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 ?
9251	13736^11949+11949^13736	56007	Hans Havermann	04/2016
9252	(5*2^186036-1)/11	56003	Lelio R Paula	01/2014
9253	(299*10^55998-17)/3	56000	Robert Price	01/2017
9254	p(12103)#/2-128	55994	Robert Price	05/2017
9255	2^186003-174337	55993	Gary Barnes	09/2009
9257	(2^186010+78557)/123	55993	Lelio R Paula	05/2012
9256	20^43037-93	55993	Lelio R Paula	02/2013
9258	16375^2626+2626^16375	55991	Hans Havermann	03/2016
9259	11083^13842-13842^11083	55987	Norbert Schneider	11/2018
9260	15631^3816+3816^15631	55985	Hans Havermann	03/2016
9261	21^42335-2	55977	Lelio R Paula	08/2013
9262	Phi(64736,139)	55959	Enzo Doria	07/2012
9263	15215^4762+4762^15215	55958	Hans Havermann	03/2016
9264	19317^788+788^19317	55953	Anatoly F. Selevich	12/2006
9265	13582^13165+13165^13582	55950	Hans Havermann	08/2016
9266	(78557*2^185842+1)/189	55947	Lelio R Paula	06/2014
9267	11867^13730-13730^11867	55941	Norbert Schneider	09/2018
9268	15^47562-86	55938	Lelio R Paula	02/2013
9269	4*10^55932+91	55933	Robert Price	11/2017
9270	3^117222+4	55930	Lelio R Paula	03/2012
9271	24^40519-23^40519	55925	Robert Price	07/2012
9272	13636^12623+12623^13636	55924	Hans Havermann	07/2016
9273	2^185767-99	55922	Lelio R Paula	03/2011
9274	(19*2^185750-1)/15	55917	Lelio R Paula	01/2014
9275	15^47542-58	55914	Lelio R Paula	02/2013
9276	52211!4+2	55914	Robert Price	08/2017
9277	20^42973-5583	55910	Enzo Doria	03/2013
9278	4*10^55906+21	55907	Robert Price	08/2016
9279	2^185713-111	55906	Lelio R Paula	03/2011
9280	13^50174+88	55891	Lelio R Paula	01/2013
9281	14569^6846+6846^14569	55879	Hans Havermann	08/2016
9282	Pell-LucasQ(145969)/2	55874	Eric W. Weisstein	08/2006
9283	3^117087-80	55865	Lelio R Paula	10/2012
9284	(7*10^55851-43)/9	55851	Robert Price	10/2014
9285	2^185519-169	55847	Lelio R Paula	03/2011
9286	7^66074+10	55840	Lelio R Paula	10/2012
9287	(19*10^55833-49)/3	55834	Robert Price	02/2017
9288	(2*10^55834-59)/3	55834	Robert Price	05/2017
9289	2^185463-4237	55830	Yves Minet	08/2018
9290	12^51732+5	55829	Lelio R Paula	01/2013
9291	11252^13779-13779^11252	55822	Norbert Schneider	10/2018
9292	3*2^185429+7	55821	Lelio R Paula	03/2014
9293	(60^31393+1)/61	55820	Paul Bourdelais	08/2017
9295	(9787*2^185420-1)/381	55819	Lelio R Paula	04/2015
9294	14427^7396+7396^14427	55819	Hans Havermann	08/2016
9296	10^55811+21	55812	Robert Price	01/2011
9297	10^55811-74103	55811	Patrick De Geest	12/2012
9298	11^53591-1530	55810	Enzo Doria	11/2012
9299	(5^79841-5^39921+1)/15334159	55800	Lelio R Paula	09/2017
9300	2^185355-2145	55798	Lelio R Paula	03/2011
9301	14531^6912+6912^14531	55794	Hans Havermann	07/2016
9302	2^185327-1615	55789	Lelio R Paula	03/2011
9303	2^185280-12779	55775	Enzo Doria	10/2012
9304	15504^3955+3955^15504	55771	Hans Havermann	07/2016
9305	(2*10^55762-59)/3	55762	Robert Price	05/2017
9306	5^79770-44	55757	Lelio R Paula	10/2012
9307	18^44416-85	55755	Lelio R Paula	02/2013
9308	2^185208-459995	55754	Enzo Doria	06/2015
9309	2^185200+1185	55751	Lelio R Paula	03/2011
9310	(536*10^55748-23)/9	55750	Robert Price	11/2017
9311	7^65964+6^(65964-1)	55747	Robert Price	03/2016
9312	2^185151-237157	55737	Gary Barnes	09/2009
9313	110017^11055-102	55734	Enzo Doria	07/2012
9315	14754^5987+5987^14754	55729	Hans Havermann	07/2016
9314	12591^13592-13592^12591	55729	Norbert Schneider	07/2018
9316	40090!3-9	55711	Robert Price	09/2014
9317	9*10^55707+89	55708	Robert Price	11/2016
9318	2^185023-2257	55698	Yves Minet	06/2009
9319	18628^977+977^18628	55696	Anatoly F. Selevich	01/2007
9320	2^185006-93	55693	Lelio R Paula	03/2011
9321	2^185003-2515	55692	Yves Minet	07/2014
9322	2^184992-78557	55689	Jorge Menendez	02/2018
9323	3*10^55679+37	55680	Robert Price	10/2017
9324	6^71524-19	55657	Lelio R Paula	10/2012
9325	2^184872-2195	55653	Yves Minet	08/2013
9326	507^20572+20572^507	55648	Norbert Schneider	06/2016
9327	(86*10^55645-311)/9	55646	Robert Price	10/2017
9328	134^26151-133	55626	Norbert Schneider	03/2015
9329	15340^4221+4221^15340	55614	Hans Havermann	07/2016
9330	27743!2+2	55612	Robert Price	01/2013
9331	20^42744+81	55612	Lelio R Paula	02/2013
9332	14609^6406+6406^14609	55611	Hans Havermann	07/2016
9333	2^184724-112883	55608	Enzo Doria	06/2014
9334	13507^13074+13074^13507	55601	Hans Havermann	07/2016
9335	2^184689+129	55597	Lelio R Paula	03/2011
9336	(9179*2^184672-1)/193	55594	Lelio R Paula	03/2015
9337	(22*10^55592-19)/3	55593	Robert Price	02/2017
9338	Phi(59984,89)	55582	Enzo Doria	05/2012
9339	8815^14088-14088^8815	55581	Norbert Schneider	11/2018
9340	11^53368+16	55578	Lelio R Paula	01/2013
9341	20^42717-1923	55577	Enzo Doria	03/2013
9342	117^26870+26870^117	55573	Serge Batalov	05/2014
9343	12^51488+55	55565	Lelio R Paula	01/2013
9345	(44*10^55558-17)/9	55559	Robert Price	06/2015
9344	(2*10^55559-23)/3	55559	Robert Price	09/2017
9346	10^55555+32857	55556	Patrick De Geest	06/2010
9347	10^55555-136721	55555	Patrick De Geest	06/2010
9348	(11*2^184541-1)/351	55551	Lelio R Paula	01/2014
9349	20^42696-2043	55549	Enzo Doria	03/2013
9350	(35*10^55547-737)/9	55548	Robert Price	11/2017
9351	(2*10^55544+1)/3	55544	Serge Batalov	06/2009
9352	(-lucasV(1,2,369056)+2)/(389109*457)	55542	Mike Oakes	04/2017
9353	5003^15013-160	55537	Enzo Doria	07/2012
9354	39^34896-2	55522	Lelio R Paula	08/2013
9355	(6^71345-61)/5	55517	Lelio R Paula	05/2014
9356	2^184407-3019	55513	Yves Minet	10/2014
9357	(43*10^55512-61)/9	55513	Robert Price	06/2015
9358	20^42667-843	55512	Enzo Doria	03/2013
9359	133^26134-132	55505	Norbert Schneider	03/2015
9360	(31*2^184378-1)/711	55502	Lelio R Paula	01/2014
9361	9*7^65667-4	55497	Lelio R Paula	09/2014
9362	2^184342-173	55493	Lelio R Paula	03/2011
9363	15^47182+92	55491	Lelio R Paula	02/2013
9364	5^79378+6	55483	Lelio R Paula	10/2012
9365	581^20068+20068^581	55472	Norbert Schneider	06/2016
9366	(2^184232+1)/257	55457	Donovan Johnson	03/2005
9367	18^44177-1415	55455	Enzo Doria	03/2013
9368	2^184203-2797867	55451	Enzo Doria	04/2016
9369	2^184189+17	55447	Lelio R Paula	03/2011
9370	2^184183+26123	55445	Yves Minet	01/2010
9371	Phi(77077,10)	55441	Ray Chandler	05/2009
9372	2^184141-113251	55432	Enzo Doria	07/2014
9373	2^184093-504613	55418	Gary Barnes	09/2009
9374	6517^14528-14528^6517	55411	Norbert Schneider	12/2018
9375	(lucasV(1,2,368167)+2)/(1111031307*5647)	55404	Mike Oakes	04/2017
9376	2^184044-111269	55403	Enzo Doria	05/2014
9377	14051^8766+8766^14051	55401	Hans Havermann	07/2016
9378	98^27819+27819^98	55394	Serge Batalov	05/2014
9379	(178*10^55390-7)/9	55392	Robert Price	08/2017
9380	58046^9+9^58046	55390	Andrey Kulsha	02/2004
9381	7^65536+2*59232-2	55385	Jiahao He	07/2017
9382	2^183980+75241	55384	Enzo Doria	04/2016
9383	10^55372+37	55373	Robert Price	01/2011
9384	10^55372-49967	55372	Patrick De Geest	12/2012
9385	(13*10^55367+17)/3	55368	Robert Price	06/2015
9386	2*6^71150+7	55366	Lelio R Paula	09/2014
9387	19^43296-62	55365	Lelio R Paula	02/2013
9388	19^43295+10	55364	Lelio R Paula	02/2013
9389	(29*10^55362-11)/9	55363	Robert Price	04/2015
9390	(37*10^55359+53)/9	55360	Robert Price	05/2015
9391	19^43283+72	55349	Lelio R Paula	02/2013
9392	2^183800-65	55330	Lelio R Paula	03/2011
9393	21001^12801-110	55329	Enzo Doria	07/2012
9394	33^36433-32^36433	55325	Robert Price	04/2012
9395	(17*2^183729+1)/145	55308	Lelio R Paula	07/2012
9396	9932^13837-13837^9932	55307	Norbert Schneider	11/2018
9398	9^57952+8^(57952-1)	55301	Robert Price	03/2016
9397	14872^5229+5229^14872	55301	Hans Havermann	08/2016
9399	61^30972-2	55296	Lelio R Paula	08/2013
9400	2^183671-112537	55291	Enzo Doria	06/2014
9401	(2^183687+7)/497939745	55287	Lelio R Paula	02/2012
9402	3^115873+56	55286	Lelio R Paula	10/2012
9403	13^49629-84	55284	Lelio R Paula	01/2013
9404	2^183632-5	55279	Henri Lifchitz	08/2005
9405	13981^8988+8988^13981	55277	Hans Havermann	07/2016
9406	10688^13719-13719^10688	55273	Norbert Schneider	09/2018
9407	(5*2^183585+1)/13	55265	Lelio R Paula	07/2012
9408	2^183576+171	55262	Lelio R Paula	03/2011
9409	13^49604+82	55257	Lelio R Paula	01/2013
9410	(11*10^55254+1)/3	55255	Erik Branger	03/2014
9411	12609^13474-13474^12609	55253	Norbert Schneider	05/2018
9412	3^115802-26	55252	Lelio R Paula	10/2012
9413	2^183534-3645	55250	Lelio R Paula	01/2011
9414	(15*2^183533-1)/113	55249	Lelio R Paula	01/2014
9415	5^79032-13766	55241	Enzo Doria	02/2013
9416	8*3^115759-7	55232	Lelio R Paula	03/2014
9418	6^70974-137	55229	Lelio R Paula	10/2012
9417	2^183466+524287	55229	Paul Underwood	08/2018
9419	2^183446-113073	55223	Enzo Doria	07/2014
9420	2^183441+577294575	55222	Lelio R Paula	03/2013
9421	5^79000-6	55219	Lelio R Paula	10/2012
9422	2^183413-901	55213	Yves Minet	01/2012
9423	19^43168-50	55202	Lelio R Paula	02/2013
9424	2^183340+19683	55191	Lelio R Paula	02/2012
9425	6^70923+35	55189	Lelio R Paula	10/2012
9426	2^183317-4035	55184	Lelio R Paula	01/2011
9427	2^183284-15	55174	Lelio R Paula	03/2011
9428	2^183255+149	55166	Lelio R Paula	02/2011
9429	4*10^55165+87	55166	Robert Price	05/2016
9431	(3^115574+4)/63037	55139	Lelio R Paula	03/2012
9430	2^183165-112333	55139	Enzo Doria	06/2014
9432	(109^27061-1)/108	55133	Richard Fischer	09/2017
9433	2^183142+855	55132	Lelio R Paula	01/2011
9434	(49*10^55129+383)/9	55130	Robert Price	04/2017
9435	2^183019+255255	55095	Lelio R Paula	01/2011
9436	(10^55084-19)/9	55084	Robert Price	10/2017
9437	3*10^55077+7	55078	Erik Branger	11/2013
9438	(62*10^55075-71)/9	55076	Robert Price	09/2015
9439	27499!2-32	55070	Robert Price	10/2015
9440	15307^3958+3958^15307	55067	Hans Havermann	08/2016
9441	155^25137-154	55059	Norbert Schneider	12/2018
9442	70^29836-69	55051	Norbert Schneider	10/2012
9443	18^43854-83	55049	Lelio R Paula	02/2013
9444	7^65126+58	55038	Lelio R Paula	10/2012
9445	2^182827-1615	55037	Lelio R Paula	11/2009
9446	7*10^55030-9	55031	Dmitry Domanov	11/2010
9447	9027^13912-13912^9027	55030	Norbert Schneider	08/2018
9448	2^182768-4055	55019	Yves Minet	02/2018
9449	6^70702+23	55017	Lelio R Paula	10/2012
9450	(23*2^182753+1)/151	55014	Lelio R Paula	07/2012
9451	2^182743-1615	55012	Lelio R Paula	11/2009
9452	(24737*2^182736+1)/399	55011	Lelio R Paula	05/2014
9453	3^115280-9568	55003	Enzo Doria	02/2013
9454	2^182656-12849	54985	Enzo Doria	10/2012
9455	12791^13388-13388^12791	54984	Norbert Schneider	03/2018
9456	9*19^42995+16	54981	Curtis Bright	05/2015
9457	2^182627+28425	54977	Lelio R Paula	11/2009
9458	2^182597-113053	54968	Enzo Doria	07/2014
9459	(3^115213+2)/30906725	54964	Lelio R Paula	03/2012
9460	2^182581-1975	54963	Yves Minet	09/2012
9461	(2*10^54960-179)/3	54960	Robert Price	11/2017
9462	27449!!-16	54959	Robert Price	06/2015
9463	(22*10^54958-73)/3	54959	Robert Price	09/2017
9465	4^91283-3^91283	54958	Jean-Louis Charton	01/2004
9464	2^182565+107	54958	Lelio R Paula	11/2009
9466	2^182560+2053	54957	Lelio R Paula	12/2010
9467	126892#-p(126892)	54927	Henri Lifchitz	12/2018
9468	2^182451-182451	54924	Henri Lifchitz	10/2004
9469	2^182444+81	54922	Henri Lifchitz	10/2005
9470	7589^14154-14154^7589	54921	Norbert Schneider	01/2019
9471	2^182433+74105	54918	Enzo Doria	04/2016
9472	20^42206-5243	54912	Enzo Doria	03/2013
9473	2^182394+85	54907	Lelio R Paula	02/2011
9474	2^182374-112287	54901	Enzo Doria	06/2014
9475	(47^32833-33^32833)/14	54899	Serge Batalov	12/2016
9476	10188^13697-13697^10188	54899	Norbert Schneider	09/2018
9477	2^182363-113167	54897	Enzo Doria	07/2014
9478	2^182359-112221	54896	Enzo Doria	06/2014
9479	(F(1905)^139-F(1904)^139)/F(1903)	54893	Wayne Halsdorf	05/2010
9480	(17*2^182274+1)/1467	54869	Lelio R Paula	01/2012
9481	18^43698-5	54853	Lelio R Paula	02/2013
9482	2^182209-1893	54851	Yves Minet	09/2012
9483	2^182194-3443	54846	Yves Minet	12/2016
9484	15023^4468+4468^15023	54836	Hans Havermann	08/2016
9485	2^182135+90143	54829	Yves Minet	10/2010
9486	2^182119+74333	54824	Enzo Doria	04/2016
9487	14289^6860+6860^14289	54818	Hans Havermann	08/2016
9488	3^114892-114892^3	54818	Norbert Schneider	03/2017
9489	2^182070-47355	54809	Lelio R Paula	01/2011
9490	3^114869+76	54807	Lelio R Paula	10/2012
9491	8^60681-60681^8	54801	Norbert Schneider	12/2016
9492	1897^16710+16710^1897	54777	Serge Batalov	05/2014
9493	Phi(61868,59)	54776	Enzo Doria	04/2012
9494	113^26679+2	54775	Lelio R Paula	05/2013
9495	3^114789-74	54769	Lelio R Paula	10/2012
9496	15^46567+98	54768	Lelio R Paula	02/2013
9497	(2*10^54767-71)/3	54767	Robert Price	01/2017
9498	(298*10^54765-7)/3	54767	Robert Price	06/2017
9499	(21*2^181931-1)/169997	54763	Lelio R Paula	01/2014
9500	(31*10^54761-121)/9	54762	Robert Price	06/2016

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PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)