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	(23*2^187174-1)/20719883	56340	Lelio R Paula	01/2014
8252	2^187125-2833	56331	Yves Minet	09/2014
8253	9*7^66655-4	56331	Lelio R Paula	09/2014
8254	18^44874-97	56330	Lelio R Paula	02/2013
8255	60*79^29679+19	56322	Serge Batalov	03/2016
8256	5^80571+56	56317	Lelio R Paula	10/2012
8257	5^80551-22	56303	Lelio R Paula	10/2012
8258	(76*10^56281+41)/9	56282	Robert Price	10/2015
8259	(88*10^56271-43)/9	56272	Robert Price	11/2015
8260	(5*10^56256-119)/3	56257	Robert Price	04/2016
8261	1508^17691+17691^1508	56230	Serge Batalov	05/2014
8262	3^117844-58	56226	Lelio R Paula	10/2012
8263	(19*10^56224+737)/9	56225	Robert Price	10/2017
8264	95^28427+2	56221	Lelio R Paula	05/2013
8265	2^186713+76817	56207	Enzo Doria	05/2016
8266	16534^2505+2505^16534	56196	Hans Havermann	06/2016
8267	14428^7849+7849^14428	56195	Hans Havermann	06/2016
8268	14898^5909+5909^14898	56189	Hans Havermann	06/2016
8269	18^44758+95	56184	Lelio R Paula	02/2013
8270	2^186555-741	56159	Lelio R Paula	05/2011
8271	(4*10^56156+173)/3	56157	Robert Price	01/2017
8272	(3^117708+7)/447896	56156	Lelio R Paula	03/2012
8273	15711^3752+3752^15711	56156	Hans Havermann	06/2016
8274	(23*2^186549-1)/2429025	56152	Lelio R Paula	01/2014
8275	387^21694+21694^387	56138	Norbert Schneider	08/2014
8276	2^186422+17239	56119	Yves Minet	01/2010
8277	2^186418+4242429	56118	Jason Earls	10/2008
8278	136^26300+135	56113	Norbert Schneider	04/2015
8279	5*2^186392+9	56111	Lelio R Paula	03/2014
8280	14345^8152+8152^14345	56108	Hans Havermann	07/2016
8281	(5*2^186351-1)/39	56097	Lelio R Paula	01/2014
8282	2^186319-541237	56088	Paul Bourdelais	11/2012
8283	2*10^56083-43	56084	Robert Price	07/2017
8284	(16*10^56082-61)/9	56083	Serge Batalov	05/2009
8285	(14*10^56080-143)/3	56081	Robert Price	01/2017
8286	(265*10^56076+17)/3	56078	Robert Price	05/2016
8287	7^66346-50	56069	Lelio R Paula	10/2012
8288	20^43094-33	56067	Lelio R Paula	02/2013
8289	20^43090-1383	56062	Enzo Doria	03/2013
8290	3^117482+2660	56054	Lelio R Paula	10/2012
8291	(22699*2^186193+1)/111	56052	Lelio R Paula	05/2014
8292	(68*10^56042+13)/9	56043	Ray Chandler	09/2010
8293	3*6^71992+5^71992	56022	Mike Oakes	03/2010
8294	13691^12352+12352^13691	56020	Hans Havermann	07/2016
8295	(2^186095+7)/75	56019	Lelio R Paula	02/2012
8296	247^23412+23412^247	56018	Norbert Schneider	08/2014
8297	1839^17156+17156^1839	56008	Serge Batalov	05/2014
8298	13736^11949+11949^13736	56007	Hans Havermann	04/2016
8299	(5*2^186036-1)/11	56003	Lelio R Paula	01/2014
8300	(299*10^55998-17)/3	56000	Robert Price	01/2017
8301	p(12103)#/2-128	55994	Robert Price	05/2017
8302	2^186003-174337	55993	Gary Barnes	09/2009
8303	(2^186010+78557)/123	55993	Lelio R Paula	05/2012
8304	20^43037-93	55993	Lelio R Paula	02/2013
8305	16375^2626+2626^16375	55991	Hans Havermann	03/2016
8306	15631^3816+3816^15631	55985	Hans Havermann	03/2016
8307	21^42335-2	55977	Lelio R Paula	08/2013
8308	Phi(64736,139)	55959	Enzo Doria	07/2012
8309	15215^4762+4762^15215	55958	Hans Havermann	03/2016
8310	19317^788+788^19317	55953	Anatoly F. Selevich	12/2006
8311	13582^13165+13165^13582	55950	Hans Havermann	08/2016
8312	(78557*2^185842+1)/189	55947	Lelio R Paula	06/2014
8313	15^47562-86	55938	Lelio R Paula	02/2013
8314	3^117222+4	55930	Lelio R Paula	03/2012
8315	24^40519-23^40519	55925	Robert Price	07/2012
8316	13636^12623+12623^13636	55924	Hans Havermann	07/2016
8317	2^185767-99	55922	Lelio R Paula	03/2011
8318	(19*2^185750-1)/15	55917	Lelio R Paula	01/2014
8319	15^47542-58	55914	Lelio R Paula	02/2013
8320	52211!4+2	55914	Robert Price	08/2017
8321	20^42973-5583	55910	Enzo Doria	03/2013
8322	4*10^55906+21	55907	Robert Price	08/2016
8323	2^185713-111	55906	Lelio R Paula	03/2011
8324	13^50174+88	55891	Lelio R Paula	01/2013
8325	14569^6846+6846^14569	55879	Hans Havermann	08/2016
8326	Pell-LucasQ(145969)/2	55874	Eric W. Weisstein	08/2006
8327	3^117087-80	55865	Lelio R Paula	10/2012
8328	(7*10^55851-43)/9	55851	Robert Price	10/2014
8329	2^185519-169	55847	Lelio R Paula	03/2011
8330	7^66074+10	55840	Lelio R Paula	10/2012
8331	(19*10^55833-49)/3	55834	Robert Price	02/2017
8332	(2*10^55834-59)/3	55834	Robert Price	05/2017
8333	12^51732+5	55829	Lelio R Paula	01/2013
8334	3*2^185429+7	55821	Lelio R Paula	03/2014
8335	(60^31393+1)/61	55820	Paul Bourdelais	08/2017
8336	(9787*2^185420-1)/381	55819	Lelio R Paula	04/2015
8337	14427^7396+7396^14427	55819	Hans Havermann	08/2016
8338	10^55811+21	55812	Robert Price	01/2011
8339	10^55811-74103	55811	Patrick De Geest	12/2012
8340	11^53591-1530	55810	Enzo Doria	11/2012
8341	(5^79841-5^39921+1)/15334159	55800	Lelio R Paula	09/2017
8342	2^185355-2145	55798	Lelio R Paula	03/2011
8343	14531^6912+6912^14531	55794	Hans Havermann	07/2016
8344	2^185327-1615	55789	Lelio R Paula	03/2011
8345	2^185280-12779	55775	Enzo Doria	10/2012
8346	15504^3955+3955^15504	55771	Hans Havermann	07/2016
8347	(2*10^55762-59)/3	55762	Robert Price	05/2017
8348	5^79770-44	55757	Lelio R Paula	10/2012
8349	18^44416-85	55755	Lelio R Paula	02/2013
8350	2^185208-459995	55754	Enzo Doria	06/2015
8351	2^185200+1185	55751	Lelio R Paula	03/2011
8352	7^65964+6^(65964-1)	55747	Robert Price	03/2016
8353	2^185151-237157	55737	Gary Barnes	09/2009
8354	110017^11055-102	55734	Enzo Doria	07/2012
8355	14754^5987+5987^14754	55729	Hans Havermann	07/2016
8356	40090!3-9	55711	Robert Price	09/2014
8357	9*10^55707+89	55708	Robert Price	11/2016
8358	2^185023-2257	55698	Yves Minet	06/2009
8359	18628^977+977^18628	55696	Anatoly F. Selevich	01/2007
8360	2^185006-93	55693	Lelio R Paula	03/2011
8361	2^185003-2515	55692	Yves Minet	07/2014
8362	6^71524-19	55657	Lelio R Paula	10/2012
8363	2^184872-2195	55653	Yves Minet	08/2013
8364	507^20572+20572^507	55648	Norbert Schneider	06/2016
8365	134^26151-133	55626	Norbert Schneider	03/2015
8366	15340^4221+4221^15340	55614	Hans Havermann	07/2016
8367	27743!2+2	55612	Robert Price	01/2013
8368	20^42744+81	55612	Lelio R Paula	02/2013
8369	14609^6406+6406^14609	55611	Hans Havermann	07/2016
8370	2^184724-112883	55608	Enzo Doria	06/2014
8371	13507^13074+13074^13507	55601	Hans Havermann	07/2016
8372	2^184689+129	55597	Lelio R Paula	03/2011
8373	(9179*2^184672-1)/193	55594	Lelio R Paula	03/2015
8374	(22*10^55592-19)/3	55593	Robert Price	02/2017
8375	Phi(59984,89)	55582	Enzo Doria	05/2012
8376	11^53368+16	55578	Lelio R Paula	01/2013
8377	20^42717-1923	55577	Enzo Doria	03/2013
8378	117^26870+26870^117	55573	Serge Batalov	05/2014
8379	12^51488+55	55565	Lelio R Paula	01/2013
8381	(44*10^55558-17)/9	55559	Robert Price	06/2015
8380	(2*10^55559-23)/3	55559	Robert Price	09/2017
8382	10^55555+32857	55556	Patrick De Geest	06/2010
8383	10^55555-136721	55555	Patrick De Geest	06/2010
8384	(11*2^184541-1)/351	55551	Lelio R Paula	01/2014
8385	20^42696-2043	55549	Enzo Doria	03/2013
8386	(2*10^55544+1)/3	55544	Serge Batalov	06/2009
8387	(-lucasV(1,2,369056)+2)/(389109*457)	55542	Mike Oakes	04/2017
8388	5003^15013-160	55537	Enzo Doria	07/2012
8389	39^34896-2	55522	Lelio R Paula	08/2013
8390	(6^71345-61)/5	55517	Lelio R Paula	05/2014
8391	2^184407-3019	55513	Yves Minet	10/2014
8392	(43*10^55512-61)/9	55513	Robert Price	06/2015
8393	20^42667-843	55512	Enzo Doria	03/2013
8394	133^26134-132	55505	Norbert Schneider	03/2015
8395	(31*2^184378-1)/711	55502	Lelio R Paula	01/2014
8396	9*7^65667-4	55497	Lelio R Paula	09/2014
8397	2^184342-173	55493	Lelio R Paula	03/2011
8398	15^47182+92	55491	Lelio R Paula	02/2013
8399	5^79378+6	55483	Lelio R Paula	10/2012
8400	581^20068+20068^581	55472	Norbert Schneider	06/2016
8401	(2^184232+1)/257	55457	Donovan Johnson	03/2005
8402	18^44177-1415	55455	Enzo Doria	03/2013
8403	2^184203-2797867	55451	Enzo Doria	04/2016
8404	2^184189+17	55447	Lelio R Paula	03/2011
8405	2^184183+26123	55445	Yves Minet	01/2010
8406	Phi(77077,10)	55441	Ray Chandler	05/2009
8407	2^184141-113251	55432	Enzo Doria	07/2014
8408	2^184093-504613	55418	Gary Barnes	09/2009
8409	(lucasV(1,2,368167)+2)/(1111031307*5647)	55404	Mike Oakes	04/2017
8410	2^184044-111269	55403	Enzo Doria	05/2014
8411	14051^8766+8766^14051	55401	Hans Havermann	07/2016
8412	98^27819+27819^98	55394	Serge Batalov	05/2014
8413	(178*10^55390-7)/9	55392	Robert Price	08/2017
8414	58046^9+9^58046	55390	Andrey Kulsha	02/2004
8415	7^65536+2*59232-2	55385	Jiahao He	07/2017
8416	2^183980+75241	55384	Enzo Doria	04/2016
8417	10^55372+37	55373	Robert Price	01/2011
8418	10^55372-49967	55372	Patrick De Geest	12/2012
8419	(13*10^55367+17)/3	55368	Robert Price	06/2015
8420	2*6^71150+7	55366	Lelio R Paula	09/2014
8421	19^43296-62	55365	Lelio R Paula	02/2013
8422	19^43295+10	55364	Lelio R Paula	02/2013
8423	(29*10^55362-11)/9	55363	Robert Price	04/2015
8424	(37*10^55359+53)/9	55360	Robert Price	05/2015
8425	19^43283+72	55349	Lelio R Paula	02/2013
8426	2^183800-65	55330	Lelio R Paula	03/2011
8427	21001^12801-110	55329	Enzo Doria	07/2012
8428	33^36433-32^36433	55325	Robert Price	04/2012
8429	(17*2^183729+1)/145	55308	Lelio R Paula	07/2012
8430	9^57952+8^(57952-1)	55301	Robert Price	03/2016
8431	14872^5229+5229^14872	55301	Hans Havermann	08/2016
8432	61^30972-2	55296	Lelio R Paula	08/2013
8433	2^183671-112537	55291	Enzo Doria	06/2014
8434	(2^183687+7)/497939745	55287	Lelio R Paula	02/2012
8435	3^115873+56	55286	Lelio R Paula	10/2012
8436	13^49629-84	55284	Lelio R Paula	01/2013
8437	2^183632-5	55279	Henri Lifchitz	08/2005
8438	13981^8988+8988^13981	55277	Hans Havermann	07/2016
8439	(5*2^183585+1)/13	55265	Lelio R Paula	07/2012
8440	2^183576+171	55262	Lelio R Paula	03/2011
8441	13^49604+82	55257	Lelio R Paula	01/2013
8442	(11*10^55254+1)/3	55255	Erik Branger	03/2014
8443	3^115802-26	55252	Lelio R Paula	10/2012
8444	2^183534-3645	55250	Lelio R Paula	01/2011
8445	(15*2^183533-1)/113	55249	Lelio R Paula	01/2014
8446	5^79032-13766	55241	Enzo Doria	02/2013
8447	8*3^115759-7	55232	Lelio R Paula	03/2014
8448	6^70974-137	55229	Lelio R Paula	10/2012
8449	2^183446-113073	55223	Enzo Doria	07/2014
8450	2^183441+577294575	55222	Lelio R Paula	03/2013
8451	5^79000-6	55219	Lelio R Paula	10/2012
8452	2^183413-901	55213	Yves Minet	01/2012
8453	19^43168-50	55202	Lelio R Paula	02/2013
8454	2^183340+19683	55191	Lelio R Paula	02/2012
8455	6^70923+35	55189	Lelio R Paula	10/2012
8456	2^183317-4035	55184	Lelio R Paula	01/2011
8457	2^183284-15	55174	Lelio R Paula	03/2011
8458	2^183255+149	55166	Lelio R Paula	02/2011
8459	4*10^55165+87	55166	Robert Price	05/2016
8460	(3^115574+4)/63037	55139	Lelio R Paula	03/2012
8461	2^183165-112333	55139	Enzo Doria	06/2014
8462	(109^27061-1)/108	55133	Richard Fischer	09/2017
8463	2^183142+855	55132	Lelio R Paula	01/2011
8464	(49*10^55129+383)/9	55130	Robert Price	04/2017
8465	2^183019+255255	55095	Lelio R Paula	01/2011
8466	(10^55084-19)/9	55084	Robert Price	10/2017
8467	3*10^55077+7	55078	Erik Branger	11/2013
8468	(62*10^55075-71)/9	55076	Robert Price	09/2015
8469	27499!2-32	55070	Robert Price	10/2015
8470	15307^3958+3958^15307	55067	Hans Havermann	08/2016
8471	70^29836-69	55051	Norbert Schneider	10/2012
8472	18^43854-83	55049	Lelio R Paula	02/2013
8473	7^65126+58	55038	Lelio R Paula	10/2012
8474	2^182827-1615	55037	Lelio R Paula	11/2009
8475	7*10^55030-9	55031	Dmitry Domanov	11/2010
8476	6^70702+23	55017	Lelio R Paula	10/2012
8477	(23*2^182753+1)/151	55014	Lelio R Paula	07/2012
8478	2^182743-1615	55012	Lelio R Paula	11/2009
8479	(24737*2^182736+1)/399	55011	Lelio R Paula	05/2014
8480	3^115280-9568	55003	Enzo Doria	02/2013
8481	2^182656-12849	54985	Enzo Doria	10/2012
8482	9*19^42995+16	54981	Curtis Bright	05/2015
8483	2^182627+28425	54977	Lelio R Paula	11/2009
8484	2^182597-113053	54968	Enzo Doria	07/2014
8485	(3^115213+2)/30906725	54964	Lelio R Paula	03/2012
8486	2^182581-1975	54963	Yves Minet	09/2012
8487	27449!!-16	54959	Robert Price	06/2015
8488	(22*10^54958-73)/3	54959	Robert Price	09/2017
8490	4^91283-3^91283	54958	Jean-Louis Charton	01/2004
8489	2^182565+107	54958	Lelio R Paula	11/2009
8491	2^182560+2053	54957	Lelio R Paula	12/2010
8492	2^182451-182451	54924	Henri Lifchitz	10/2004
8493	2^182444+81	54922	Henri Lifchitz	10/2005
8494	2^182433+74105	54918	Enzo Doria	04/2016
8495	20^42206-5243	54912	Enzo Doria	03/2013
8496	2^182394+85	54907	Lelio R Paula	02/2011
8497	2^182374-112287	54901	Enzo Doria	06/2014
8498	(47^32833-33^32833)/14	54899	Serge Batalov	12/2016
8499	2^182363-113167	54897	Enzo Doria	07/2014
8500	2^182359-112221	54896	Enzo Doria	06/2014

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PRP Records

Probable Primes Top 10000

(183432 PRPs in the top)