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 ?
8251	2^181874+181874^2-1	54750	Robert Price	04/2014
8252	(2^181865+9)/7339	54743	Lelio R Paula	02/2012
8253	5^78314-92	54740	Lelio R Paula	10/2012
8254	(163*10^54727-1)/9	54729	Serge Batalov	12/2014
8255	15^46531+74	54725	Lelio R Paula	02/2013
8256	277^22400-348	54712	Enzo Doria	07/2012
8257	6^70302+101	54706	Lelio R Paula	10/2012
8258	3^114622-10408	54689	Enzo Doria	02/2013
8260	(23*2^181674+1)/489	54688	Lelio R Paula	01/2012
8259	2^181669-1551	54688	Yves Minet	08/2012
8261	(57352^11491-1)/57351	54676	Serge Batalov	04/2015
8262	(31*2^181629-1)/10734721	54671	Lelio R Paula	01/2014
8263	(F(1048)^251-F(1047)^251)/F(1046)	54668	Wayne Halsdorf	05/2010
8264	13^49073+46	54665	Lelio R Paula	01/2013
8265	(57042^11491-1)/57041	54649	Serge Batalov	04/2015
8267	20^42000+73	54644	Lelio R Paula	02/2013
8266	(67607*2^181517+1)/1655	54644	Lelio R Paula	05/2014
8268	33*10^54634+7	54636	Robert Price	07/2016
8269	20^41988+61	54628	Lelio R Paula	01/2013
8270	20^41988-8123	54628	Enzo Doria	03/2013
8271	2^181420+21181	54613	Yves Minet	03/2011
8272	(19*10^54608+161)/9	54609	Robert Price	07/2016
8273	19^42696-24	54598	Lelio R Paula	02/2013
8274	(74*10^54583+61)/9	54584	Robert Price	10/2015
8275	2^181316-94395	54582	Lelio R Paula	09/2011
8276	14751^5006+5006^14751	54572	Hans Havermann	08/2016
8277	14^47609+39	54567	Lelio R Paula	02/2013
8278	3^114327-74	54548	Lelio R Paula	10/2012
8279	gcd(V(995625),5F(199125)(F(199125)-1)+1)	54546	Serge Batalov	04/2015
8280	(17*10^54537-47)/3	54538	Robert Price	05/2017
8281	2^181155-1155*181155	54534	Henri Lifchitz	02/2005
8282	Phi(61672,83)	54533	Enzo Doria	05/2012
8283	9*2^181128+7	54526	Lelio R Paula	03/2014
8284	89*10^54518-7	54520	Robert Price	03/2017
8285	2^181090-113247	54514	Enzo Doria	07/2014
8286	14031^7670+7670^14031	54508	Hans Havermann	08/2016
8287	14210^6849+6849^14210	54505	Hans Havermann	08/2016
8288	2^181043-199	54500	Lelio R Paula	02/2011
8289	12^50499+5	54498	Lelio R Paula	01/2013
8290	12^50491+5	54489	Lelio R Paula	01/2013
8291	6^70016-145	54484	Lelio R Paula	10/2012
8292	11^52313-9600	54479	Enzo Doria	02/2013
8293	2^64459+3^64459+5^64459+7^64459	54475	Henri Lifchitz	08/2001
8294	2^180946-111041	54471	Enzo Doria	05/2014
8295	(64*10^54467+287)/9	54468	Robert Price	04/2016
8296	5^77907-2*3^77907	54455	Mike Oakes	11/2009
8297	20^41853-5623	54453	Enzo Doria	03/2013
8298	14^47506-75	54448	Lelio R Paula	02/2013
8299	2^180839-113437	54438	Enzo Doria	08/2014
8300	3^114085+28	54433	Lelio R Paula	10/2012
8301	Phi(141230,10)	54432	Ray Chandler	08/2009
8302	6^69946-55	54429	Lelio R Paula	10/2012
8303	5*2^180796+3	54426	Lelio R Paula	03/2014
8304	(23*2^180782-1)/91	54421	Lelio R Paula	01/2014
8305	9*6^69928-7	54416	Lelio R Paula	09/2014
8306	92^27701-91^27701	54399	Robert Price	08/2015
8307	(2^180687-3)*6-7	54393	Gilbert Mozzo	04/2016
8308	(5*10^54388-11)/3	54389	Erik Branger	12/2013
8309	20^41799-3043	54382	Enzo Doria	03/2013
8310	13860^8387+8387^13860	54382	Hans Havermann	08/2016
8311	(F(19)^15017-F(18)^15017)/F(17)	54378	Wayne Halsdorf	05/2010
8312	7^64329-18	54365	Lelio R Paula	10/2012
8313	2^180551-967	54352	Yves Minet	01/2012
8314	15^46209-74	54347	Lelio R Paula	02/2013
8315	10^54345+29739	54346	Patrick De Geest	08/2013
8316	10^54345-141381	54345	Patrick De Geest	09/2013
8317	lucasU(2098,1,16360)-lucasU(2098,1,16359)	54342	Mike Oakes	05/2009
8318	2^180496+15	54335	Lelio R Paula	02/2011
8319	1845^16636+16636^1845	54334	Serge Batalov	05/2014
8320	11^52169-70	54329	Lelio R Paula	01/2013
8321	13693^9262+9262^13693	54317	Hans Havermann	06/2016
8322	2^180429-113101	54315	Enzo Doria	07/2014
8323	2^180423-112051	54313	Enzo Doria	05/2014
8324	16112^2349+2349^16112	54312	Hans Havermann	06/2016
8325	(13^48751+4^48751)/17	54305	Robert Price	05/2013
8326	2^180370+12915	54297	Lelio R Paula	09/2012
8327	(10^54290+41)/3	54290	Robert Price	01/2017
8328	15108^3917+3917^15108	54283	Hans Havermann	06/2016
8329	2^180317-3019	54281	Yves Minet	10/2014
8330	2^180314+855	54280	Lelio R Paula	10/2009
8331	19^42425+94	54252	Lelio R Paula	02/2013
8332	2^180180-1005449	54240	Paul Bourdelais	11/2012
8334	2^180173-2773	54238	Yves Minet	07/2014
8333	13367^11418+11418^13367	54238	Hans Havermann	06/2016
8335	427^20614+20614^427	54224	Norbert Schneider	06/2016
8336	2^180124-87959	54223	Gary Barnes	08/2009
8337	2^180111-113101	54219	Enzo Doria	07/2014
8338	2^180101-114871	54216	Enzo Doria	05/2015
8339	(11*2^180099+1)/51617	54212	Lelio R Paula	07/2012
8341	2^180070+465	54207	Lelio R Paula	09/2012
8340	13683^9154+9154^13683	54207	Hans Havermann	06/2016
8342	8105225132^180009-95312^9531-1	54198	Jiong Sun	12/2003
8343	2^180014+613	54190	Jason Earls	04/2008
8344	2^180007+101	54188	Lelio R Paula	02/2011
8345	2^180001+41877	54186	Jim Fougeron	08/2002
8346	2^180000+130153	54186	Jim Fougeron	09/2002
8347	3^113565-74	54185	Lelio R Paula	10/2012
8348	50^31891-49	54182	Norbert Schneider	07/2014
8349	(5*2^179991-1)/11427	54180	Lelio R Paula	01/2014
8351	3^113548+26	54177	Lelio R Paula	10/2012
8350	(lucasV(1,2,360029)-2)/(3^3522251725981)	54177	Mike Oakes	04/2017
8352	4159^14969-138	54173	Enzo Doria	07/2012
8354	2^179955+5775	54172	Lelio R Paula	10/2009
8353	2^179953-231313	54172	Enzo Doria	05/2014
8355	5^77485+6	54160	Lelio R Paula	10/2012
8356	18^43141+85	54154	Lelio R Paula	02/2013
8357	3^113489-340	54149	Lelio R Paula	10/2012
8358	10^54149-800001	54149	Robert Price	06/2017
8359	7^64070+90	54146	Lelio R Paula	10/2012
8360	18^43131+71	54142	Lelio R Paula	02/2013
8361	2^179826-131	54134	Lelio R Paula	02/2011
8362	2^179815-112735	54130	Enzo Doria	06/2014
8363	2^179806+73849	54127	Enzo Doria	04/2016
8364	2^179790+33	54123	Donovan Johnson	02/2006
8365	14287^6138+6138^14287	54120	Hans Havermann	06/2016
8366	(17*10^54117+1)/9	54118	Serge Batalov	05/2010
8367	2^179763-189	54115	Lelio R Paula	02/2011
8368	(21181*2^179770+1)/3029105	54115	Lelio R Paula	05/2014
8369	1828^16589+16589^1828	54113	Serge Batalov	05/2014
8371	20^41588-5883	54108	Enzo Doria	03/2013
8370	50^31847-49	54108	Norbert Schneider	07/2014
8372	2^179733-6855	54106	Lelio R Paula	10/2009
8373	20^41584-5583	54103	Enzo Doria	03/2013
8374	10^54084+3*3^54084	54085	Mike Oakes	05/2010
8375	2^179613-1795	54069	Lelio R Paula	10/2009
8376	2^179589-1011523	54062	Paul Bourdelais	11/2012
8377	2^179574-2531	54058	Yves Minet	07/2014
8378	(41*10^54051-23)/9	54052	Robert Price	05/2015
8379	117^26131-116	54044	Norbert Schneider	10/2013
8380	(10^54038-31)/3	54038	Serge Batalov	12/2014
8381	11^51885-84	54033	Lelio R Paula	01/2013
8382	14990^4011+4011^14990	54013	Hans Havermann	07/2016
8383	(19*2^179414+1)/7	54010	Lelio R Paula	07/2012
8384	3^113182-10408	54002	Enzo Doria	02/2013
8385	35^34970-8786	53997	Enzo Doria	03/2013
8386	2^179371-1637587	53997	Enzo Doria	05/2015
8387	19^42225-92	53996	Lelio R Paula	01/2013
8388	(3^113188+7)/73917675784	53994	Lelio R Paula	03/2012
8389	7*3^113162+8	53993	Lelio R Paula	03/2014
8390	(10^53991+179)/9	53991	Serge Batalov	12/2014
8391	2^179350-2145	53990	Lelio R Paula	10/2009
8392	(-lucasV(1,2,358718)-2)/(51719)	53990	Mike Oakes	04/2017
8393	8^59782-6^59782-3^59782	53989	Mike Oakes	11/2009
8394	3*7^63861+8	53970	Lelio R Paula	09/2014
8395	2^179274+71389	53967	Enzo Doria	04/2016
8396	2^179259-58695	53963	Lelio R Paula	10/2009
8397	6^69345+61	53961	Lelio R Paula	10/2012
8398	(-lucasV(1,2,358635)+2)/(71793172321719602511716271)	53957	Mike Oakes	04/2017
8399	(40216^11719-1)/40215	53955	Serge Batalov	04/2015
8400	89*10^53951-9	53953	Robert Price	05/2017
8401	14^47067-3	53945	Lelio R Paula	01/2013
8402	(2^179168-5)/59	53934	Lelio R Paula	02/2012
8403	2^179128+8415	53923	Lelio R Paula	07/2012
8404	2^179120+2533	53921	Henri Lifchitz	09/2004
8405	(2^179126+78557)/4649321187	53913	Lelio R Paula	05/2012
8407	74^28842+73	53913	Norbert Schneider	11/2012
8406	1271^17368+17368^1271	53913	Serge Batalov	05/2014
8408	2^179079+53	53909	Lelio R Paula	02/2011
8409	17^43807+54	53903	Lelio R Paula	01/2013
8410	17^43807+30	53903	Lelio R Paula	01/2013
8411	3^112951-310	53892	Lelio R Paula	10/2012
8412	Phi(7,2957!)	53888	Robert Price	05/2015
8413	(10223*2^178975+1)/33985	53877	Lelio R Paula	05/2014
8414	2^178944-219209	53868	Enzo Doria	11/2012
8415	(10^53859+149)/3	53859	Serge Batalov	12/2014
8416	2^178910-191	53858	Lelio R Paula	02/2011
8417	16170^2141+2141^16170	53857	Hans Havermann	07/2016
8418	(5*10^53855-107)/3	53856	Robert Price	01/2017
8419	(72*10^53847-27)/99	53847	Patrick De Geest	08/2004
8420	2^178841-869688105	53837	Lelio R Paula	06/2012
8421	2*10^53834-27	53835	Robert Price	02/2017
8422	2^178821-1011523	53831	Paul Bourdelais	11/2012
8423	2^178819-15	53830	Lelio R Paula	02/2011
8424	(14450!-1)/225296581	53829	Donovan Johnson	04/2006
8425	2^178761-465	53813	Lelio R Paula	10/2009
8426	18900^703+703^18900	53808	Anatoly F. Selevich	02/2007
8427	13918^7343+7343^13918	53806	Hans Havermann	08/2016
8428	10^53804+31749	53805	Patrick De Geest	12/2012
8430	10^53804-71	53804	Robert Price	05/2011
8429	t(178994)	53804	Robert Price	03/2015
8431	(2^178693-lucasV(1,2,178693)+1)/2	53792	Mike Oakes	11/2016
8432	2^178671-113215	53786	Enzo Doria	07/2014
8433	15110^3621+3621^15110	53774	Hans Havermann	07/2016
8434	2^178611+95	53768	Lelio R Paula	02/2011
8435	2^178597+5711	53764	Lelio R Paula	10/2011
8436	2^178598+12915	53764	Lelio R Paula	07/2012
8437	(9179*2^178579-1)/303	53760	Lelio R Paula	03/2015
8438	5*7^63589+2	53740	Lelio R Paula	09/2014
8439	2^178516-112515	53739	Enzo Doria	06/2014
8440	20^41302-27	53736	Lelio R Paula	01/2013
8441	6^69054-39209	53735	Mike Oakes	12/2010
8442	13086^12769+12769^13086	53734	Hans Havermann	07/2016
8443	2^178455+76043	53721	Enzo Doria	04/2016
8444	(10^53718-7)/3	53718	Makoto Kamada	10/2004
8445	(67607*2^178426+1)/3	53716	Lelio R Paula	05/2014
8446	9*10^53707+11	53708	Robert Kinser	01/2017
8447	94601!8-2	53708	Robert Price	04/2017
8448	13214^11595+11595^13214	53706	Hans Havermann	07/2016
8449	Phi(134350,10)/537401/8011962251	53705	Maksym Voznyy	10/2011
8450	2^178367-379	53694	Yves Minet	03/2013
8451	(2^178364-5)/11	53692	Lelio R Paula	02/2012
8452	4339^14760-168	53688	Enzo Doria	06/2012
8453	12^49746-11	53685	Lelio R Paula	01/2013
8454	(9913*2^178266-1)/2247	53665	Lelio R Paula	03/2015
8455	13725^8128+8128^13725	53665	Hans Havermann	07/2016
8456	2^178250-113261	53659	Enzo Doria	07/2014
8457	2^178226+11715	53652	Lelio R Paula	10/2009
8458	35^34742-1976	53645	Enzo Doria	03/2013
8459	20^41228-563	53639	Enzo Doria	03/2013
8460	359^20992+20992^359	53637	Norbert Schneider	08/2014
8461	(27*2^178183-1)/29065	53636	Lelio R Paula	01/2014
8462	(3^112414+7)/37381696	53628	Lelio R Paula	03/2012
8463	17994^955+955^17994	53623	Anatoly F. Selevich	10/2006
8464	2^178117-1551	53619	Yves Minet	08/2012
8465	2^178099-11287	53614	Enzo Doria	06/2014
8466	(15*2^178080-1)/309071	53604	Lelio R Paula	01/2014
8467	5^76672-13766	53592	Enzo Doria	02/2013
8468	6^68868-137	53590	Lelio R Paula	10/2012
8469	(5*2^178021+1)/8173	53587	Lelio R Paula	07/2012
8470	5^76654-26	53579	Lelio R Paula	10/2012
8471	(3^112297-2)/7627	53576	Lelio R Paula	03/2012
8472	3*2^177948-7	53569	Lelio R Paula	03/2014
8473	10^53558+18543	53559	Patrick De Geest	12/2012
8474	10^53558-21	53558	Robert Price	03/2011
8475	2^177792-95	53521	Lelio R Paula	02/2011
8476	13392^9919+9919^13392	53521	Hans Havermann	07/2016
8477	13105^12132+12132^13105	53520	Hans Havermann	07/2016
8478	13^48042+82	53517	Lelio R Paula	01/2013
8479	2^177768+39121	53514	Yves Minet	10/2010
8480	13835^7366+7366^13835	53504	Hans Havermann	07/2016
8481	17^43477+84	53497	Lelio R Paula	01/2013
8482	5*10^53492+9	53493	Dmitry Domanov	11/2010
8483	2^177683+95	53488	Lelio R Paula	01/2011
8484	(2^177678+3)/514627	53481	Lelio R Paula	02/2012
8485	2^177641-255463	53476	Gary Barnes	08/2009
8486	p(11608)#/2+16	53469	Robert Price	12/2016
8487	37302#*10^(37302+52)+p(37302+1)	53457	Jason Earls	08/2008
8488	1829^16384+1828^16384	53449	Henri Lifchitz	01/2007
8489	35^34608-9602	53438	Enzo Doria	03/2013
8490	(3^111992+8)/14867	53430	Lelio R Paula	03/2012
8491	2^177480+1869661	53427	Enzo Doria	05/2016
8492	(8*10^53411+1)/9	53411	Serge Batalov	12/2008
8493	4*5^76410-3	53409	Lelio R Paula	09/2014
8494	2^177380-113045	53397	Enzo Doria	07/2014
8495	5^76362-2*3^76362	53375	Mike Oakes	11/2009
8496	4159^14747-140	53370	Enzo Doria	07/2012
8497	(lucasV(1,2,354503)-2)/3	53358	Mike Oakes	03/2017
8498	p(11586)#/2+32	53357	Robert Price	12/2016
8499	15^45362-46	53350	Lelio R Paula	01/2013
8500	14147^5892+5892^14147	53338	Hans Havermann	07/2016

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PRP Records

Probable Primes Top 10000

(174961 PRPs in the top)