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	18567^7892+7892^18567	72360	Hans Havermann	11/2019
9252	(2^240381+3)/51655	72358	Lelio R Paula	05/2012
9253	6^92974-55	72348	Lelio R Paula	01/2015
9254	2^240295+11	72337	Lelio R Paula	02/2012
9255	(2^240294+1342)/2	72336	Stefano Morozzi	01/2020
9256	(14*10^72326-53)/3	72327	Robert Price	12/2016
9257	15^61493-46	72322	Lelio R Paula	01/2015
9258	(2^240245+2094)/2	72321	Stefano Morozzi	01/2020
9259	(2^240237+1554)/2	72319	Stefano Morozzi	01/2020
9260	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
9261	(2^240211+1514)/2	72311	Stefano Morozzi	01/2020
9263	5*10^72302+9	72303	Dmitry Domanov	11/2010
9262	(9787*2^240179-1)/265	72303	Lelio R Paula	04/2015
9264	(2^240171+3246)/2	72299	Stefano Morozzi	01/2020
9265	11^69419-3120	72293	Enzo Doria	12/2012
9266	18069^10016+10016^18069	72289	Hans Havermann	11/2019
9267	(25883^16381-1)/25882	72286	Serge Batalov	08/2020
9268	(2^240095+594)/2	72276	Stefano Morozzi	01/2020
9269	(25848^16381-1)/25847	72276	Serge Batalov	08/2020
9270	4*10^72274-83	72275	Robert Price	10/2017
9271	(2^240075+2790)/2	72270	Stefano Morozzi	01/2020
9272	10^72267+33	72268	Robert Price	01/2011
9273	10^72267-553947	72267	Patrick De Geest	05/2013
9274	(2^240066+1030)/2	72267	Stefano Morozzi	01/2020
9276	11^69389-1380	72262	Enzo Doria	12/2012
9277	(16^60013-5^60013)/11	72262	Robert Price	07/2013
9275	7^85507-30	72262	Lelio R Paula	08/2014
9278	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
9279	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
9280	(2^239940+3850)/2	72229	Stefano Morozzi	01/2020
9281	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
9282	(2789^20959-1)/2788	72210	Serge Batalov	08/2020
9283	2^239863-112267	72206	Enzo Doria	06/2014
9284	2^239853-114853	72203	Enzo Doria	05/2015
9285	(14068^17401-1)/14067	72180	Serge Batalov	08/2020
9286	(5669^19231-1)/5668	72180	Serge Batalov	08/2020
9287	(4*10^72174+149)/9	72174	Robert Price	03/2017
9289	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
9288	2^239651-110665	72143	Enzo Doria	05/2014
9290	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
9291	(17099^17041-1)/17098	72130	Serge Batalov	08/2020
9293	241^30280+30280^241	72128	Norbert Schneider	11/2014
9292	(2^239603+950)/2	72128	Stefano Morozzi	01/2020
9294	(2^239594+3058)/2	72125	Stefano Morozzi	01/2020
9295	(68*10^72120-23)/9	72121	Robert Price	10/2015
9296	(9^75571+8^75571)/17	72112	Robert Price	12/2012
9297	(15661^17191-1)/15660	72109	Serge Batalov	08/2020
9298	(3508^20341-1)/3507	72107	Serge Batalov	08/2020
9299	(15*2^239530-1)/173	72105	Lelio R Paula	01/2014
9300	(2^239523+2378)/2	72104	Stefano Morozzi	01/2020
9301	2^239513-112519	72101	Enzo Doria	06/2014
9302	(10^72097+149)/3	72097	Serge Batalov	12/2014
9303	2^239442-6555	72080	Lelio R Paula	05/2012
9304	2*5^103106+3	72069	Lelio R Paula	10/2014
9305	2^239402-197	72068	Lelio R Paula	02/2012
9306	2^239356-111875	72054	Enzo Doria	05/2014
9307	(38*10^72050-119)/9	72051	Robert Price	11/2016
9308	2^239339+15015	72049	Lelio R Paula	01/2013
9309	159^32728+2	72048	Lelio R Paula	05/2013
9310	15^61259-38	72047	Lelio R Paula	01/2015
9311	92^36683-91^36683	72038	Robert Price	08/2015
9312	2^239280+54615	72031	Lelio R Paula	05/2012
9313	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015
9314	(85*10^72025-1)/3	72027	Robert Price	07/2017
9315	(2^239269+1730)/2	72027	Stefano Morozzi	01/2020
9316	2^239236-97305	72018	Lelio R Paula	05/2012
9318	144^33361-143	72006	Norbert Schneider	11/2018
9317	(2^239198+1422)/2	72006	Stefano Morozzi	01/2020
9319	2^239169+59	71998	Lelio R Paula	02/2012
9320	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
9321	(15*2^239171-1)/106301	71994	Lelio R Paula	01/2014
9322	(2^239121+1926)/2	71983	Stefano Morozzi	01/2020
9324	(29^49211-1)/28	71965	Robert Price	04/2012
9323	(299*10^71963+1)/3	71965	Robert Price	11/2017
9325	L(344293)	71953	Renaud Lifchitz	09/2003
9326	V(344293)	71953	Serge Batalov	03/2015
9327	6*10^71951+7	71952	Dmitry Domanov	11/2010
9328	3^150798+40	71949	Lelio R Paula	01/2015
9329	2^238961+95	71935	Lelio R Paula	02/2012
9330	12511^17556+17556^12511	71933	Norbert Schneider	09/2019
9331	2^238936-407	71927	Yves Minet	02/2012
9332	(2^238930+2982)/2	71925	Stefano Morozzi	01/2020
9333	2^238923-28635	71923	Lelio R Paula	05/2012
9334	(8116^18397-1)/8115	71917	Serge Batalov	08/2020
9335	10^71910+25119	71911	Patrick De Geest	05/2016
9336	10^71910-801	71910	Robert Price	04/2016
9337	(2^238862+1230)/2	71905	Stefano Morozzi	01/2020
9338	(2^238864+3198)/2	71905	Stefano Morozzi	01/2020
9339	2^238845-112651	71900	Enzo Doria	06/2014
9340	2^238792-111245	71884	Enzo Doria	05/2014
9341	6*7^85059+5	71884	Lelio R Paula	10/2014
9342	19312^5273+5273^19312	71881	Hans Havermann	11/2019
9343	19176^5603+5603^19176	71880	Hans Havermann	11/2019
9344	2^238752-110589	71872	Enzo Doria	05/2014
9345	(2^238739+2738)/2	71868	Stefano Morozzi	01/2020
9346	12^66581+7	71853	Lelio R Paula	07/2014
9347	(7*2^238691+1)/41229	71850	Lelio R Paula	06/2012
9348	4*3^150568-5	71840	Lelio R Paula	04/2014
9349	6^92301+67	71825	Lelio R Paula	01/2015
9350	2^238568+98765331	71817	Jason Earls	01/2009
9351	2^238541-112723	71808	Enzo Doria	06/2014
9352	2^238529-15949	71805	Enzo Doria	04/2013
9353	9*5^102721-8	71800	Lelio R Paula	10/2014
9354	2^238494-165	71794	Lelio R Paula	02/2012
9355	18035^9562+9562^18035	71790	Hans Havermann	10/2019
9356	18390^7993+7993^18390	71771	Hans Havermann	11/2019
9357	2^238389-110905	71763	Enzo Doria	05/2014
9358	(145*10^71760-1)/9	71762	Serge Batalov	12/2014
9359	7^84913+5062	71760	Mike Oakes	02/2010
9360	21218^2409+2409^21218	71756	Hans Havermann	10/2019
9361	(F(11446)^31-F(11445)^31)/F(11444)	71753	Wayne Halsdorf	03/2012
9362	(1227^23227-1)/1226	71742	Serge Batalov	08/2020
9363	2^238268-97305	71726	Lelio R Paula	05/2012
9364	gcd(V(1330365),5F(266073)(F(266073)-1)+1)	71724	Serge Batalov	04/2015
9365	(2^238249+3770)/2	71720	Stefano Morozzi	01/2020
9366	2^238235-113247	71716	Enzo Doria	07/2014
9367	2*12^66450-5^66450	71712	Mike Oakes	11/2010
9368	(2^238213+lucasV(1,2,238213)+1)/4	71709	Mike Oakes	11/2016
9369	2^238199-111817	71706	Enzo Doria	05/2014
9370	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
9371	2^238144+98765331	71689	Jason Earls	01/2009
9372	(2^238137+2810)/2	71687	Stefano Morozzi	01/2020
9373	18^57102-4265	71679	Enzo Doria	03/2013
9374	(73*10^71670-1)/9	71671	Robert Price	01/2015
9375	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
9376	2^238067-111925	71666	Enzo Doria	05/2014
9377	(2^238024+3690)/2	71653	Stefano Morozzi	01/2020
9378	(7388^18523-1)/7387	71653	Serge Batalov	08/2020
9379	19143^5528+5528^19143	71644	Hans Havermann	10/2019
9380	65401!4+128	71638	Robert Price	09/2019
9381	36^46030+35	71637	Norbert Schneider	04/2014
9382	(74*10^71621+313)/9	71622	Robert Price	11/2017
9383	2^237905-91	71617	Lelio R Paula	02/2012
9384	(31*2^237902-1)/123	71616	Lelio R Paula	01/2014
9385	(15185*2^237866-1)/43967	71605	Lelio R Paula	04/2015
9386	16696^16957+16957^16696	71603	Norbert Schneider	09/2019
9387	(24737*2^237841+1)/25	71601	Lelio R Paula	06/2014
9388	2^237846+1299	71599	Lelio R Paula	05/2012
9389	6^92004+199801	71594	Mike Oakes	02/2011
9390	159^32516+2	71581	Lelio R Paula	05/2013
9391	2^237781+855	71580	Lelio R Paula	05/2012
9392	(2^237754+814)/2	71571	Stefano Morozzi	01/2020
9393	2^237720-4079	71561	Yves Minet	06/2011
9394	2^237698-110945	71555	Enzo Doria	05/2014
9395	2^237695-113239	71554	Enzo Doria	07/2014
9396	8*5^102362-9	71549	Lelio R Paula	10/2014
9397	(4*10^71546-31)/9	71546	Erik Branger	05/2011
9398	2^237650+37	71540	Lelio R Paula	02/2012
9399	18^56977-4391	71522	Enzo Doria	03/2013
9401	(22699*2^237565+1)/4136637	71512	Lelio R Paula	06/2014
9400	((1+sqrt(7)+sqrt(6))^48479-1)((1+sqrt(7)-sqrt(6))^48479-1)((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(7	71512	Mike Oakes	05/2009
9402	(26*10^71503+7)/3	71504	Erik Branger	11/2013
9403	(4*10^71498+173)/3	71499	Robert Price	01/2017
9404	3^149848+110	71496	Lelio R Paula	11/2014
9405	2^237498+513	71495	Lelio R Paula	05/2012
9406	2^237485+107	71491	Lelio R Paula	02/2012
9407	(2^237465+9)/2419	71481	Lelio R Paula	05/2012
9408	2^237439-112237	71477	Enzo Doria	06/2014
9409	(2^237427+2510)/2	71473	Stefano Morozzi	01/2020
9410	2^237407-9787	71467	Lelio R Paula	11/2009
9411	2^237383+72953	71460	Enzo Doria	04/2016
9412	19768^4119+4119^19768	71458	Hans Havermann	11/2019
9413	82^37337-81^37337	71457	Robert Price	01/2015
9414	(1017*2^237313-1)/19	71441	Lelio R Paula	04/2015
9415	2^237311+191	71438	Lelio R Paula	02/2012
9416	11699^17560+17560^11699	71437	Norbert Schneider	09/2019
9417	(25188^16231-1)/25187	71432	Serge Batalov	08/2020
9418	2^237280-59	71429	Lelio R Paula	02/2012
9419	(2^237275+1038)/2	71427	Stefano Morozzi	01/2020
9420	(2^237265+2774)/2	71424	Stefano Morozzi	01/2020
9421	11^68564-98	71403	Lelio R Paula	01/2015
9422	2^237173+74801	71397	Enzo Doria	04/2016
9423	(2^237150+1458)/2	71389	Stefano Morozzi	01/2020
9424	15^60697+56	71386	Lelio R Paula	01/2015
9425	2^237118+177	71380	Lelio R Paula	02/2012
9426	2^237110+69	71378	Lelio R Paula	02/2012
9427	15^60690-58	71377	Lelio R Paula	01/2015
9428	(5*2^237125-1)/599851191	71374	Lelio R Paula	01/2014
9429	20311^3262+3262^20311	71363	Hans Havermann	11/2019
9430	(3^149567+2)/539	71359	Lelio R Paula	06/2012
9431	(5*10^71357-143)/3	71358	Robert Price	04/2016
9432	2^237039-114621	71356	Enzo Doria	05/2015
9433	(2^237037+3462)/2	71355	Stefano Morozzi	01/2020
9434	12^66116-37	71352	Lelio R Paula	02/2015
9435	(3^149497+2^149497)/5	71328	Jean-Louis Charton	10/2010
9436	2^236941-66945	71327	Lelio R Paula	05/2012
9437	2^236911-1147	71318	Yves Minet	10/2009
9438	65^39337+42	71315	Lelio R Paula	01/2016
9439	(13319^17291-1)/13318	71313	Serge Batalov	08/2020
9440	(2^236863+3234)/2	71303	Stefano Morozzi	01/2020
9441	6*10^71299+7	71300	Dmitry Domanov	11/2010
9442	(25*2^236843+1)/3753	71295	Lelio R Paula	06/2012
9443	10^71291+15187	71292	Patrick De Geest	03/2016
9445	10^71291-5587309119	71291	Robert Price	03/2015
9444	10^71291-273581	71291	Patrick De Geest	03/2016
9446	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
9447	(2^236781+1514)/2	71278	Stefano Morozzi	01/2020
9448	(2^236775+2886)/2	71277	Stefano Morozzi	01/2020
9449	15105^17054+17054^15105	71271	Norbert Schneider	08/2018
9450	(2^236738+9)/13	71265	Lelio R Paula	05/2012
9451	5^101949+42	71260	Lelio R Paula	07/2014
9452	(9811^17851-1)/9810	71253	Serge Batalov	08/2020
9453	7*10^71238-39	71239	Robert Price	07/2020
9454	5*10^71237+9	71238	Dmitry Domanov	11/2010
9455	2^236634-16025	71234	Enzo Doria	04/2013
9456	71^38478+70	71233	Norbert Schneider	12/2014
9457	9*7^84280+8	71226	Lelio R Paula	10/2014
9458	(2^236603+2378)/2	71225	Stefano Morozzi	01/2020
9459	(10^71223+59)/3	71223	Serge Batalov	12/2014
9460	23260^1153+1153^23260	71219	Hans Havermann	10/2019
9461	(15185*2^236569-1)/453	71216	Lelio R Paula	04/2015
9462	51829#+(216091#)/(51829#)	71208	Makoto Morimoto	03/2016
9463	2^236528-173	71203	Lelio R Paula	02/2012
9464	3*2^236511-5	71198	Lelio R Paula	04/2014
9465	2^236477-99	71187	Lelio R Paula	02/2012
9466	11^68356-2130	71186	Enzo Doria	12/2012
9467	15128^17031+17031^15128	71186	Norbert Schneider	08/2018
9468	11^68355-3120	71185	Enzo Doria	12/2012
9469	(2^236463+998)/2	71183	Stefano Morozzi	01/2020
9470	36^45737-35^45737	71181	Robert Price	10/2012
9471	(3^149183-lucasV(1,3,149183)+1)/3	71178	Paul Vanderveen	12/2017
9472	2^236432+25	71174	Lelio R Paula	02/2012
9473	5^101818-12806	71168	Enzo Doria	02/2013
9474	(7*10^71166-457)/9	71166	Robert Price	09/2017
9475	65^39253+62	71163	Lelio R Paula	01/2016
9476	39^44718+38	71150	Norbert Schneider	05/2014
9477	18996^5557+5557^18996	71137	Hans Havermann	10/2019
9478	64983!4-256	71135	Robert Price	11/2019
9479	2^236296-407	71133	Yves Minet	02/2012
9480	2^236286-117	71130	Lelio R Paula	02/2012
9481	(2^236283+1074)/2	71128	Stefano Morozzi	01/2020
9482	2^236257-111193	71121	Enzo Doria	05/2014
9483	7^84149-36	71115	Lelio R Paula	08/2014
9484	164176#-p(164176)	71108	Henri Lifchitz	12/2018
9485	(2^236214+2934)/2	71108	Stefano Morozzi	01/2020
9486	2^236209-112123	71106	Enzo Doria	06/2014
9487	18^56644-4985	71104	Enzo Doria	03/2013
9488	(46*10^71077+521)/9	71078	Robert Price	08/2017
9489	21^53753+2	71074	Ray Chandler	08/2011
9490	(5482^19009-1)/5481	71070	Serge Batalov	08/2020
9491	(86*10^71068-311)/9	71069	Robert Price	10/2017
9492	2^236081-110923	71068	Enzo Doria	05/2014
9493	(293*27^49642-1736)/13	71058	Curtis Bright	05/2015
9494	65^39192+22	71052	Lelio R Paula	01/2016
9495	(2^236016+1246)/2	71048	Stefano Morozzi	01/2020
9496	(439#+1)^397-439#^397	71038	Mike Oakes	11/2010
9497	7^84050-2	71031	Lelio R Paula	09/2013
9498	15813^16916+16916^15813	71031	Norbert Schneider	09/2019
9499	(2^235956+3978)/2	71030	Stefano Morozzi	01/2020
9500	(3568^19993-1)/3567	71021	Serge Batalov	08/2020

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Probable Primes Top 10000

(271067 PRPs in the top)