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 ?
9501	2^179790+33	54123	Donovan Johnson	02/2006
9502	14287^6138+6138^14287	54120	Hans Havermann	06/2016
9503	(17*10^54117+1)/9	54118	Serge Batalov	05/2010
9504	2^179763-189	54115	Lelio R Paula	02/2011
9505	(21181*2^179770+1)/3029105	54115	Lelio R Paula	05/2014
9506	1828^16589+16589^1828	54113	Serge Batalov	05/2014
9508	20^41588-5883	54108	Enzo Doria	03/2013
9507	50^31847-49	54108	Norbert Schneider	07/2014
9509	2^179733-6855	54106	Lelio R Paula	10/2009
9510	20^41584-5583	54103	Enzo Doria	03/2013
9511	10^54084+3*3^54084	54085	Mike Oakes	05/2010
9512	2^179613-1795	54069	Lelio R Paula	10/2009
9513	2^179589-1011523	54062	Paul Bourdelais	11/2012
9514	2^179574-2531	54058	Yves Minet	07/2014
9515	(41*10^54051-23)/9	54052	Robert Price	05/2015
9516	117^26131-116	54044	Norbert Schneider	10/2013
9517	(10^54038-31)/3	54038	Serge Batalov	12/2014
9518	11^51885-84	54033	Lelio R Paula	01/2013
9519	14990^4011+4011^14990	54013	Hans Havermann	07/2016
9520	(19*2^179414+1)/7	54010	Lelio R Paula	07/2012
9521	3^113182-10408	54002	Enzo Doria	02/2013
9522	35^34970-8786	53997	Enzo Doria	03/2013
9523	2^179371-1637587	53997	Enzo Doria	05/2015
9524	19^42225-92	53996	Lelio R Paula	01/2013
9525	10190^13471-13471^10190	53995	Norbert Schneider	05/2018
9526	(3^113188+7)/73917675784	53994	Lelio R Paula	03/2012
9527	7*3^113162+8	53993	Lelio R Paula	03/2014
9528	(10^53991+179)/9	53991	Serge Batalov	12/2014
9530	2^179350-2145	53990	Lelio R Paula	10/2009
9529	(-lucasV(1,2,358718)-2)/(51719)	53990	Mike Oakes	04/2017
9531	8^59782-6^59782-3^59782	53989	Mike Oakes	11/2009
9532	3*7^63861+8	53970	Lelio R Paula	09/2014
9533	2^179274+71389	53967	Enzo Doria	04/2016
9534	2^179259-58695	53963	Lelio R Paula	10/2009
9535	6^69345+61	53961	Lelio R Paula	10/2012
9536	(-lucasV(1,2,358635)+2)/(71793172321719602511716271)	53957	Mike Oakes	04/2017
9537	(40216^11719-1)/40215	53955	Serge Batalov	04/2015
9538	89*10^53951-9	53953	Robert Price	05/2017
9539	6703^14100-14100^6703	53951	Norbert Schneider	11/2018
9540	14^47067-3	53945	Lelio R Paula	01/2013
9541	p(11700)#/2-512	53937	Robert Price	07/2017
9542	(2^179168-5)/59	53934	Lelio R Paula	02/2012
9543	2^179128+8415	53923	Lelio R Paula	07/2012
9544	2^179120+2533	53921	Henri Lifchitz	09/2004
9546	(2^179126+78557)/4649321187	53913	Lelio R Paula	05/2012
9545	74^28842+73	53913	Norbert Schneider	11/2012
9547	1271^17368+17368^1271	53913	Serge Batalov	05/2014
9548	2^179079+53	53909	Lelio R Paula	02/2011
9549	17^43807+54	53903	Lelio R Paula	01/2013
9550	17^43807+30	53903	Lelio R Paula	01/2013
9551	3^112951-310	53892	Lelio R Paula	10/2012
9552	Phi(7,2957!)	53888	Robert Price	05/2015
9553	8275^13754-13754^8275	53885	Norbert Schneider	10/2018
9554	(10223*2^178975+1)/33985	53877	Lelio R Paula	05/2014
9555	2^178944-219209	53868	Enzo Doria	11/2012
9556	(10^53859+149)/3	53859	Serge Batalov	12/2014
9557	2^178910-191	53858	Lelio R Paula	02/2011
9558	16170^2141+2141^16170	53857	Hans Havermann	07/2016
9559	(5*10^53855-107)/3	53856	Robert Price	01/2017
9560	(72*10^53847-27)/99	53847	Patrick De Geest	08/2004
9561	2^178841-869688105	53837	Lelio R Paula	06/2012
9562	2*10^53834-27	53835	Robert Price	02/2017
9564	2^178821-1011523	53831	Paul Bourdelais	11/2012
9563	12601^13128-13128^12601	53831	Norbert Schneider	10/2017
9565	2^178819-15	53830	Lelio R Paula	02/2011
9566	(14450!-1)/225296581	53829	Donovan Johnson	04/2006
9567	(124351#+125386)/(2^57188344891039820259)	53826	Makoto Morimoto	10/2017
9568	10530^13381-13381^10530	53825	Norbert Schneider	03/2018
9569	2^178761-465	53813	Lelio R Paula	10/2009
9570	18900^703+703^18900	53808	Anatoly F. Selevich	02/2007
9571	13918^7343+7343^13918	53806	Hans Havermann	08/2016
9572	10^53804+31749	53805	Patrick De Geest	12/2012
9573	10^53804-71	53804	Robert Price	05/2011
9574	t(178994)	53804	Robert Price	03/2015
9575	(2^178693-lucasV(1,2,178693)+1)/2	53792	Mike Oakes	11/2016
9576	2^178671-113215	53786	Enzo Doria	07/2014
9577	15110^3621+3621^15110	53774	Hans Havermann	07/2016
9578	2^178611+95	53768	Lelio R Paula	02/2011
9579	2^178597+5711	53764	Lelio R Paula	10/2011
9580	2^178598+12915	53764	Lelio R Paula	07/2012
9581	(9179*2^178579-1)/303	53760	Lelio R Paula	03/2015
9582	10671^13342-13342^10671	53745	Norbert Schneider	02/2018
9583	5*7^63589+2	53740	Lelio R Paula	09/2014
9584	2^178516-112515	53739	Enzo Doria	06/2014
9585	20^41302-27	53736	Lelio R Paula	01/2013
9586	6^69054-39209	53735	Mike Oakes	12/2010
9587	13086^12769+12769^13086	53734	Hans Havermann	07/2016
9588	2^178455+76043	53721	Enzo Doria	04/2016
9589	(10^53718-7)/3	53718	Makoto Kamada	10/2004
9590	(67607*2^178426+1)/3	53716	Lelio R Paula	05/2014
9591	9*10^53707+11	53708	Robert Kinser	01/2017
9592	94601!8-2	53708	Robert Price	04/2017
9593	13214^11595+11595^13214	53706	Hans Havermann	07/2016
9594	Phi(134350,10)/537401/8011962251	53705	Maksym Voznyy	10/2011
9595	2^178367-379	53694	Yves Minet	03/2013
9596	(2^178364-5)/11	53692	Lelio R Paula	02/2012
9597	4339^14760-168	53688	Enzo Doria	06/2012
9598	12^49746-11	53685	Lelio R Paula	01/2013
9599	12950^13051-13051^12950	53670	Norbert Schneider	08/2017
9601	(9913*2^178266-1)/2247	53665	Lelio R Paula	03/2015
9600	13725^8128+8128^13725	53665	Hans Havermann	07/2016
9602	2^178250-113261	53659	Enzo Doria	07/2014
9603	2^178226+11715	53652	Lelio R Paula	10/2009
9604	35^34742-1976	53645	Enzo Doria	03/2013
9605	20^41228-563	53639	Enzo Doria	03/2013
9606	359^20992+20992^359	53637	Norbert Schneider	08/2014
9607	(27*2^178183-1)/29065	53636	Lelio R Paula	01/2014
9608	(3^112414+7)/37381696	53628	Lelio R Paula	03/2012
9609	17994^955+955^17994	53623	Anatoly F. Selevich	10/2006
9610	2^178117-1551	53619	Yves Minet	08/2012
9611	2^178099-11287	53614	Enzo Doria	06/2014
9612	10751^13298-13298^10751	53611	Norbert Schneider	01/2018
9613	(15*2^178080-1)/309071	53604	Lelio R Paula	01/2014
9614	5^76672-13766	53592	Enzo Doria	02/2013
9615	6^68868-137	53590	Lelio R Paula	10/2012
9616	(5*2^178021+1)/8173	53587	Lelio R Paula	07/2012
9617	5^76654-26	53579	Lelio R Paula	10/2012
9618	(3^112297-2)/7627	53576	Lelio R Paula	03/2012
9619	3*2^177948-7	53569	Lelio R Paula	03/2014
9620	10^53558+18543	53559	Patrick De Geest	12/2012
9621	10^53558-21	53558	Robert Price	03/2011
9622	2^177792-95	53521	Lelio R Paula	02/2011
9623	13392^9919+9919^13392	53521	Hans Havermann	07/2016
9624	13105^12132+12132^13105	53520	Hans Havermann	07/2016
9625	13^48042+82	53517	Lelio R Paula	01/2013
9626	2^177768+39121	53514	Yves Minet	10/2010
9627	13835^7366+7366^13835	53504	Hans Havermann	07/2016
9628	17^43477+84	53497	Lelio R Paula	01/2013
9629	5*10^53492+9	53493	Dmitry Domanov	11/2010
9630	2^177683+95	53488	Lelio R Paula	01/2011
9631	11057^13226-13226^11057	53482	Norbert Schneider	12/2017
9632	(2^177678+3)/514627	53481	Lelio R Paula	02/2012
9633	2^177641-255463	53476	Gary Barnes	08/2009
9634	p(11608)#/2+16	53469	Robert Price	12/2016
9635	(14*10^53465+211)/9	53466	Robert Price	11/2017
9636	37302#*10^(37302+52)+p(37302+1)	53457	Jason Earls	08/2008
9637	12001^13104-13104^12001	53455	Norbert Schneider	10/2017
9638	1829^16384+1828^16384	53449	Henri Lifchitz	01/2007
9639	10^53442+12621	53443	Patrick De Geest	06/2018
9640	10^53442-2007	53442	Patrick De Geest	06/2018
9641	35^34608-9602	53438	Enzo Doria	03/2013
9642	(3^111992+8)/14867	53430	Lelio R Paula	03/2012
9644	2^177480+1869661	53427	Enzo Doria	05/2016
9643	11791^13122-13122^11791	53427	Norbert Schneider	10/2017
9645	(8*10^53411+1)/9	53411	Serge Batalov	12/2008
9646	4*5^76410-3	53409	Lelio R Paula	09/2014
9647	2^177380-113045	53397	Enzo Doria	07/2014
9649	5^76362-2*3^76362	53375	Mike Oakes	11/2009
9648	72365!6-24	53375	Robert Price	08/2018
9650	4159^14747-140	53370	Enzo Doria	07/2012
9651	(lucasV(1,2,354503)-2)/3	53358	Mike Oakes	03/2017
9652	p(11586)#/2+32	53357	Robert Price	12/2016
9653	15^45362-46	53350	Lelio R Paula	01/2013
9654	14147^5892+5892^14147	53338	Hans Havermann	07/2016
9655	7^63109+46	53334	Lelio R Paula	10/2012
9656	20^40986-1343	53325	Enzo Doria	03/2013
9657	4*10^53324-89	53325	Robert Price	08/2017
9658	20^40977-8883	53313	Enzo Doria	03/2013
9659	3^111711+2660	53300	Lelio R Paula	10/2012
9660	2^177040-11865	53295	Enzo Doria	10/2012
9661	(7*10^53287+17)/3	53288	Erik Branger	03/2014
9662	35^34506-10758	53280	Enzo Doria	03/2013
9663	(11*10^53274-17)/3	53275	Erik Branger	03/2014
9664	(1017*2^176971-1)/335	53275	Lelio R Paula	03/2015
9665	2^176961-2833	53271	Yves Minet	09/2014
9666	3^111642+110	53267	Lelio R Paula	10/2012
9667	17^43290-98	53267	Lelio R Paula	01/2013
9668	7^63028+36	53265	Lelio R Paula	10/2012
9669	(22*10^53264+71)/3	53265	Robert Price	05/2017
9670	7^63023-36	53261	Lelio R Paula	10/2012
9671	19783^492+492^19783	53256	Anatoly F. Selevich	02/2007
9672	13350^9739+9739^13350	53247	Hans Havermann	10/2015
9673	14394^4993+4993^14394	53235	Hans Havermann	10/2015
9674	2^176823-112807	53230	Enzo Doria	06/2014
9675	1684^16495+16495^1684	53219	Serge Batalov	05/2014
9676	15277^3042+3042^15277	53213	Hans Havermann	06/2016
9677	(50322^11317-1)/50321	53206	Serge Batalov	04/2015
9678	2^176742-1595	53205	Lelio R Paula	10/2009
9679	(27*2^176767-1)/20455056355	53204	Lelio R Paula	01/2014
9680	72149!6-12	53200	Robert Price	08/2018
9681	(-lucasV(1,2,353460)-2)/(3^2*5^2)	53199	Mike Oakes	03/2017
9682	(3*2^176696-1)/299	53189	Lelio R Paula	01/2014
9683	(7*10^53185-1)/3	53186	Erik Branger	03/2014
9684	2^176629+465	53171	Lelio R Paula	07/2012
9685	(3*2^176604-1)/359	53162	Lelio R Paula	01/2014
9686	10955^13158-13158^10955	53154	Norbert Schneider	11/2017
9687	5^76038-14366	53149	Enzo Doria	02/2013
9688	15156^3209+3209^15156	53143	Hans Havermann	06/2016
9689	2^176532-2837	53142	Yves Minet	09/2014
9690	52^30967-51	53140	Norbert Schneider	08/2014
9691	9*5^76023-2	53139	Lelio R Paula	09/2014
9692	(14283!+1)/464216177	53135	Michael Porter	03/2016
9693	2^176461-165	53121	Lelio R Paula	02/2011
9694	(62*10^53111+1)/9	53112	Serge Batalov	05/2010
9695	2^176403-139	53103	Lelio R Paula	02/2011
9696	55^30508-2	53095	Lelio R Paula	08/2013
9697	(48591^11329-1)/48590	53090	Serge Batalov	04/2015
9698	3^111254-88	53082	Lelio R Paula	10/2012
9699	15^45129-56	53076	Lelio R Paula	01/2013
9700	(640^18913-1)/639	53071	Eric Chen	09/2018
9701	2^176293-73	53070	Lelio R Paula	01/2011
9702	(67*10^53068+41)/9	53069	Robert Price	09/2015
9703	15271^2986+2986^15271	53069	Hans Havermann	06/2016
9704	2^176255-667	53059	Yves Minet	01/2012
9705	36471*2^176221+8647	53053	Paul Vanderveen	04/2016
9706	(19*10^53049-1)/9	53050	Serge Batalov	03/2009
9707	9*2^176203-5	53044	Lelio R Paula	03/2014
9708	2^176205-94395	53043	Lelio R Paula	08/2011
9709	(19*2^176224-1)/217916913	53042	Lelio R Paula	01/2014
9710	8600^13481-13481^8600	53041	Norbert Schneider	05/2018
9711	17^43103+14	53037	Lelio R Paula	01/2013
9712	(31*2^176188-1)/3555	53036	Lelio R Paula	01/2014
9713	2^176177+60947	53035	David Broadhurst	05/2002
9714	(22*10^53033-7)/3	53034	Erik Branger	09/2014
9715	13810^6909+6909^13810	53023	Hans Havermann	06/2016
9716	2^176108+16095	53014	Lelio R Paula	10/2009
9717	2^176107+18915	53014	Lelio R Paula	07/2012
9718	3^111080-9628	52999	Enzo Doria	02/2013
9719	2^176047-1551	52996	Yves Minet	08/2012
9720	2^176042+73519	52994	Enzo Doria	04/2016
9721	lucasV(1715,1,2^14)/65537	52986	Mike Oakes	04/2009
9722	2^175984-112259	52977	Enzo Doria	06/2014
9723	11^50870+10	52976	Lelio R Paula	01/2013
9724	(11*10^52956+19)/3	52957	Robert Price	03/2016
9725	6773^13820-13820^6773	52942	Norbert Schneider	11/2018
9726	gcd(V(949965),5F(189993)(F(189993)+1)+1)	52941	Serge Batalov	04/2015
9727	(-lucasV(1,2,351735)+2)/(37263)	52938	Mike Oakes	03/2017
9728	(98*10^52931-89)/99	52931	Ray Chandler	11/2010
9729	13774^6963+6963^13774	52931	Hans Havermann	06/2016
9730	2^175812-1367	52925	Yves Minet	05/2013
9731	2^175801+1155*175801	52922	Henri Lifchitz	01/2005
9732	11^50801-9090	52904	Enzo Doria	02/2013
9733	7803^13592-13592^7803	52904	Norbert Schneider	07/2018
9734	43^32374+12	52882	Robert Price	11/2013
9735	155^24138+154	52871	Norbert Schneider	12/2018
9736	2^175628+13	52870	Lelio R Paula	01/2011
9737	2^175615-1747	52866	Yves Minet	09/2012
9738	(13*10^52861+107)/3	52862	Robert Price	11/2017
9739	9*2^175586-7	52858	Lelio R Paula	03/2014
9740	12174^12937+12937^12174	52854	Norbert Schneider	04/2016
9741	(15*2^175565+1)/8359	52848	Lelio R Paula	07/2012
9742	(2^175631-1)/330463093135534238072561/92733169	52839	Robert Kinser	03/2017
9743	14256^5077+5077^14256	52828	Hans Havermann	06/2016
9744	2^175467+82875	52821	Lelio R Paula	07/2012
9745	(7*10^52819+167)/3	52820	Robert Kinser	10/2017
9747	(67607*2^175426+1)/3	52813	Lelio R Paula	05/2014
9746	71671!6-32	52813	Robert Price	08/2018
9748	13^47400-60	52801	Lelio R Paula	01/2013
9749	4*10^52792+63	52793	Robert Price	06/2016
9750	18^42055-2929	52791	Enzo Doria	03/2013

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Probable Primes Top 10000

(252402 PRPs in the top)