	53934	Lelio R Paula	02/2012
9063	2^179128+8415	53923	Lelio R Paula	07/2012
9064	2^179120+2533	53921	Henri Lifchitz	09/2004
9066	(2^179126+78557)/4649321187	53913	Lelio R Paula	05/2012
9065	74^28842+73	53913	Norbert Schneider	11/2012
9067	1271^17368+17368^1271	53913	Serge Batalov	05/2014
9068	2^179079+53	53909	Lelio R Paula	02/2011
9069	17^43807+54	53903	Lelio R Paula	01/2013
9070	17^43807+30	53903	Lelio R Paula	01/2013
9071	3^112951-310	53892	Lelio R Paula	10/2012
9072	Phi(7,2957!)	53888	Robert Price	05/2015
9073	(10223*2^178975+1)/33985	53877	Lelio R Paula	05/2014
9074	2^178944-219209	53868	Enzo Doria	11/2012
9075	(10^53859+149)/3	53859	Serge Batalov	12/2014
9076	2^178910-191	53858	Lelio R Paula	02/2011
9077	16170^2141+2141^16170	53857	Hans Havermann	07/2016
9078	(5*10^53855-107)/3	53856	Robert Price	01/2017
9079	(72*10^53847-27)/99	53847	Patrick De Geest	08/2004
9080	2^178841-869688105	53837	Lelio R Paula	06/2012
9081	2*10^53834-27	53835	Robert Price	02/2017
9083	2^178821-1011523	53831	Paul Bourdelais	11/2012
9082	12601^13128-13128^12601	53831	Norbert Schneider	10/2017
9084	2^178819-15	53830	Lelio R Paula	02/2011
9085	(14450!-1)/225296581	53829	Donovan Johnson	04/2006
9086	(124351#+125386)/(2^57188344891039820259)	53826	Makoto Morimoto	10/2017
9087	10530^13381-13381^10530	53825	Norbert Schneider	03/2018
9088	2^178761-465	53813	Lelio R Paula	10/2009
9089	18900^703+703^18900	53808	Anatoly F. Selevich	02/2007
9090	13918^7343+7343^13918	53806	Hans Havermann	08/2016
9091	10^53804+31749	53805	Patrick De Geest	12/2012
9092	10^53804-71	53804	Robert Price	05/2011
9093	t(178994)	53804	Robert Price	03/2015
9094	(2^178693-lucasV(1,2,178693)+1)/2	53792	Mike Oakes	11/2016
9095	2^178671-113215	53786	Enzo Doria	07/2014
9096	15110^3621+3621^15110	53774	Hans Havermann	07/2016
9097	2^178611+95	53768	Lelio R Paula	02/2011
9098	2^178597+5711	53764	Lelio R Paula	10/2011
9099	2^178598+12915	53764	Lelio R Paula	07/2012
9100	(9179*2^178579-1)/303	53760	Lelio R Paula	03/2015
9101	10671^13342-13342^10671	53745	Norbert Schneider	02/2018
9102	5*7^63589+2	53740	Lelio R Paula	09/2014
9103	2^178516-112515	53739	Enzo Doria	06/2014
9104	20^41302-27	53736	Lelio R Paula	01/2013
9105	6^69054-39209	53735	Mike Oakes	12/2010
9106	13086^12769+12769^13086	53734	Hans Havermann	07/2016
9107	2^178455+76043	53721	Enzo Doria	04/2016
9108	(10^53718-7)/3	53718	Makoto Kamada	10/2004
9109	(67607*2^178426+1)/3	53716	Lelio R Paula	05/2014
9110	9*10^53707+11	53708	Robert Kinser	01/2017
9111	94601!8-2	53708	Robert Price	04/2017
9112	13214^11595+11595^13214	53706	Hans Havermann	07/2016
9113	Phi(134350,10)/537401/8011962251	53705	Maksym Voznyy	10/2011
9114	2^178367-379	53694	Yves Minet	03/2013
9115	(2^178364-5)/11	53692	Lelio R Paula	02/2012
9116	4339^14760-168	53688	Enzo Doria	06/2012
9117	12^49746-11	53685	Lelio R Paula	01/2013
9118	12950^13051-13051^12950	53670	Norbert Schneider	08/2017
9119	(9913*2^178266-1)/2247	53665	Lelio R Paula	03/2015
9120	13725^8128+8128^13725	53665	Hans Havermann	07/2016
9121	2^178250-113261	53659	Enzo Doria	07/2014
9122	2^178226+11715	53652	Lelio R Paula	10/2009
9123	35^34742-1976	53645	Enzo Doria	03/2013
9124	20^41228-563	53639	Enzo Doria	03/2013
9125	359^20992+20992^359	53637	Norbert Schneider	08/2014
9126	(27*2^178183-1)/29065	53636	Lelio R Paula	01/2014
9127	(3^112414+7)/37381696	53628	Lelio R Paula	03/2012
9128	17994^955+955^17994	53623	Anatoly F. Selevich	10/2006
9129	2^178117-1551	53619	Yves Minet	08/2012
9130	2^178099-11287	53614	Enzo Doria	06/2014
9131	10751^13298-13298^10751	53611	Norbert Schneider	01/2018
9132	(15*2^178080-1)/309071	53604	Lelio R Paula	01/2014
9133	5^76672-13766	53592	Enzo Doria	02/2013
9134	6^68868-137	53590	Lelio R Paula	10/2012
9135	(5*2^178021+1)/8173	53587	Lelio R Paula	07/2012
9136	5^76654-26	53579	Lelio R Paula	10/2012
9137	(3^112297-2)/7627	53576	Lelio R Paula	03/2012
9138	3*2^177948-7	53569	Lelio R Paula	03/2014
9139	10^53558+18543	53559	Patrick De Geest	12/2012
9140	10^53558-21	53558	Robert Price	03/2011
9141	2^177792-95	53521	Lelio R Paula	02/2011
9142	13392^9919+9919^13392	53521	Hans Havermann	07/2016
9143	13105^12132+12132^13105	53520	Hans Havermann	07/2016
9144	13^48042+82	53517	Lelio R Paula	01/2013
9145	2^177768+39121	53514	Yves Minet	10/2010
9146	13835^7366+7366^13835	53504	Hans Havermann	07/2016
9147	17^43477+84	53497	Lelio R Paula	01/2013
9148	5*10^53492+9	53493	Dmitry Domanov	11/2010
9149	2^177683+95	53488	Lelio R Paula	01/2011
9150	11057^13226-13226^11057	53482	Norbert Schneider	12/2017
9151	(2^177678+3)/514627	53481	Lelio R Paula	02/2012
9152	2^177641-255463	53476	Gary Barnes	08/2009
9153	p(11608)#/2+16	53469	Robert Price	12/2016
9154	(14*10^53465+211)/9	53466	Robert Price	11/2017
9155	37302#*10^(37302+52)+p(37302+1)	53457	Jason Earls	08/2008
9156	12001^13104-13104^12001	53455	Norbert Schneider	10/2017
9157	1829^16384+1828^16384	53449	Henri Lifchitz	01/2007
9158	35^34608-9602	53438	Enzo Doria	03/2013
9159	(3^111992+8)/14867	53430	Lelio R Paula	03/2012
9161	2^177480+1869661	53427	Enzo Doria	05/2016
9160	11791^13122-13122^11791	53427	Norbert Schneider	10/2017
9162	(8*10^53411+1)/9	53411	Serge Batalov	12/2008
9163	4*5^76410-3	53409	Lelio R Paula	09/2014
9164	2^177380-113045	53397	Enzo Doria	07/2014
9165	5^76362-2*3^76362	53375	Mike Oakes	11/2009
9166	4159^14747-140	53370	Enzo Doria	07/2012
9167	(lucasV(1,2,354503)-2)/3	53358	Mike Oakes	03/2017
9168	p(11586)#/2+32	53357	Robert Price	12/2016
9169	15^45362-46	53350	Lelio R Paula	01/2013
9170	14147^5892+5892^14147	53338	Hans Havermann	07/2016
9171	7^63109+46	53334	Lelio R Paula	10/2012
9172	20^40986-1343	53325	Enzo Doria	03/2013
9173	4*10^53324-89	53325	Robert Price	08/2017
9174	20^40977-8883	53313	Enzo Doria	03/2013
9175	3^111711+2660	53300	Lelio R Paula	10/2012
9176	2^177040-11865	53295	Enzo Doria	10/2012
9177	(7*10^53287+17)/3	53288	Erik Branger	03/2014
9178	35^34506-10758	53280	Enzo Doria	03/2013
9179	(11*10^53274-17)/3	53275	Erik Branger	03/2014
9180	(1017*2^176971-1)/335	53275	Lelio R Paula	03/2015
9181	2^176961-2833	53271	Yves Minet	09/2014
9182	3^111642+110	53267	Lelio R Paula	10/2012
9183	17^43290-98	53267	Lelio R Paula	01/2013
9184	7^63028+36	53265	Lelio R Paula	10/2012
9185	(22*10^53264+71)/3	53265	Robert Price	05/2017
9186	7^63023-36	53261	Lelio R Paula	10/2012
9187	19783^492+492^19783	53256	Anatoly F. Selevich	02/2007
9188	13350^9739+9739^13350	53247	Hans Havermann	10/2015
9189	14394^4993+4993^14394	53235	Hans Havermann	10/2015
9190	2^176823-112807	53230	Enzo Doria	06/2014
9191	1684^16495+16495^1684	53219	Serge Batalov	05/2014
9192	15277^3042+3042^15277	53213	Hans Havermann	06/2016
9193	(50322^11317-1)/50321	53206	Serge Batalov	04/2015
9194	2^176742-1595	53205	Lelio R Paula	10/2009
9195	(27*2^176767-1)/20455056355	53204	Lelio R Paula	01/2014
9196	(-lucasV(1,2,353460)-2)/(3^2*5^2)	53199	Mike Oakes	03/2017
9197	(3*2^176696-1)/299	53189	Lelio R Paula	01/2014
9198	(7*10^53185-1)/3	53186	Erik Branger	03/2014
9199	2^176629+465	53171	Lelio R Paula	07/2012
9200	(3*2^176604-1)/359	53162	Lelio R Paula	01/2014
9201	10955^13158-13158^10955	53154	Norbert Schneider	11/2017
9202	5^76038-14366	53149	Enzo Doria	02/2013
9203	15156^3209+3209^15156	53143	Hans Havermann	06/2016
9204	2^176532-2837	53142	Yves Minet	09/2014
9205	52^30967-51	53140	Norbert Schneider	08/2014
9206	9*5^76023-2	53139	Lelio R Paula	09/2014
9207	(14283!+1)/464216177	53135	Michael Porter	03/2016
9208	2^176461-165	53121	Lelio R Paula	02/2011
9209	(62*10^53111+1)/9	53112	Serge Batalov	05/2010
9210	2^176403-139	53103	Lelio R Paula	02/2011
9211	55^30508-2	53095	Lelio R Paula	08/2013
9212	(48591^11329-1)/48590	53090	Serge Batalov	04/2015
9213	3^111254-88	53082	Lelio R Paula	10/2012
9214	15^45129-56	53076	Lelio R Paula	01/2013
9215	2^176293-73	53070	Lelio R Paula	01/2011
9216	(67*10^53068+41)/9	53069	Robert Price	09/2015
9217	15271^2986+2986^15271	53069	Hans Havermann	06/2016
9218	2^176255-667	53059	Yves Minet	01/2012
9219	36471*2^176221+8647	53053	Paul Vanderveen	04/2016
9220	(19*10^53049-1)/9	53050	Serge Batalov	03/2009
9221	9*2^176203-5	53044	Lelio R Paula	03/2014
9222	2^176205-94395	53043	Lelio R Paula	08/2011
9223	(19*2^176224-1)/217916913	53042	Lelio R Paula	01/2014
9224	17^43103+14	53037	Lelio R Paula	01/2013
9225	(31*2^176188-1)/3555	53036	Lelio R Paula	01/2014
9226	2^176177+60947	53035	David Broadhurst	05/2002
9227	(22*10^53033-7)/3	53034	Erik Branger	09/2014
9228	13810^6909+6909^13810	53023	Hans Havermann	06/2016
9229	2^176108+16095	53014	Lelio R Paula	10/2009
9230	2^176107+18915	53014	Lelio R Paula	07/2012
9231	3^111080-9628	52999	Enzo Doria	02/2013
9232	2^176047-1551	52996	Yves Minet	08/2012
9233	2^176042+73519	52994	Enzo Doria	04/2016
9234	lucasV(1715,1,2^14)/65537	52986	Mike Oakes	04/2009
9235	2^175984-112259	52977	Enzo Doria	06/2014
9236	11^50870+10	52976	Lelio R Paula	01/2013
9237	(11*10^52956+19)/3	52957	Robert Price	03/2016
9238	gcd(V(949965),5F(189993)(F(189993)+1)+1)	52941	Serge Batalov	04/2015
9239	(-lucasV(1,2,351735)+2)/(37263)	52938	Mike Oakes	03/2017
9241	(98*10^52931-89)/99	52931	Ray Chandler	11/2010
9240	13774^6963+6963^13774	52931	Hans Havermann	06/2016
9242	2^175812-1367	52925	Yves Minet	05/2013
9243	2^175801+1155*175801	52922	Henri Lifchitz	01/2005
9244	11^50801-9090	52904	Enzo Doria	02/2013
9245	43^32374+12	52882	Robert Price	11/2013
9246	2^175628+13	52870	Lelio R Paula	01/2011
9247	2^175615-1747	52866	Yves Minet	09/2012
9248	(13*10^52861+107)/3	52862	Robert Price	11/2017
9249	9*2^175586-7	52858	Lelio R Paula	03/2014
9250	12174^12937+12937^12174	52854	Norbert Schneider	04/2016

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)