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 ?
8501	(5*10^53855-107)/3	53856	Robert Price	01/2017
8502	(72*10^53847-27)/99	53847	Patrick De Geest	08/2004
8503	2^178841-869688105	53837	Lelio R Paula	06/2012
8504	2*10^53834-27	53835	Robert Price	02/2017
8505	2^178821-1011523	53831	Paul Bourdelais	11/2012
8506	2^178819-15	53830	Lelio R Paula	02/2011
8507	(14450!-1)/225296581	53829	Donovan Johnson	04/2006
8508	2^178761-465	53813	Lelio R Paula	10/2009
8509	18900^703+703^18900	53808	Anatoly F. Selevich	02/2007
8510	13918^7343+7343^13918	53806	Hans Havermann	08/2016
8511	10^53804+31749	53805	Patrick De Geest	12/2012
8512	10^53804-71	53804	Robert Price	05/2011
8513	t(178994)	53804	Robert Price	03/2015
8514	(2^178693-lucasV(1,2,178693)+1)/2	53792	Mike Oakes	11/2016
8515	2^178671-113215	53786	Enzo Doria	07/2014
8516	15110^3621+3621^15110	53774	Hans Havermann	07/2016
8517	2^178611+95	53768	Lelio R Paula	02/2011
8518	2^178597+5711	53764	Lelio R Paula	10/2011
8519	2^178598+12915	53764	Lelio R Paula	07/2012
8520	(9179*2^178579-1)/303	53760	Lelio R Paula	03/2015
8521	5*7^63589+2	53740	Lelio R Paula	09/2014
8522	2^178516-112515	53739	Enzo Doria	06/2014
8523	20^41302-27	53736	Lelio R Paula	01/2013
8524	6^69054-39209	53735	Mike Oakes	12/2010
8525	13086^12769+12769^13086	53734	Hans Havermann	07/2016
8526	2^178455+76043	53721	Enzo Doria	04/2016
8527	(10^53718-7)/3	53718	Makoto Kamada	10/2004
8528	(67607*2^178426+1)/3	53716	Lelio R Paula	05/2014
8529	9*10^53707+11	53708	Robert Kinser	01/2017
8530	94601!8-2	53708	Robert Price	04/2017
8531	13214^11595+11595^13214	53706	Hans Havermann	07/2016
8532	Phi(134350,10)/537401/8011962251	53705	Maksym Voznyy	10/2011
8533	2^178367-379	53694	Yves Minet	03/2013
8534	(2^178364-5)/11	53692	Lelio R Paula	02/2012
8535	4339^14760-168	53688	Enzo Doria	06/2012
8536	12^49746-11	53685	Lelio R Paula	01/2013
8538	(9913*2^178266-1)/2247	53665	Lelio R Paula	03/2015
8537	13725^8128+8128^13725	53665	Hans Havermann	07/2016
8539	2^178250-113261	53659	Enzo Doria	07/2014
8540	2^178226+11715	53652	Lelio R Paula	10/2009
8541	35^34742-1976	53645	Enzo Doria	03/2013
8542	20^41228-563	53639	Enzo Doria	03/2013
8543	359^20992+20992^359	53637	Norbert Schneider	08/2014
8544	(27*2^178183-1)/29065	53636	Lelio R Paula	01/2014
8545	(3^112414+7)/37381696	53628	Lelio R Paula	03/2012
8546	17994^955+955^17994	53623	Anatoly F. Selevich	10/2006
8547	2^178117-1551	53619	Yves Minet	08/2012
8548	2^178099-11287	53614	Enzo Doria	06/2014
8549	(15*2^178080-1)/309071	53604	Lelio R Paula	01/2014
8550	5^76672-13766	53592	Enzo Doria	02/2013
8551	6^68868-137	53590	Lelio R Paula	10/2012
8552	(5*2^178021+1)/8173	53587	Lelio R Paula	07/2012
8553	5^76654-26	53579	Lelio R Paula	10/2012
8554	(3^112297-2)/7627	53576	Lelio R Paula	03/2012
8555	3*2^177948-7	53569	Lelio R Paula	03/2014
8556	10^53558+18543	53559	Patrick De Geest	12/2012
8557	10^53558-21	53558	Robert Price	03/2011
8558	2^177792-95	53521	Lelio R Paula	02/2011
8559	13392^9919+9919^13392	53521	Hans Havermann	07/2016
8560	13105^12132+12132^13105	53520	Hans Havermann	07/2016
8561	13^48042+82	53517	Lelio R Paula	01/2013
8562	2^177768+39121	53514	Yves Minet	10/2010
8563	13835^7366+7366^13835	53504	Hans Havermann	07/2016
8564	17^43477+84	53497	Lelio R Paula	01/2013
8565	5*10^53492+9	53493	Dmitry Domanov	11/2010
8566	2^177683+95	53488	Lelio R Paula	01/2011
8567	(2^177678+3)/514627	53481	Lelio R Paula	02/2012
8568	2^177641-255463	53476	Gary Barnes	08/2009
8569	p(11608)#/2+16	53469	Robert Price	12/2016
8570	37302#*10^(37302+52)+p(37302+1)	53457	Jason Earls	08/2008
8571	1829^16384+1828^16384	53449	Henri Lifchitz	01/2007
8572	35^34608-9602	53438	Enzo Doria	03/2013
8573	(3^111992+8)/14867	53430	Lelio R Paula	03/2012
8574	2^177480+1869661	53427	Enzo Doria	05/2016
8575	(8*10^53411+1)/9	53411	Serge Batalov	12/2008
8576	4*5^76410-3	53409	Lelio R Paula	09/2014
8577	2^177380-113045	53397	Enzo Doria	07/2014
8578	5^76362-2*3^76362	53375	Mike Oakes	11/2009
8579	4159^14747-140	53370	Enzo Doria	07/2012
8580	(lucasV(1,2,354503)-2)/3	53358	Mike Oakes	03/2017
8581	p(11586)#/2+32	53357	Robert Price	12/2016
8582	15^45362-46	53350	Lelio R Paula	01/2013
8583	14147^5892+5892^14147	53338	Hans Havermann	07/2016
8584	7^63109+46	53334	Lelio R Paula	10/2012
8585	20^40986-1343	53325	Enzo Doria	03/2013
8586	4*10^53324-89	53325	Robert Price	08/2017
8587	20^40977-8883	53313	Enzo Doria	03/2013
8588	3^111711+2660	53300	Lelio R Paula	10/2012
8589	2^177040-11865	53295	Enzo Doria	10/2012
8590	(7*10^53287+17)/3	53288	Erik Branger	03/2014
8591	35^34506-10758	53280	Enzo Doria	03/2013
8592	(11*10^53274-17)/3	53275	Erik Branger	03/2014
8593	(1017*2^176971-1)/335	53275	Lelio R Paula	03/2015
8594	2^176961-2833	53271	Yves Minet	09/2014
8595	3^111642+110	53267	Lelio R Paula	10/2012
8596	17^43290-98	53267	Lelio R Paula	01/2013
8597	7^63028+36	53265	Lelio R Paula	10/2012
8598	(22*10^53264+71)/3	53265	Robert Price	05/2017
8599	7^63023-36	53261	Lelio R Paula	10/2012
8600	19783^492+492^19783	53256	Anatoly F. Selevich	02/2007
8601	13350^9739+9739^13350	53247	Hans Havermann	10/2015
8602	14394^4993+4993^14394	53235	Hans Havermann	10/2015
8603	2^176823-112807	53230	Enzo Doria	06/2014
8604	1684^16495+16495^1684	53219	Serge Batalov	05/2014
8605	15277^3042+3042^15277	53213	Hans Havermann	06/2016
8606	(50322^11317-1)/50321	53206	Serge Batalov	04/2015
8607	2^176742-1595	53205	Lelio R Paula	10/2009
8608	(27*2^176767-1)/20455056355	53204	Lelio R Paula	01/2014
8609	(-lucasV(1,2,353460)-2)/(3^2*5^2)	53199	Mike Oakes	03/2017
8610	(3*2^176696-1)/299	53189	Lelio R Paula	01/2014
8611	(7*10^53185-1)/3	53186	Erik Branger	03/2014
8612	2^176629+465	53171	Lelio R Paula	07/2012
8613	(3*2^176604-1)/359	53162	Lelio R Paula	01/2014
8614	5^76038-14366	53149	Enzo Doria	02/2013
8615	15156^3209+3209^15156	53143	Hans Havermann	06/2016
8616	2^176532-2837	53142	Yves Minet	09/2014
8617	52^30967-51	53140	Norbert Schneider	08/2014
8618	9*5^76023-2	53139	Lelio R Paula	09/2014
8619	(14283!+1)/464216177	53135	Michael Porter	03/2016
8620	2^176461-165	53121	Lelio R Paula	02/2011
8621	(62*10^53111+1)/9	53112	Serge Batalov	05/2010
8622	2^176403-139	53103	Lelio R Paula	02/2011
8623	55^30508-2	53095	Lelio R Paula	08/2013
8624	(48591^11329-1)/48590	53090	Serge Batalov	04/2015
8625	3^111254-88	53082	Lelio R Paula	10/2012
8626	15^45129-56	53076	Lelio R Paula	01/2013
8627	2^176293-73	53070	Lelio R Paula	01/2011
8628	(67*10^53068+41)/9	53069	Robert Price	09/2015
8629	15271^2986+2986^15271	53069	Hans Havermann	06/2016
8630	2^176255-667	53059	Yves Minet	01/2012
8631	36471*2^176221+8647	53053	Paul Vanderveen	04/2016
8632	(19*10^53049-1)/9	53050	Serge Batalov	03/2009
8633	9*2^176203-5	53044	Lelio R Paula	03/2014
8634	2^176205-94395	53043	Lelio R Paula	08/2011
8635	(19*2^176224-1)/217916913	53042	Lelio R Paula	01/2014
8636	17^43103+14	53037	Lelio R Paula	01/2013
8637	(31*2^176188-1)/3555	53036	Lelio R Paula	01/2014
8638	2^176177+60947	53035	David Broadhurst	05/2002
8639	(22*10^53033-7)/3	53034	Erik Branger	09/2014
8640	13810^6909+6909^13810	53023	Hans Havermann	06/2016
8642	2^176108+16095	53014	Lelio R Paula	10/2009
8641	2^176107+18915	53014	Lelio R Paula	07/2012
8643	3^111080-9628	52999	Enzo Doria	02/2013
8644	2^176047-1551	52996	Yves Minet	08/2012
8645	2^176042+73519	52994	Enzo Doria	04/2016
8646	lucasV(1715,1,2^14)/65537	52986	Mike Oakes	04/2009
8647	2^175984-112259	52977	Enzo Doria	06/2014
8648	11^50870+10	52976	Lelio R Paula	01/2013
8649	(11*10^52956+19)/3	52957	Robert Price	03/2016
8650	gcd(V(949965),5F(189993)(F(189993)+1)+1)	52941	Serge Batalov	04/2015
8651	(-lucasV(1,2,351735)+2)/(37263)	52938	Mike Oakes	03/2017
8652	(98*10^52931-89)/99	52931	Ray Chandler	11/2010
8653	13774^6963+6963^13774	52931	Hans Havermann	06/2016
8654	2^175812-1367	52925	Yves Minet	05/2013
8655	2^175801+1155*175801	52922	Henri Lifchitz	01/2005
8656	11^50801-9090	52904	Enzo Doria	02/2013
8657	43^32374+12	52882	Robert Price	11/2013
8658	2^175628+13	52870	Lelio R Paula	01/2011
8659	2^175615-1747	52866	Yves Minet	09/2012
8660	9*2^175586-7	52858	Lelio R Paula	03/2014
8661	12174^12937+12937^12174	52854	Norbert Schneider	04/2016
8662	(15*2^175565+1)/8359	52848	Lelio R Paula	07/2012
8663	(2^175631-1)/330463093135534238072561/92733169	52839	Robert Kinser	03/2017
8664	14256^5077+5077^14256	52828	Hans Havermann	06/2016
8665	2^175467+82875	52821	Lelio R Paula	07/2012
8666	(67607*2^175426+1)/3	52813	Lelio R Paula	05/2014
8667	13^47400-60	52801	Lelio R Paula	01/2013
8668	4*10^52792+63	52793	Robert Price	06/2016
8670	(78557*2^175360+1)/3087	52791	Lelio R Paula	06/2014
8669	18^42055-2929	52791	Enzo Doria	03/2013
8671	9*5^75521+2	52788	Lelio R Paula	09/2014
8672	6^67814+31	52770	Lelio R Paula	10/2012
8673	70^28600+69	52770	Norbert Schneider	10/2012
8674	14^46038+97	52766	Lelio R Paula	01/2013
8675	(61*10^52763-7)/9	52764	Serge Batalov	02/2009
8676	2*5^75474+9	52755	Lelio R Paula	09/2014
8677	10^52753+2826430609	52754	Robert Price	05/2015
8678	10^52753+183997	52754	Patrick De Geest	01/2016
8679	10^52753-50153	52753	Patrick De Geest	03/2016
8680	19846^455+455^19846	52751	Anatoly F. Selevich	02/2007
8681	2^175217+72977	52746	Enzo Doria	04/2016
8682	p(11466)#/2-256	52746	Robert Price	05/2017
8683	(4*10^52740+41)/9	52740	Robert Price	11/2014
8684	2^175189+5385	52738	Lelio R Paula	08/2009
8685	2^175160+9385	52729	Lelio R Paula	07/2008
8686	12356^12885+12885^12356	52724	Norbert Schneider	03/2016
8687	2^175137+11	52722	Lelio R Paula	01/2011
8688	65^29077-64^29077	52715	Robert Price	08/2013
8689	2*10^52713-87	52714	Robert Price	06/2016
8690	2^175106-465	52713	Lelio R Paula	08/2009
8691	2^175089-58695	52708	Lelio R Paula	08/2009
8692	2^175045+195	52694	Lelio R Paula	02/2011
8693	2^175025+149	52688	Lelio R Paula	02/2011
8694	(19^41201+1)/20	52685	Paul Bourdelais	03/2010
8695	2*12^48815-5^48815	52681	Mike Oakes	10/2010
8696	335^20862-20862^335	52678	Norbert Schneider	09/2015
8697	2^174983-7605	52676	Lelio R Paula	07/2009
8698	4*10^52667+19	52668	Robert Price	04/2016
8699	(10^52667+77)/3	52667	Robert Price	01/2017
8700	11434^12977+12977^11434	52664	Norbert Schneider	04/2016
8701	2^174941-1203	52663	Lelio R Paula	07/2009
8702	2^174910+12705	52654	Lelio R Paula	07/2012
8703	3^110338+74	52645	Lelio R Paula	10/2012
8704	5^75303+12	52635	Lelio R Paula	10/2012
8705	2^174836+255255	52631	Lelio R Paula	07/2009
8706	20^40443+9	52618	Lelio R Paula	01/2013
8707	(11*2^174788+1)/9	52617	Lelio R Paula	01/2012
8708	(11*2^174786-1)/703	52615	Lelio R Paula	01/2014
8709	11^50520-1290	52612	Enzo Doria	11/2012
8710	(9913*2^174736-1)/333	52603	Lelio R Paula	03/2015
8711	13145^10024+10024^13145	52594	Hans Havermann	05/2016
8712	5003^14217-150	52592	Enzo Doria	07/2012
8713	19^41123+10	52587	Lelio R Paula	01/2013
8714	2^174683+12909	52585	Lelio R Paula	01/2011
8715	2^174643+59	52573	Lelio R Paula	01/2011
8716	(1017*2^174640-1)/773	52572	Lelio R Paula	03/2015
8717	13529^7662+7662^13529	52552	Hans Havermann	06/2016
8718	121421#+188767	52548	Makoto Morimoto	02/2016
8719	20^40375-5923	52530	Enzo Doria	03/2013
8720	(67607*2^174503+1)/90948079	52528	Lelio R Paula	05/2014
8721	(-lucasV(1,2,349014)+2)/(7508731047043)	52521	Mike Oakes	03/2017
8722	2^174462+345	52519	Lelio R Paula	07/2009
8723	t(178863)	52509	Robert Price	10/2014
8724	2^174416+855	52505	Lelio R Paula	07/2009
8725	6^67467-103	52500	Lelio R Paula	10/2012
8726	(2^174533-1)/(193594572654550537*91917886778031629891960890057)	52494	Dario Alpern	06/2017
8727	2^174329-11265	52479	Enzo Doria	06/2014
8728	2^174314-1241	52474	Yves Minet	05/2009
8729	52^30577-51	52471	Norbert Schneider	08/2014
8730	15692^2205+2205^15692	52465	Hans Havermann	06/2016
8731	(2^174281-7)/628817029615	52453	Lelio R Paula	02/2012
8732	(2^174240+5)/3	52451	Lelio R Paula	02/2012
8733	(86*10^52450-221)/9	52451	Robert Price	06/2017
8734	(15*2^174221+1)/403	52445	Lelio R Paula	07/2012
8735	26313!2-32	52443	Robert Price	10/2015
8736	(3*2^174214-1)/3748729	52438	Lelio R Paula	01/2014
8737	2*3^109900-5	52436	Lelio R Paula	03/2014
8739	4159^14488-150	52432	Enzo Doria	07/2012
8738	(89*10^52431-71)/9	52432	Robert Price	11/2015
8740	2^174170-3941	52431	Yves Minet	04/2017
8741	(7*2^174171-1)/685	52429	Lelio R Paula	01/2014
8743	(260137^9679+1)/260138	52409	Faysal YAtim	03/2008
8742	2^174098+79	52409	Lelio R Paula	01/2011
8744	35^33940-2214	52406	Enzo Doria	03/2013
8745	15^44557+2	52404	Ray Chandler	07/2011
8746	2^174049-439	52394	Yves Minet	01/2012
8747	6^67329+115	52393	Lelio R Paula	10/2012
8749	2^174041+262145	52392	Lelio R Paula	07/2009
8748	141^24377+2	52392	Lelio R Paula	05/2013
8750	lucasU(285,1,21339)-lucasU(285,1,21338)	52382	Mike Oakes	05/2009

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Probable Primes Top 10000

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