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	(77*10^93249-257)/9	93250	Robert Price	10/2017
9252	21822^18749+18749^21822	93245	Hans Havermann	09/2020
9253	3^195430-2	93244	Theodore Burton	02/2007
9254	(13*10^93236+47)/3	93237	Robert Price	01/2017
9255	(67*10^93226-7)/3	93228	Robert Price	10/2017
9256	(86*10^93217-221)/9	93218	Robert Price	06/2017
9257	2^309637-16329	93211	Enzo Doria	04/2013
9258	(41*10^93207+49)/9	93208	Robert Price	04/2016
9259	14^81312-57	93194	Lelio R Paula	06/2016
9260	41^57783-40	93192	Theodore Burton	02/2007
9261	3*10^93179-97	93180	Robert Price	08/2017
9262	5*7^110252-4	93175	Lelio R Paula	11/2014
9263	22022^16959+16959^22022	93140	Hans Havermann	08/2020
9264	83061!4-512	93137	Robert Price	11/2019
9265	25169^5016+5016^25169	93135	Hans Havermann	08/2020
9266	(483641^16384+1)/2	93135	Richard Fischer	02/2021
9267	2^309380-27	93133	Lelio R Paula	11/2012
9268	25653^4268+4268^25653	93127	Hans Havermann	08/2020
9269	(2^309355+1826)/2	93125	Stefano Morozzi	02/2021
9270	(2^309334+2710)/2	93119	Stefano Morozzi	09/2020
9271	23*10^93116-7	93118	Robert Price	03/2016
9272	(2^309270+3214)/2	93100	Stefano Morozzi	09/2020
9273	(29*10^93082+1)/3	93083	Robert Price	11/2015
9274	(2^309198+3738)/2	93078	Stefano Morozzi	09/2020
9275	(58*10^93062-13)/9	93063	Robert Price	09/2015
9276	(2^309138+1794)/2	93060	Stefano Morozzi	01/2021
9277	2^309131+1869383	93058	Enzo Doria	05/2016
9278	(2^309114+3610)/2	93053	Stefano Morozzi	09/2020
9279	2^309066-93	93039	Lelio R Paula	11/2012
9280	2^309063-113269	93038	Enzo Doria	07/2014
9281	3^194965+16	93022	Robert Price	10/2013
9282	(89*10^93019-737)/9	93020	Robert Price	01/2022
9283	2^308979+1869143	93012	Enzo Doria	05/2016
9284	5^133064+54	93008	Lelio R Paula	04/2016
9285	(2^308947+2750)/2	93003	Stefano Morozzi	01/2021
9286	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
9287	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
9288	(2*10^92976-17)/3	92976	Robert Price	08/2014
9289	24783^5642+5642^24783	92972	Hans Havermann	08/2020
9290	(472489^16384+1)/2	92969	Richard Fischer	01/2021
9291	2^308809+37967	92961	Phil Moore	03/2008
9292	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
9293	norm(Mod(x,x^3-x-1)^760951-1)	92930	Paul Vanderveen	08/2022
9294	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
9295	2^308650+513	92913	Lelio R Paula	02/2016
9296	5*7^109936+6	92908	Lelio R Paula	10/2014
9297	2*10^92897+89	92898	Robert Price	07/2016
9298	(2^308585+3182)/2	92894	Stefano Morozzi	09/2020
9299	(467307^16384+1)/2	92891	Richard Fischer	01/2021
9300	12^86073-29	92889	Lelio R Paula	06/2016
9301	2^308566-117	92888	Lelio R Paula	11/2012
9302	11594^22851-22851^11594	92872	Norbert Schneider	03/2022
9303	(17*10^92869-11)/3	92870	Robert Price	07/2015
9304	2^308459+75431	92856	Enzo Doria	04/2016
9305	2^308426-1866377	92846	Enzo Doria	03/2016
9306	24810^5521+5521^24810	92840	Hans Havermann	09/2020
9307	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
9308	2^308349-112111	92823	Enzo Doria	06/2014
9309	9*10^92821+19	92822	Robert Price	05/2016
9310	2^308337-75	92819	Lelio R Paula	11/2012
9311	4*3^194508+7	92805	Lelio R Paula	08/2014
9312	22*25^66379-113	92796	Curtis Bright	05/2015
9313	24538^6047+6047^24538	92792	Hans Havermann	09/2020
9314	11^89101-1080	92790	Enzo Doria	12/2012
9315	2^308236-1867859	92789	Enzo Doria	04/2016
9316	12^85963+25	92770	Lelio R Paula	06/2016
9317	23692^8221+8221^23692	92753	Hans Havermann	08/2020
9318	7^109750-66	92750	Lelio R Paula	04/2016
9319	9*10^92742+11	92743	Robert Kinser	01/2017
9320	(2^308054+778)/2	92734	Stefano Morozzi	09/2020
9321	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
9322	2^307997-110655	92717	Enzo Doria	05/2014
9323	L(443609)	92709	Renaud Lifchitz	11/2003
9324	10^92691+9	92692	Robert Price	03/2011
9325	10^92691-252291	92691	Patrick De Geest	08/2013
9326	(2^307883+3506)/2	92682	Stefano Morozzi	09/2020
9327	2^307879-2521	92681	Yves Minet	07/2014
9328	21269^21412+21412^21269	92666	Norbert Schneider	04/2020
9329	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
9330	14^80831+47	92643	Lelio R Paula	06/2016
9331	15^78744+92	92611	Lelio R Paula	07/2016
9332	65^51083-64	92610	Norbert Schneider	11/2014
9333	(2^307639+506)/2	92609	Stefano Morozzi	09/2020
9334	131^43737-130	92604	Norbert Schneider	02/2019
9335	6^118996-16943	92597	Enzo Doria	02/2013
9336	(16*10^92591+41)/3	92592	Robert Price	10/2017
9337	(2^307566+3094)/2	92587	Stefano Morozzi	09/2020
9338	(2^307528+1578)/2	92575	Stefano Morozzi	09/2020
9339	9*10^92573+83	92574	Robert Price	11/2020
9340	(3^194014-7)/2	92568	Lelio R Paula	04/2013
9341	(2^307498+570)/2	92566	Stefano Morozzi	09/2020
9342	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
9343	(26*10^92546-77)/3	92547	Robert Price	02/2017
9344	3^193954+340	92540	Lelio R Paula	04/2016
9345	2^307407-307407^2	92539	Henri Lifchitz	05/2005
9346	24299^6430+6430^24299	92536	Hans Havermann	08/2020
9348	(17*10^92513-11)/3	92514	Robert Price	07/2015
9347	2^307322-399071	92514	Harrison Mesh	06/2022
9349	2^307318-4211	92512	Yves Minet	06/2011
9350	2^307280+193	92501	Lelio R Paula	11/2012
9351	20^71075-33	92471	Lelio R Paula	05/2016
9352	2^307126-78795	92455	Lelio R Paula	02/2016
9353	2^307125-49789	92454	Henri Lifchitz	08/2005
9354	2^307099+23	92447	Lelio R Paula	11/2012
9355	129^43798+128	92440	Norbert Schneider	01/2019
9356	21826^17181+17181^21826	92435	Hans Havermann	09/2020
9357	Phi(277314,10)/3327769	92430	Makoto Kamada	05/2019
9358	(2^307022+1038)/2	92423	Stefano Morozzi	09/2020
9359	7*10^92414-69	92415	Robert Price	01/2017
9360	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
9361	22280^14037+14037^22280	92402	Hans Havermann	09/2020
9362	2^306915+1873373	92391	Enzo Doria	06/2016
9363	2^306908+12915	92389	Lelio R Paula	02/2016
9364	21620^18759+18759^21620	92387	Hans Havermann	09/2020
9365	(2^306897+1142)/2	92385	Stefano Morozzi	09/2020
9366	19^72244-80	92383	Lelio R Paula	06/2016
9368	2^306849+75	92371	Lelio R Paula	11/2012
9367	(397*10^92369+53)/9	92371	Robert Price	11/2017
9369	2^306813-869688105	92360	Lelio R Paula	08/2016
9370	(2^306797+2694)/2	92355	Stefano Morozzi	09/2020
9371	21713^17914+17914^21713	92350	Hans Havermann	09/2020
9372	2^306672-109059	92318	Enzo Doria	04/2014
9373	(430463^16384+1)/2	92307	Richard Fischer	09/2020
9374	6^118604-17063	92292	Enzo Doria	02/2013
9375	21969^15878+15878^21969	92288	Hans Havermann	08/2020
9376	21690^17959+17959^21690	92276	Hans Havermann	08/2020
9377	(7613^23773-1)/7612	92273	Serge Batalov	08/2020
9378	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
9379	2^306467-1835611	92256	Enzo Doria	04/2015
9380	2^306433+76427	92246	Enzo Doria	05/2016
9381	2^306430-113313	92245	Enzo Doria	07/2014
9382	(23*10^92244-59)/9	92245	Robert Price	03/2017
9383	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
9384	21436^20043+20043^21436	92217	Hans Havermann	09/2020
9385	(25*10^92186+59)/3	92187	Robert Price	05/2016
9386	2^306213-286183	92180	Enzo Doria	06/2015
9387	10^92178+61	92179	Robert Price	04/2011
9388	10^92178-175509	92178	Patrick De Geest	07/2013
9389	2^306200+1185	92176	Lelio R Paula	02/2016
9390	(2^306171+1514)/2	92167	Stefano Morozzi	09/2020
9391	2^306153+11	92162	Lelio R Paula	11/2012
9392	(2^306141-7)/5	92157	Lelio R Paula	06/2013
9393	21725^17454+17454^21725	92156	Hans Havermann	09/2020
9394	(26*10^92152-23)/3	92153	Robert Price	08/2016
9395	(2*10^92152+67)/3	92152	Robert Price	04/2017
9396	21368^20457+20457^21368	92115	Hans Havermann	08/2020
9397	(2^305996+3018)/2	92114	Stefano Morozzi	09/2020
9398	410^92099+37^92099	92100	Mike Oakes	12/2010
9399	30504^1045+1045^30504	92096	Hans Havermann	08/2020
9400	24334^6085+6085^24334	92087	Hans Havermann	08/2020
9401	(2^305898+2262)/2	92085	Stefano Morozzi	01/2021
9402	(4591^25147-1)/4590	92083	Serge Batalov	08/2020
9403	115^44684+114	92081	Norbert Schneider	07/2018
9404	(416771^16384+1)/2	92077	Richard Fischer	08/2020
9405	(2^305867-2^152934+1)/5	92075		11/2006
9406	2^305851-109495	92071	Enzo Doria	04/2014
9407	(416213^16384+1)/2	92067	Richard Fischer	08/2020
9409	12^85300+35	92055	Lelio R Paula	06/2016
9408	((10^46026-1)1000/9+739)10^46026+(10^46026-1)/9	92055	Hans Havermann	05/2019
9410	21732^17201+17201^21732	92048	Hans Havermann	08/2020
9411	7*10^92043-39	92044	Robert Price	07/2020
9412	3^192911+92	92042	Lelio R Paula	04/2016
9413	2^305723-276271	92032	Enzo Doria	07/2015
9414	(2^305714+3738)/2	92029	Stefano Morozzi	09/2020
9415	(2^305707+798)/2	92027	Stefano Morozzi	01/2021
9416	(2^305682+3202)/2	92020	Stefano Morozzi	09/2020
9417	2^305676+93	92018	Donovan Johnson	06/2008
9418	3^192819+4	91999	Lelio R Paula	04/2013
9419	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
9420	2^305539+72911	91977	Enzo Doria	04/2016
9421	Phi(212014,10)	91960	Makoto Kamada	04/2019
9422	(2^305423+2666)/2	91942	Stefano Morozzi	09/2020
9423	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
9424	82077!4-128	91928	Robert Price	11/2019
9425	85^47642+84	91922	Norbert Schneider	10/2015
9426	10^91920+187651	91921	Patrick De Geest	07/2013
9427	10^91920-39	91920	Robert Price	05/2011
9428	(3975^25537-1)/3974	91913	Serge Batalov	08/2020
9429	(22*10^91903+41)/9	91904	Robert Price	02/2015
9431	2^305275-27	91897	Lelio R Paula	11/2012
9430	3^192607-7726	91897	Enzo Doria	05/2014
9432	(2^305243+2274)/2	91887	Stefano Morozzi	02/2021
9433	(2^305220+1278)/2	91881	Stefano Morozzi	01/2021
9435	(6958^23911-1)/6957	91874	Serge Batalov	08/2020
9434	9*10^91873-91	91874	Robert Price	06/2021
9436	(7*10^91856-61)/9	91856	Erik Branger	12/2009
9437	(2^305107+1274)/2	91847	Stefano Morozzi	01/2021
9438	(89*10^91839-53)/9	91840	Robert Price	11/2015
9439	1678^28479+28479^1678	91839	Norbert Schneider	08/2020
9440	(2^304996+406)/2	91813	Stefano Morozzi	02/2021
9441	8*5^131351+7	91812	Lelio R Paula	10/2014
9442	3^192426-68	91811	Lelio R Paula	04/2016
9443	2^304979-375607	91808	Harrison Mesh	06/2022
9445	2^304973+117	91807	Lelio R Paula	11/2012
9444	(2^304974+234)/2	91807	Stefano Morozzi	09/2020
9446	2^304939-1863727	91796	Enzo Doria	03/2016
9447	2^304902+8415	91785	Lelio R Paula	02/2016
9448	18^73119+61	91785	Lelio R Paula	06/2016
9449	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
9450	2^304747+71355	91738	Lelio R Paula	02/2016
9451	(2^304738+2262)/2	91735	Stefano Morozzi	01/2021
9452	8*3^192251+5	91728	Lelio R Paula	08/2014
9453	(2^304693+3746)/2	91722	Stefano Morozzi	01/2021
9454	2^304674-87	91717	Lelio R Paula	11/2012
9455	(28*10^91715+701)/9	91716	Robert Price	11/2017
9456	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
9457	(2^304671+1046)/2	91715	Stefano Morozzi	09/2020
9458	(2^304667+3614)/2	91714	Stefano Morozzi	09/2020
9459	(5*10^91707-119)/3	91708	Robert Price	04/2016
9460	2^304633-112771	91704	Enzo Doria	06/2014
9461	(5*10^91702+19)/3	91703	Robert Price	07/2022
9462	(395347^16384+1)/2	91701	Richard Fischer	06/2020
9463	9*10^91693+23	91694	Robert Price	11/2017
9464	2^304578-16713	91688	Enzo Doria	05/2013
9465	6^117824-18713	91685	Enzo Doria	03/2013
9466	(17^74509-1)/16	91679	Paul Bourdelais	03/2010
9467	(2^304551-7)/8912231	91673	Lelio R Paula	06/2013
9468	(2^304532-3)/3013	91670	Lelio R Paula	06/2013
9469	2^304507-16645	91666	Enzo Doria	04/2013
9470	(29*2^304489+1)/31	91661	Lelio R Paula	09/2013
9471	21221^20860+20860^21221	91661	Hans Havermann	08/2020
9472	2^304471-1836127	91655	Enzo Doria	04/2015
9473	2^304433+32769	91644	Lelio R Paula	02/2016
9474	2^304410-16625	91637	Enzo Doria	04/2013
9475	183^40500-2	91630	Lelio R Paula	10/2017
9476	(2^304373+1850)/2	91626	Stefano Morozzi	02/2021
9477	(203*10^91613+1)/3	91615	Robert Price	09/2017
9478	4*5^131052+7	91603	Lelio R Paula	10/2014
9480	21725^16458+16458^21725	91601	Hans Havermann	08/2020
9479	(2^304290+3270)/2	91601	Stefano Morozzi	02/2021
9481	2^304278-4001	91597	Yves Minet	04/2017
9482	2^304272-1866377	91595	Enzo Doria	03/2016
9483	2^304268+19683	91594	Lelio R Paula	02/2016
9484	21718^16497+16497^21718	91594	Hans Havermann	08/2020
9485	22759^10576+10576^22759	91590	Hans Havermann	08/2020
9486	(29*10^91584-119)/9	91585	Robert Price	12/2021
9487	2^304162-161	91562	Lelio R Paula	11/2012
9488	5*7^108331+6	91552	Lelio R Paula	10/2014
9489	2^304082-2787821	91538	Enzo Doria	03/2016
9490	2^304015+64133	91518	David Broadhurst	06/2002
9491	(7*2^303963+1)/3	91503	Lelio R Paula	09/2013
9492	(2^303945-9)/3617	91494	Lelio R Paula	06/2013
9493	(384007^16384+1)/2	91494	Richard Fischer	05/2020
9494	2^303930+1880527	91493	Enzo Doria	10/2016
9495	24810^4859+4859^24810	91464	Hans Havermann	08/2020
9496	2*10^91457+29	91458	Robert Price	02/2021
9497	3^191684-68	91457	Lelio R Paula	04/2016
9498	(21*2^303813-1)/169	91456	Lelio R Paula	02/2014
9499	(298*10^91446+11)/3	91448	Robert Price	11/2020
9500	11^87797-120	91432	Enzo Doria	07/2012

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