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 ?
9501	35^34970-8786	53997	Enzo Doria	03/2013
9502	2^179371-1637587	53997	Enzo Doria	05/2015
9503	19^42225-92	53996	Lelio R Paula	01/2013
9504	10190^13471-13471^10190	53995	Norbert Schneider	05/2018
9505	(3^113188+7)/73917675784	53994	Lelio R Paula	03/2012
9506	7*3^113162+8	53993	Lelio R Paula	03/2014
9507	(10^53991+179)/9	53991	Serge Batalov	12/2014
9509	2^179350-2145	53990	Lelio R Paula	10/2009
9508	(-lucasV(1,2,358718)-2)/(51719)	53990	Mike Oakes	04/2017
9510	8^59782-6^59782-3^59782	53989	Mike Oakes	11/2009
9511	3*7^63861+8	53970	Lelio R Paula	09/2014
9512	2^179274+71389	53967	Enzo Doria	04/2016
9513	2^179259-58695	53963	Lelio R Paula	10/2009
9514	6^69345+61	53961	Lelio R Paula	10/2012
9515	(-lucasV(1,2,358635)+2)/(71793172321719602511716271)	53957	Mike Oakes	04/2017
9516	(40216^11719-1)/40215	53955	Serge Batalov	04/2015
9517	89*10^53951-9	53953	Robert Price	05/2017
9518	6703^14100-14100^6703	53951	Norbert Schneider	11/2018
9519	14^47067-3	53945	Lelio R Paula	01/2013
9520	p(11700)#/2-512	53937	Robert Price	07/2017
9521	(2^179168-5)/59	53934	Lelio R Paula	02/2012
9522	2^179128+8415	53923	Lelio R Paula	07/2012
9523	2^179120+2533	53921	Henri Lifchitz	09/2004
9524	(2^179126+78557)/4649321187	53913	Lelio R Paula	05/2012
9525	74^28842+73	53913	Norbert Schneider	11/2012
9526	1271^17368+17368^1271	53913	Serge Batalov	05/2014
9527	2^179079+53	53909	Lelio R Paula	02/2011
9528	17^43807+54	53903	Lelio R Paula	01/2013
9529	17^43807+30	53903	Lelio R Paula	01/2013
9530	3^112951-310	53892	Lelio R Paula	10/2012
9531	Phi(7,2957!)	53888	Robert Price	05/2015
9532	8275^13754-13754^8275	53885	Norbert Schneider	10/2018
9533	(10223*2^178975+1)/33985	53877	Lelio R Paula	05/2014
9534	2^178944-219209	53868	Enzo Doria	11/2012
9535	(10^53859+149)/3	53859	Serge Batalov	12/2014
9536	2^178910-191	53858	Lelio R Paula	02/2011
9537	16170^2141+2141^16170	53857	Hans Havermann	07/2016
9538	(5*10^53855-107)/3	53856	Robert Price	01/2017
9539	(72*10^53847-27)/99	53847	Patrick De Geest	08/2004
9540	2^178841-869688105	53837	Lelio R Paula	06/2012
9541	2*10^53834-27	53835	Robert Price	02/2017
9543	2^178821-1011523	53831	Paul Bourdelais	11/2012
9542	12601^13128-13128^12601	53831	Norbert Schneider	10/2017
9544	2^178819-15	53830	Lelio R Paula	02/2011
9545	(14450!-1)/225296581	53829	Donovan Johnson	04/2006
9546	(124351#+125386)/(2^57188344891039820259)	53826	Makoto Morimoto	10/2017
9547	10530^13381-13381^10530	53825	Norbert Schneider	03/2018
9548	2^178761-465	53813	Lelio R Paula	10/2009
9549	18900^703+703^18900	53808	Anatoly F. Selevich	02/2007
9550	13918^7343+7343^13918	53806	Hans Havermann	08/2016
9551	10^53804+31749	53805	Patrick De Geest	12/2012
9552	10^53804-71	53804	Robert Price	05/2011
9553	t(178994)	53804	Robert Price	03/2015
9554	(2^178693-lucasV(1,2,178693)+1)/2	53792	Mike Oakes	11/2016
9555	2^178671-113215	53786	Enzo Doria	07/2014
9556	15110^3621+3621^15110	53774	Hans Havermann	07/2016
9557	2^178611+95	53768	Lelio R Paula	02/2011
9558	2^178597+5711	53764	Lelio R Paula	10/2011
9559	2^178598+12915	53764	Lelio R Paula	07/2012
9560	(9179*2^178579-1)/303	53760	Lelio R Paula	03/2015
9561	10671^13342-13342^10671	53745	Norbert Schneider	02/2018
9562	5*7^63589+2	53740	Lelio R Paula	09/2014
9563	2^178516-112515	53739	Enzo Doria	06/2014
9564	20^41302-27	53736	Lelio R Paula	01/2013
9565	6^69054-39209	53735	Mike Oakes	12/2010
9566	13086^12769+12769^13086	53734	Hans Havermann	07/2016
9567	2^178455+76043	53721	Enzo Doria	04/2016
9568	(10^53718-7)/3	53718	Makoto Kamada	10/2004
9569	(67607*2^178426+1)/3	53716	Lelio R Paula	05/2014
9570	9*10^53707+11	53708	Robert Kinser	01/2017
9571	94601!8-2	53708	Robert Price	04/2017
9572	13214^11595+11595^13214	53706	Hans Havermann	07/2016
9573	Phi(134350,10)/537401/8011962251	53705	Maksym Voznyy	10/2011
9574	2^178367-379	53694	Yves Minet	03/2013
9575	(2^178364-5)/11	53692	Lelio R Paula	02/2012
9576	4339^14760-168	53688	Enzo Doria	06/2012
9577	12^49746-11	53685	Lelio R Paula	01/2013
9578	12950^13051-13051^12950	53670	Norbert Schneider	08/2017
9580	(9913*2^178266-1)/2247	53665	Lelio R Paula	03/2015
9579	13725^8128+8128^13725	53665	Hans Havermann	07/2016
9581	2^178250-113261	53659	Enzo Doria	07/2014
9582	2^178226+11715	53652	Lelio R Paula	10/2009
9583	35^34742-1976	53645	Enzo Doria	03/2013
9584	20^41228-563	53639	Enzo Doria	03/2013
9585	359^20992+20992^359	53637	Norbert Schneider	08/2014
9586	(27*2^178183-1)/29065	53636	Lelio R Paula	01/2014
9587	(3^112414+7)/37381696	53628	Lelio R Paula	03/2012
9588	17994^955+955^17994	53623	Anatoly F. Selevich	10/2006
9589	2^178117-1551	53619	Yves Minet	08/2012
9590	2^178099-11287	53614	Enzo Doria	06/2014
9591	10751^13298-13298^10751	53611	Norbert Schneider	01/2018
9592	(15*2^178080-1)/309071	53604	Lelio R Paula	01/2014
9593	5^76672-13766	53592	Enzo Doria	02/2013
9594	6^68868-137	53590	Lelio R Paula	10/2012
9595	(5*2^178021+1)/8173	53587	Lelio R Paula	07/2012
9596	5^76654-26	53579	Lelio R Paula	10/2012
9597	(3^112297-2)/7627	53576	Lelio R Paula	03/2012
9598	3*2^177948-7	53569	Lelio R Paula	03/2014
9599	10^53558+18543	53559	Patrick De Geest	12/2012
9600	10^53558-21	53558	Robert Price	03/2011
9601	2^177792-95	53521	Lelio R Paula	02/2011
9602	13392^9919+9919^13392	53521	Hans Havermann	07/2016
9603	13105^12132+12132^13105	53520	Hans Havermann	07/2016
9604	13^48042+82	53517	Lelio R Paula	01/2013
9605	2^177768+39121	53514	Yves Minet	10/2010
9606	13835^7366+7366^13835	53504	Hans Havermann	07/2016
9607	17^43477+84	53497	Lelio R Paula	01/2013
9608	5*10^53492+9	53493	Dmitry Domanov	11/2010
9609	2^177683+95	53488	Lelio R Paula	01/2011
9610	11057^13226-13226^11057	53482	Norbert Schneider	12/2017
9611	(2^177678+3)/514627	53481	Lelio R Paula	02/2012
9612	2^177641-255463	53476	Gary Barnes	08/2009
9613	p(11608)#/2+16	53469	Robert Price	12/2016
9614	(14*10^53465+211)/9	53466	Robert Price	11/2017
9615	37302#*10^(37302+52)+p(37302+1)	53457	Jason Earls	08/2008
9616	12001^13104-13104^12001	53455	Norbert Schneider	10/2017
9617	1829^16384+1828^16384	53449	Henri Lifchitz	01/2007
9618	10^53442+12621	53443	Patrick De Geest	06/2018
9619	10^53442-2007	53442	Patrick De Geest	06/2018
9620	35^34608-9602	53438	Enzo Doria	03/2013
9621	(3^111992+8)/14867	53430	Lelio R Paula	03/2012
9623	2^177480+1869661	53427	Enzo Doria	05/2016
9622	11791^13122-13122^11791	53427	Norbert Schneider	10/2017
9624	(8*10^53411+1)/9	53411	Serge Batalov	12/2008
9625	4*5^76410-3	53409	Lelio R Paula	09/2014
9626	2^177380-113045	53397	Enzo Doria	07/2014
9628	5^76362-2*3^76362	53375	Mike Oakes	11/2009
9627	72365!6-24	53375	Robert Price	08/2018
9629	4159^14747-140	53370	Enzo Doria	07/2012
9630	(lucasV(1,2,354503)-2)/3	53358	Mike Oakes	03/2017
9631	p(11586)#/2+32	53357	Robert Price	12/2016
9632	15^45362-46	53350	Lelio R Paula	01/2013
9633	14147^5892+5892^14147	53338	Hans Havermann	07/2016
9634	7^63109+46	53334	Lelio R Paula	10/2012
9635	20^40986-1343	53325	Enzo Doria	03/2013
9636	4*10^53324-89	53325	Robert Price	08/2017
9637	20^40977-8883	53313	Enzo Doria	03/2013
9638	3^111711+2660	53300	Lelio R Paula	10/2012
9639	2^177040-11865	53295	Enzo Doria	10/2012
9640	(7*10^53287+17)/3	53288	Erik Branger	03/2014
9641	35^34506-10758	53280	Enzo Doria	03/2013
9642	(11*10^53274-17)/3	53275	Erik Branger	03/2014
9643	(1017*2^176971-1)/335	53275	Lelio R Paula	03/2015
9644	2^176961-2833	53271	Yves Minet	09/2014
9645	3^111642+110	53267	Lelio R Paula	10/2012
9646	17^43290-98	53267	Lelio R Paula	01/2013
9647	7^63028+36	53265	Lelio R Paula	10/2012
9648	(22*10^53264+71)/3	53265	Robert Price	05/2017
9649	7^63023-36	53261	Lelio R Paula	10/2012
9650	19783^492+492^19783	53256	Anatoly F. Selevich	02/2007
9651	13350^9739+9739^13350	53247	Hans Havermann	10/2015
9652	14394^4993+4993^14394	53235	Hans Havermann	10/2015
9653	2^176823-112807	53230	Enzo Doria	06/2014
9654	1684^16495+16495^1684	53219	Serge Batalov	05/2014
9655	15277^3042+3042^15277	53213	Hans Havermann	06/2016
9656	(50322^11317-1)/50321	53206	Serge Batalov	04/2015
9657	2^176742-1595	53205	Lelio R Paula	10/2009
9658	(27*2^176767-1)/20455056355	53204	Lelio R Paula	01/2014
9659	72149!6-12	53200	Robert Price	08/2018
9660	(-lucasV(1,2,353460)-2)/(3^2*5^2)	53199	Mike Oakes	03/2017
9661	(3*2^176696-1)/299	53189	Lelio R Paula	01/2014
9662	(7*10^53185-1)/3	53186	Erik Branger	03/2014
9663	2^176629+465	53171	Lelio R Paula	07/2012
9664	(3*2^176604-1)/359	53162	Lelio R Paula	01/2014
9665	10955^13158-13158^10955	53154	Norbert Schneider	11/2017
9666	5^76038-14366	53149	Enzo Doria	02/2013
9667	15156^3209+3209^15156	53143	Hans Havermann	06/2016
9668	2^176532-2837	53142	Yves Minet	09/2014
9669	52^30967-51	53140	Norbert Schneider	08/2014
9670	9*5^76023-2	53139	Lelio R Paula	09/2014
9671	(14283!+1)/464216177	53135	Michael Porter	03/2016
9672	2^176461-165	53121	Lelio R Paula	02/2011
9673	(62*10^53111+1)/9	53112	Serge Batalov	05/2010
9674	2^176403-139	53103	Lelio R Paula	02/2011
9675	55^30508-2	53095	Lelio R Paula	08/2013
9676	(48591^11329-1)/48590	53090	Serge Batalov	04/2015
9677	3^111254-88	53082	Lelio R Paula	10/2012
9678	15^45129-56	53076	Lelio R Paula	01/2013
9679	(640^18913-1)/639	53071	Eric Chen	09/2018
9680	2^176293-73	53070	Lelio R Paula	01/2011
9681	(67*10^53068+41)/9	53069	Robert Price	09/2015
9682	15271^2986+2986^15271	53069	Hans Havermann	06/2016
9683	2^176255-667	53059	Yves Minet	01/2012
9684	36471*2^176221+8647	53053	Paul Vanderveen	04/2016
9685	(19*10^53049-1)/9	53050	Serge Batalov	03/2009
9686	9*2^176203-5	53044	Lelio R Paula	03/2014
9687	2^176205-94395	53043	Lelio R Paula	08/2011
9688	(19*2^176224-1)/217916913	53042	Lelio R Paula	01/2014
9689	8600^13481-13481^8600	53041	Norbert Schneider	05/2018
9690	17^43103+14	53037	Lelio R Paula	01/2013
9691	(31*2^176188-1)/3555	53036	Lelio R Paula	01/2014
9692	2^176177+60947	53035	David Broadhurst	05/2002
9693	(22*10^53033-7)/3	53034	Erik Branger	09/2014
9694	13810^6909+6909^13810	53023	Hans Havermann	06/2016
9695	2^176108+16095	53014	Lelio R Paula	10/2009
9696	2^176107+18915	53014	Lelio R Paula	07/2012
9697	3^111080-9628	52999	Enzo Doria	02/2013
9698	2^176047-1551	52996	Yves Minet	08/2012
9699	2^176042+73519	52994	Enzo Doria	04/2016
9700	lucasV(1715,1,2^14)/65537	52986	Mike Oakes	04/2009
9701	2^175984-112259	52977	Enzo Doria	06/2014
9702	11^50870+10	52976	Lelio R Paula	01/2013
9703	(11*10^52956+19)/3	52957	Robert Price	03/2016
9704	6773^13820-13820^6773	52942	Norbert Schneider	11/2018
9705	gcd(V(949965),5F(189993)(F(189993)+1)+1)	52941	Serge Batalov	04/2015
9706	(-lucasV(1,2,351735)+2)/(37263)	52938	Mike Oakes	03/2017
9708	(98*10^52931-89)/99	52931	Ray Chandler	11/2010
9707	13774^6963+6963^13774	52931	Hans Havermann	06/2016
9709	2^175812-1367	52925	Yves Minet	05/2013
9710	2^175801+1155*175801	52922	Henri Lifchitz	01/2005
9711	11^50801-9090	52904	Enzo Doria	02/2013
9712	7803^13592-13592^7803	52904	Norbert Schneider	07/2018
9713	43^32374+12	52882	Robert Price	11/2013
9714	2^175628+13	52870	Lelio R Paula	01/2011
9715	2^175615-1747	52866	Yves Minet	09/2012
9716	(13*10^52861+107)/3	52862	Robert Price	11/2017
9717	9*2^175586-7	52858	Lelio R Paula	03/2014
9718	12174^12937+12937^12174	52854	Norbert Schneider	04/2016
9719	(15*2^175565+1)/8359	52848	Lelio R Paula	07/2012
9720	(2^175631-1)/330463093135534238072561/92733169	52839	Robert Kinser	03/2017
9721	14256^5077+5077^14256	52828	Hans Havermann	06/2016
9722	2^175467+82875	52821	Lelio R Paula	07/2012
9723	(7*10^52819+167)/3	52820	Robert Kinser	10/2017
9725	(67607*2^175426+1)/3	52813	Lelio R Paula	05/2014
9724	71671!6-32	52813	Robert Price	08/2018
9726	13^47400-60	52801	Lelio R Paula	01/2013
9727	4*10^52792+63	52793	Robert Price	06/2016
9729	(78557*2^175360+1)/3087	52791	Lelio R Paula	06/2014
9728	18^42055-2929	52791	Enzo Doria	03/2013
9730	9*5^75521+2	52788	Lelio R Paula	09/2014
9731	6^67814+31	52770	Lelio R Paula	10/2012
9732	70^28600+69	52770	Norbert Schneider	10/2012
9733	14^46038+97	52766	Lelio R Paula	01/2013
9734	(61*10^52763-7)/9	52764	Serge Batalov	02/2009
9735	2*5^75474+9	52755	Lelio R Paula	09/2014
9736	10^52753+2826430609	52754	Robert Price	05/2015
9737	10^52753+183997	52754	Patrick De Geest	01/2016
9738	10^52753-50153	52753	Patrick De Geest	03/2016
9739	19846^455+455^19846	52751	Anatoly F. Selevich	02/2007
9741	2^175217+72977	52746	Enzo Doria	04/2016
9740	p(11466)#/2-256	52746	Robert Price	05/2017
9742	(4*10^52740+41)/9	52740	Robert Price	11/2014
9743	2^175189+5385	52738	Lelio R Paula	08/2009
9744	2^175160+9385	52729	Lelio R Paula	07/2008
9745	12356^12885+12885^12356	52724	Norbert Schneider	03/2016
9746	2^175137+11	52722	Lelio R Paula	01/2011
9747	65^29077-64^29077	52715	Robert Price	08/2013
9748	2*10^52713-87	52714	Robert Price	06/2016
9749	2^175106-465	52713	Lelio R Paula	08/2009
9750	2^175089-58695	52708	Lelio R Paula	08/2009

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Probable Primes Top 10000

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