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 ?
9251	(2^183687+7)/497939745	55287	Lelio R Paula	02/2012
9252	3^115873+56	55286	Lelio R Paula	10/2012
9253	13^49629-84	55284	Lelio R Paula	01/2013
9254	2^183632-5	55279	Henri Lifchitz	08/2005
9255	13981^8988+8988^13981	55277	Hans Havermann	07/2016
9256	10688^13719-13719^10688	55273	Norbert Schneider	09/2018
9257	(5*2^183585+1)/13	55265	Lelio R Paula	07/2012
9258	2^183576+171	55262	Lelio R Paula	03/2011
9259	13^49604+82	55257	Lelio R Paula	01/2013
9260	(11*10^55254+1)/3	55255	Erik Branger	03/2014
9261	12609^13474-13474^12609	55253	Norbert Schneider	05/2018
9262	3^115802-26	55252	Lelio R Paula	10/2012
9263	2^183534-3645	55250	Lelio R Paula	01/2011
9264	(15*2^183533-1)/113	55249	Lelio R Paula	01/2014
9265	5^79032-13766	55241	Enzo Doria	02/2013
9266	8*3^115759-7	55232	Lelio R Paula	03/2014
9267	6^70974-137	55229	Lelio R Paula	10/2012
9268	2^183466+524287	55229	Paul Underwood	08/2018
9269	2^183446-113073	55223	Enzo Doria	07/2014
9270	2^183441+577294575	55222	Lelio R Paula	03/2013
9271	5^79000-6	55219	Lelio R Paula	10/2012
9272	2^183413-901	55213	Yves Minet	01/2012
9273	19^43168-50	55202	Lelio R Paula	02/2013
9274	2^183340+19683	55191	Lelio R Paula	02/2012
9275	6^70923+35	55189	Lelio R Paula	10/2012
9276	2^183317-4035	55184	Lelio R Paula	01/2011
9277	2^183284-15	55174	Lelio R Paula	03/2011
9278	2^183255+149	55166	Lelio R Paula	02/2011
9279	4*10^55165+87	55166	Robert Price	05/2016
9280	(3^115574+4)/63037	55139	Lelio R Paula	03/2012
9281	2^183165-112333	55139	Enzo Doria	06/2014
9282	(109^27061-1)/108	55133	Richard Fischer	09/2017
9283	2^183142+855	55132	Lelio R Paula	01/2011
9284	(49*10^55129+383)/9	55130	Robert Price	04/2017
9285	2^183019+255255	55095	Lelio R Paula	01/2011
9286	(10^55084-19)/9	55084	Robert Price	10/2017
9287	3*10^55077+7	55078	Erik Branger	11/2013
9288	(62*10^55075-71)/9	55076	Robert Price	09/2015
9289	27499!2-32	55070	Robert Price	10/2015
9290	15307^3958+3958^15307	55067	Hans Havermann	08/2016
9291	70^29836-69	55051	Norbert Schneider	10/2012
9292	18^43854-83	55049	Lelio R Paula	02/2013
9293	7^65126+58	55038	Lelio R Paula	10/2012
9294	2^182827-1615	55037	Lelio R Paula	11/2009
9295	7*10^55030-9	55031	Dmitry Domanov	11/2010
9296	9027^13912-13912^9027	55030	Norbert Schneider	08/2018
9297	2^182768-4055	55019	Yves Minet	02/2018
9298	6^70702+23	55017	Lelio R Paula	10/2012
9299	(23*2^182753+1)/151	55014	Lelio R Paula	07/2012
9300	2^182743-1615	55012	Lelio R Paula	11/2009
9301	(24737*2^182736+1)/399	55011	Lelio R Paula	05/2014
9302	3^115280-9568	55003	Enzo Doria	02/2013
9303	2^182656-12849	54985	Enzo Doria	10/2012
9304	12791^13388-13388^12791	54984	Norbert Schneider	03/2018
9305	9*19^42995+16	54981	Curtis Bright	05/2015
9306	2^182627+28425	54977	Lelio R Paula	11/2009
9307	2^182597-113053	54968	Enzo Doria	07/2014
9308	(3^115213+2)/30906725	54964	Lelio R Paula	03/2012
9309	2^182581-1975	54963	Yves Minet	09/2012
9310	(2*10^54960-179)/3	54960	Robert Price	11/2017
9311	27449!!-16	54959	Robert Price	06/2015
9312	(22*10^54958-73)/3	54959	Robert Price	09/2017
9313	4^91283-3^91283	54958	Jean-Louis Charton	01/2004
9314	2^182565+107	54958	Lelio R Paula	11/2009
9315	2^182560+2053	54957	Lelio R Paula	12/2010
9316	2^182451-182451	54924	Henri Lifchitz	10/2004
9317	2^182444+81	54922	Henri Lifchitz	10/2005
9318	2^182433+74105	54918	Enzo Doria	04/2016
9319	20^42206-5243	54912	Enzo Doria	03/2013
9320	2^182394+85	54907	Lelio R Paula	02/2011
9321	2^182374-112287	54901	Enzo Doria	06/2014
9322	(47^32833-33^32833)/14	54899	Serge Batalov	12/2016
9323	10188^13697-13697^10188	54899	Norbert Schneider	09/2018
9324	2^182363-113167	54897	Enzo Doria	07/2014
9325	2^182359-112221	54896	Enzo Doria	06/2014
9326	(F(1905)^139-F(1904)^139)/F(1903)	54893	Wayne Halsdorf	05/2010
9327	(17*2^182274+1)/1467	54869	Lelio R Paula	01/2012
9328	18^43698-5	54853	Lelio R Paula	02/2013
9329	2^182209-1893	54851	Yves Minet	09/2012
9330	2^182194-3443	54846	Yves Minet	12/2016
9331	15023^4468+4468^15023	54836	Hans Havermann	08/2016
9332	2^182135+90143	54829	Yves Minet	10/2010
9333	2^182119+74333	54824	Enzo Doria	04/2016
9334	14289^6860+6860^14289	54818	Hans Havermann	08/2016
9335	3^114892-114892^3	54818	Norbert Schneider	03/2017
9336	2^182070-47355	54809	Lelio R Paula	01/2011
9337	3^114869+76	54807	Lelio R Paula	10/2012
9338	8^60681-60681^8	54801	Norbert Schneider	12/2016
9339	1897^16710+16710^1897	54777	Serge Batalov	05/2014
9340	Phi(61868,59)	54776	Enzo Doria	04/2012
9341	113^26679+2	54775	Lelio R Paula	05/2013
9342	3^114789-74	54769	Lelio R Paula	10/2012
9343	15^46567+98	54768	Lelio R Paula	02/2013
9344	(2*10^54767-71)/3	54767	Robert Price	01/2017
9345	(298*10^54765-7)/3	54767	Robert Price	06/2017
9346	(21*2^181931-1)/169997	54763	Lelio R Paula	01/2014
9348	2^181913+29	54762	Henri Lifchitz	06/2005
9347	(31*10^54761-121)/9	54762	Robert Price	06/2016
9349	2^181887+189	54754	Lelio R Paula	02/2011
9350	2^181874+181874^2-1	54750	Robert Price	04/2014
9351	(2^181865+9)/7339	54743	Lelio R Paula	02/2012
9352	5^78314-92	54740	Lelio R Paula	10/2012
9353	(163*10^54727-1)/9	54729	Serge Batalov	12/2014
9354	15^46531+74	54725	Lelio R Paula	02/2013
9355	277^22400-348	54712	Enzo Doria	07/2012
9356	6^70302+101	54706	Lelio R Paula	10/2012
9357	3^114622-10408	54689	Enzo Doria	02/2013
9359	(23*2^181674+1)/489	54688	Lelio R Paula	01/2012
9358	2^181669-1551	54688	Yves Minet	08/2012
9360	(57352^11491-1)/57351	54676	Serge Batalov	04/2015
9361	(31*2^181629-1)/10734721	54671	Lelio R Paula	01/2014
9362	(F(1048)^251-F(1047)^251)/F(1046)	54668	Wayne Halsdorf	05/2010
9363	13^49073+46	54665	Lelio R Paula	01/2013
9364	(57042^11491-1)/57041	54649	Serge Batalov	04/2015
9366	20^42000+73	54644	Lelio R Paula	02/2013
9365	(67607*2^181517+1)/1655	54644	Lelio R Paula	05/2014
9367	33*10^54634+7	54636	Robert Price	07/2016
9368	20^41988+61	54628	Lelio R Paula	01/2013
9369	20^41988-8123	54628	Enzo Doria	03/2013
9371	2^181420+21181	54613	Yves Minet	03/2011
9370	9854^13675-13675^9854	54613	Norbert Schneider	08/2018
9372	(19*10^54608+161)/9	54609	Robert Price	07/2016
9373	19^42696-24	54598	Lelio R Paula	02/2013
9374	(44*10^54596-503)/9	54597	Robert Price	10/2017
9375	(74*10^54583+61)/9	54584	Robert Price	10/2015
9376	2^181316-94395	54582	Lelio R Paula	09/2011
9377	14751^5006+5006^14751	54572	Hans Havermann	08/2016
9378	14^47609+39	54567	Lelio R Paula	02/2013
9379	12696^13295-13295^12696	54559	Norbert Schneider	01/2018
9380	(2^124979+lucasV(2,-2,124979)+1)/3	54552	Paul Vanderveen	12/2017
9382	3^114327-74	54548	Lelio R Paula	10/2012
9381	(44*10^54547-161)/9	54548	Robert Price	11/2017
9383	gcd(V(995625),5F(199125)(F(199125)-1)+1)	54546	Serge Batalov	04/2015
9384	(17*10^54537-47)/3	54538	Robert Price	05/2017
9385	2^181155-1155*181155	54534	Henri Lifchitz	02/2005
9386	Phi(61672,83)	54533	Enzo Doria	05/2012
9387	(2*10^54527-197)/3	54527	Robert Price	11/2017
9388	9*2^181128+7	54526	Lelio R Paula	03/2014
9389	89*10^54518-7	54520	Robert Price	03/2017
9390	2^181090-113247	54514	Enzo Doria	07/2014
9391	14031^7670+7670^14031	54508	Hans Havermann	08/2016
9392	14210^6849+6849^14210	54505	Hans Havermann	08/2016
9393	2^181043-199	54500	Lelio R Paula	02/2011
9394	12^50499+5	54498	Lelio R Paula	01/2013
9395	12^50491+5	54489	Lelio R Paula	01/2013
9396	6^70016-145	54484	Lelio R Paula	10/2012
9397	11^52313-9600	54479	Enzo Doria	02/2013
9398	2^64459+3^64459+5^64459+7^64459	54475	Henri Lifchitz	08/2001
9399	2^180946-111041	54471	Enzo Doria	05/2014
9400	(64*10^54467+287)/9	54468	Robert Price	04/2016
9401	(32*10^54458+319)/9	54459	Robert Price	10/2017
9402	5^77907-2*3^77907	54455	Mike Oakes	11/2009
9403	20^41853-5623	54453	Enzo Doria	03/2013
9404	14^47506-75	54448	Lelio R Paula	02/2013
9405	(25*10^54443-67)/3	54444	Robert Price	11/2017
9406	2^180839-113437	54438	Enzo Doria	08/2014
9407	3^114085+28	54433	Lelio R Paula	10/2012
9408	Phi(141230,10)	54432	Ray Chandler	08/2009
9409	6^69946-55	54429	Lelio R Paula	10/2012
9410	p(11796)#/2-1024	54427	Robert Price	09/2017
9411	5*2^180796+3	54426	Lelio R Paula	03/2014
9412	(23*2^180782-1)/91	54421	Lelio R Paula	01/2014
9413	9*6^69928-7	54416	Lelio R Paula	09/2014
9414	92^27701-91^27701	54399	Robert Price	08/2015
9415	(2^180687-3)*6-7	54393	Gilbert Mozzo	04/2016
9416	(5*10^54388-11)/3	54389	Erik Branger	12/2013
9418	20^41799-3043	54382	Enzo Doria	03/2013
9417	13860^8387+8387^13860	54382	Hans Havermann	08/2016
9419	(F(19)^15017-F(18)^15017)/F(17)	54378	Wayne Halsdorf	05/2010
9420	7^64329-18	54365	Lelio R Paula	10/2012
9421	2^180551-967	54352	Yves Minet	01/2012
9422	9075^13732-13732^9075	54350	Norbert Schneider	09/2018
9423	15^46209-74	54347	Lelio R Paula	02/2013
9424	10^54345+29739	54346	Patrick De Geest	08/2013
9425	10^54345-141381	54345	Patrick De Geest	09/2013
9426	lucasU(2098,1,16360)-lucasU(2098,1,16359)	54342	Mike Oakes	05/2009
9427	177^24171-2	54336	Lelio R Paula	10/2017
9428	2^180496+15	54335	Lelio R Paula	02/2011
9429	1845^16636+16636^1845	54334	Serge Batalov	05/2014
9430	11^52169-70	54329	Lelio R Paula	01/2013
9431	2^180446-4031	54320	Yves Minet	02/2018
9432	13693^9262+9262^13693	54317	Hans Havermann	06/2016
9433	2^180429-113101	54315	Enzo Doria	07/2014
9434	2^180423-112051	54313	Enzo Doria	05/2014
9435	16112^2349+2349^16112	54312	Hans Havermann	06/2016
9436	(79^28621-1)/78	54311	Paul Bourdelais	08/2017
9437	(13^48751+4^48751)/17	54305	Robert Price	05/2013
9438	2^180370+12915	54297	Lelio R Paula	09/2012
9439	(10^54290+41)/3	54290	Robert Price	01/2017
9440	15108^3917+3917^15108	54283	Hans Havermann	06/2016
9441	2^180317-3019	54281	Yves Minet	10/2014
9442	2^180314+855	54280	Lelio R Paula	10/2009
9443	19^42425+94	54252	Lelio R Paula	02/2013
9444	2^180180-1005449	54240	Paul Bourdelais	11/2012
9446	2^180173-2773	54238	Yves Minet	07/2014
9445	13367^11418+11418^13367	54238	Hans Havermann	06/2016
9447	427^20614+20614^427	54224	Norbert Schneider	06/2016
9448	2^180124-87959	54223	Gary Barnes	08/2009
9449	2^180111-113101	54219	Enzo Doria	07/2014
9450	2^180101-114871	54216	Enzo Doria	05/2015
9451	(11*2^180099+1)/51617	54212	Lelio R Paula	07/2012
9453	2^180070+465	54207	Lelio R Paula	09/2012
9452	13683^9154+9154^13683	54207	Hans Havermann	06/2016
9454	8105225132^180009-95312^9531-1	54198	Jiong Sun	12/2003
9455	2^180014+613	54190	Jason Earls	04/2008
9456	2^180007+101	54188	Lelio R Paula	02/2011
9457	2^180001+41877	54186	Jim Fougeron	08/2002
9458	2^180000+130153	54186	Jim Fougeron	09/2002
9459	3^113565-74	54185	Lelio R Paula	10/2012
9460	50^31891-49	54182	Norbert Schneider	07/2014
9461	(5*2^179991-1)/11427	54180	Lelio R Paula	01/2014
9463	3^113548+26	54177	Lelio R Paula	10/2012
9462	(lucasV(1,2,360029)-2)/(3^3522251725981)	54177	Mike Oakes	04/2017
9464	181^23996-2	54176	Lelio R Paula	10/2017
9465	4159^14969-138	54173	Enzo Doria	07/2012
9467	2^179955+5775	54172	Lelio R Paula	10/2009
9466	2^179953-231313	54172	Enzo Doria	05/2014
9468	5^77485+6	54160	Lelio R Paula	10/2012
9469	18^43141+85	54154	Lelio R Paula	02/2013
9470	10^54149+187647	54150	Patrick De Geest	07/2017
9473	3^113489-340	54149	Lelio R Paula	10/2012
9471	10^54149-800001	54149	Robert Price	06/2017
9472	10^54149-36501	54149	Patrick De Geest	07/2017
9474	7^64070+90	54146	Lelio R Paula	10/2012
9475	12549^13210-13210^12549	54143	Norbert Schneider	12/2017
9476	18^43131+71	54142	Lelio R Paula	02/2013
9477	2^179826-131	54134	Lelio R Paula	02/2011
9478	2^179815-112735	54130	Enzo Doria	06/2014
9479	2^179806+73849	54127	Enzo Doria	04/2016
9480	2^179790+33	54123	Donovan Johnson	02/2006
9481	14287^6138+6138^14287	54120	Hans Havermann	06/2016
9482	(17*10^54117+1)/9	54118	Serge Batalov	05/2010
9483	2^179763-189	54115	Lelio R Paula	02/2011
9484	(21181*2^179770+1)/3029105	54115	Lelio R Paula	05/2014
9485	1828^16589+16589^1828	54113	Serge Batalov	05/2014
9487	20^41588-5883	54108	Enzo Doria	03/2013
9486	50^31847-49	54108	Norbert Schneider	07/2014
9488	2^179733-6855	54106	Lelio R Paula	10/2009
9489	20^41584-5583	54103	Enzo Doria	03/2013
9490	10^54084+3*3^54084	54085	Mike Oakes	05/2010
9491	2^179613-1795	54069	Lelio R Paula	10/2009
9492	2^179589-1011523	54062	Paul Bourdelais	11/2012
9493	2^179574-2531	54058	Yves Minet	07/2014
9494	(41*10^54051-23)/9	54052	Robert Price	05/2015
9495	117^26131-116	54044	Norbert Schneider	10/2013
9496	(10^54038-31)/3	54038	Serge Batalov	12/2014
9497	11^51885-84	54033	Lelio R Paula	01/2013
9498	14990^4011+4011^14990	54013	Hans Havermann	07/2016
9499	(19*2^179414+1)/7	54010	Lelio R Paula	07/2012
9500	3^113182-10408	54002	Enzo Doria	02/2013

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PRP Records

Probable Primes Top 10000

(247113 PRPs in the top)