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 ?
5251	(35*10^109888-89)/9	109889	Robert Price	02/2022
5252	18^87533-11	109878	Lelio R Paula	04/2017
5253	2^364982-5	109871	Henri Lifchitz	04/2006
5254	3*10^109861+59	109862	Robert Price	08/2018
5255	5*10^109860-69	109861	Robert Price	02/2021
5256	2^364936-1867979	109857	Enzo Doria	04/2016
5257	27013^11652+11652^27013	109846	Hans Havermann	10/2020
5258	2^364867-112087	109836	Enzo Doria	06/2014
5259	4^182415-85061	109825	Mike Oakes	06/2011
5260	(2^364809+1034)/2	109819	Stefano Morozzi	09/2020
5261	(53*10^109809-287)/9	109810	Robert Price	02/2022
5262	(52*10^109807-133)/9	109808	Robert Price	09/2021
5263	25708^18675+18675^25708	109806	Hans Havermann	10/2020
5264	(17^89227+16^89227)/33	109788	Robert Price	08/2013
5265	2^364687-187	109782	Lelio R Paula	01/2012
5266	2^364644+67	109769	Lelio R Paula	01/2012
5267	(9787*2^364625-1)/24947	109763	Lelio R Paula	05/2015
5268	(2^364616+5)/9	109760	Lelio R Paula	01/2014
5269	(55*10^109759+89)/9	109760	Robert Price	03/2019
5270	(14*32^72921+4171)/31	109757	Eric Chen	04/2023
5271	12^101694+73	109747	Lelio R Paula	03/2017
5272	13^98518-66	109744	Lelio R Paula	03/2017
5273	(8*10^109721-269)/9	109721	Robert Price	09/2021
5274	2^364478-113261	109719	Enzo Doria	07/2014
5275	(2^364513+1)/(3*44290516579)	109719	Gord Palameta	08/2018
5276	(24737*2^364454+1)/3	109716	Lelio R Paula	07/2014
5277	27814^8777+8777^27814	109681	Hans Havermann	10/2020
5278	(62*10^109673+1)/9	109674	Serge Batalov	11/2010
5279	3^229824+340	109654	Lelio R Paula	03/2017
5280	(16623*33^72206-8095)/16	109649	Eric Chen	05/2023
5281	(2*10^109645-71)/3	109645	Robert Price	12/2017
5282	2^364169-112813	109626	Enzo Doria	06/2014
5283	28822^6359+6359^28822	109622	Hans Havermann	11/2020
5284	10^109615+21	109616	Lelio R Paula	03/2017
5285	10^109615-456267	109615	Patrick De Geest	03/2017
5286	2^364094-113	109604	Lelio R Paula	01/2012
5287	25251^21898+21898^25251	109600	Hans Havermann	11/2020
5288	(4^182026+11)/3	109591	Robert Price	02/2017
5289	2^364041-6883	109588	Lelio R Paula	09/2011
5290	12^101545+11	109586	Lelio R Paula	03/2017
5291	26536^13475+13475^26536	109582	Hans Havermann	11/2020
5292	2^363842-2787101	109528	Enzo Doria	03/2016
5293	(2^363812+3570)/2	109519	Stefano Morozzi	09/2020
5294	(22699*2^363782+1)/763	109511	Lelio R Paula	07/2014
5295	2^363769+5711	109506	Lelio R Paula	04/2017
5296	(31*2^363748+1)/49	109499	Lelio R Paula	03/2014
5297	(2^363670+100280245065)	109476	Paul Bourdelais	05/2022
5298	p(22245)#/2-8	109462	Robert Price	01/2017
5299	2^363556+55	109442	Lelio R Paula	01/2012
5300	(509*10^109414+31)/9	109416	Robert Price	08/2022
5301	(2^363437+1682)/2	109406	Stefano Morozzi	09/2020
5302	(55459*2^363411+1)/81	109401	Lelio R Paula	07/2014
5303	2^363406+1871569	109397	Enzo Doria	05/2016
5304	(2^363370+1338)/2	109385	Stefano Morozzi	02/2021
5305	(2^363349+7)/9	109378	Lelio R Paula	01/2014
5306	3^229236+100	109374	Lelio R Paula	03/2017
5307	(2^363315+3258)/2	109369	Stefano Morozzi	02/2021
5308	2^363268-58695	109355	Lelio R Paula	04/2017
5309	2^363191-112321	109332	Enzo Doria	06/2014
5310	26231^14718+14718^26231	109327	Hans Havermann	10/2020
5311	25461^19672+19672^25461	109326	Hans Havermann	10/2020
5312	4*10^109316-63	109317	Robert Price	10/2018
5313	2^363120+3	109311	Donovan Johnson	04/2006
5314	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
5315	2^363042-114641	109287	Enzo Doria	04/2015
5316	2^363020-112793	109280	Enzo Doria	06/2014
5317	(85*10^109253+203)/9	109254	Robert Price	09/2020
5318	24990^23431+23431^24990	109202	Hans Havermann	10/2020
5319	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
5320	(2^362716+1282)/2	109189	Stefano Morozzi	01/2021
5321	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
5322	25060^22737+22737^25060	109180	Hans Havermann	10/2020
5323	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
5324	5^156181+38	109166	Lelio R Paula	02/2017
5325	(2^362623+3618)/2	109161	Stefano Morozzi	09/2020
5326	25138^21993+21993^25138	109157	Hans Havermann	10/2020
5327	4*10^109142+91	109143	Robert Price	08/2018
5328	3^228750+68	109142	Lelio R Paula	03/2017
5329	(2^362561+786)/2	109142	Stefano Morozzi	09/2020
5330	(23*10^109113+61)/3	109114	Robert Price	01/2022
5331	2*10^109100-49	109101	Robert Price	09/2020
5332	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
5333	65^60167-64^60167	109078	Robert Price	08/2013
5334	7*3^228589-2	109066	Lelio R Paula	09/2014
5335	24874^24243+24243^24874	109063	Hans Havermann	11/2020
5336	(17*10^109059-161)/9	109060	Robert Price	02/2021
5337	29158^5495+5495^29158	109050	Hans Havermann	11/2020
5338	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
5339	2*7^129008+9	109025	Lelio R Paula	11/2014
5340	88*10^109022+7	109024	Robert Price	03/2020
5341	28194^7337+7337^28194	108985	Hans Havermann	10/2020
5342	(5*10^108960+91)/3	108961	Robert Price	04/2018
5343	2^361957+76367	108960	Enzo Doria	05/2016
5344	2^361873-1411	108935	Yves Minet	01/2013
5345	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
5346	115^52842-114	108892	Norbert Schneider	07/2018
5347	13^97745-24	108883	Lelio R Paula	03/2017
5348	(2^361696+2562)/2	108882	Stefano Morozzi	09/2020
5349	17^88475+8	108864	Lelio R Paula	04/2017
5350	2^361567+51	108843	Lelio R Paula	01/2012
5351	2^361563-109501	108842	Enzo Doria	04/2014
5352	12^100852+83	108838	Lelio R Paula	03/2017
5353	2^361497+767	108822	Lelio R Paula	01/2012
5354	28019^7630+7630^28019	108785	Hans Havermann	10/2020
5355	24723^24758-24758^24723	108765	Norbert Schneider	11/2020
5356	2^361280-112349	108757	Enzo Doria	06/2014
5357	2^361271-5955	108754	Lelio R Paula	04/2017
5358	12^100757+19	108736	Lelio R Paula	03/2017
5359	25368^19333+19333^25368	108735	Hans Havermann	11/2020
5360	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
5361	2^361153-111546435	108718	Paul Bourdelais	10/2021
5362	14^94849-61	108710	Lelio R Paula	05/2017
5363	27267^9700+9700^27267	108708	Hans Havermann	11/2020
5364	(19^85009-5^85009)/14	108705	Robert Price	07/2013
5365	24832^23853+23853^24832	108704	Hans Havermann	11/2020
5366	27502^8963+8963^27502	108701	Hans Havermann	11/2020
5367	25807^16278+16278^25807	108689	Hans Havermann	11/2020
5368	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
5369	2^360973+1299	108664	Lelio R Paula	04/2017
5370	2^360959-109101	108660	Enzo Doria	04/2014
5371	6*5^155454+7	108659	Lelio R Paula	11/2014
5372	10^108656+79	108657	Lelio R Paula	02/2017
5373	10^108656-50001	108656	Patrick De Geest	03/2017
5374	2^360918-35	108648	Lelio R Paula	01/2012
5375	4*10^108646-47	108647	Robert Price	10/2021
5376	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
5377	3*10^108624-49	108625	Robert Price	07/2018
5378	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
5379	(134*10^108610+7)/3	108612	Robert Price	02/2020
5380	2*10^108609+29	108610	Robert Price	02/2021
5381	(10^108604+7)/71/191	108600	Alfred Reich	06/2021
5382	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
5383	2^360706-458903	108584	Enzo Doria	04/2015
5384	31112^3087+3087^31112	108567	Hans Havermann	11/2020
5385	2^360641-113185	108564	Enzo Doria	07/2014
5386	(29*10^108559-71)/3	108560	Robert Price	07/2021
5387	2^360618+75019	108557	Enzo Doria	04/2016
5388	2^360607-216367	108554	Harrison Mesh	06/2022
5389	(14*10^108545-221)/9	108546	Robert Price	04/2018
5390	(44*10^108544-233)/9	108545	Robert Price	01/2019
5391	3*5^155286+2	108541	Lelio R Paula	11/2014
5392	7^128422+4	108530	Lelio R Paula	11/2014
5393	7^128421-80	108529	Lelio R Paula	03/2017
5394	2^360497+53807	108521	Yves Minet	07/2010
5395	2^360468-4559	108512	Yves Minet	03/2019
5396	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
5397	2^360366+1459	108481	Lelio R Paula	09/2011
5398	2^360364-1499	108481	Yves Minet	05/2013
5399	25662^16871+16871^25662	108477	Hans Havermann	10/2020
5400	25009^21748+21748^25009	108475	Hans Havermann	10/2020
5401	14^94642-23	108472	Lelio R Paula	05/2017
5402	(197*10^108446-11)/3	108448	Robert Price	03/2020
5403	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
5404	4*10^108412+9	108413	Robert Price	05/2015
5405	(259*10^108409-1)/3	108411	Robert Price	12/2020
5406	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
5407	133^51042-132	108406	Norbert Schneider	02/2019
5408	2^360093-351103	108399	Enzo Doria	06/2015
5409	2^360042+723	108384	Lelio R Paula	01/2012
5410	85^56164-2	108364	Lelio R Paula	10/2013
5411	2^359937-29323	108352	Enzo Doria	07/2015
5412	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
5413	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
5414	2^359898-19997	108341	Enzo Doria	06/2013
5415	(2^359886+2122)/2	108337	Stefano Morozzi	09/2020
5416	2*5^154948-7	108305	Lelio R Paula	11/2014
5417	10^108303+13	108304	Lelio R Paula	02/2017
5418	10^108303-207959	108303	Patrick De Geest	03/2017
5419	7*10^108300+69	108301	Robert Price	07/2019
5420	2^359730+753	108290	Lelio R Paula	12/2011
5421	(8*10^108273+13)/3	108274	Robert Price	06/2018
5422	2^359650-19797	108266	Enzo Doria	06/2013
5423	(47*10^108261+259)/9	108262	Robert Price	03/2022
5424	91^55259-90^55259	108255	Robert Price	07/2015
5425	10^108251+85749	108252	Patrick De Geest	02/2021
5426	10^108251-50000000001	108251	Robert Price	12/2020
5427	10^108251-252081	108251	Patrick De Geest	02/2021
5428	4*10^108238-71	108239	Robert Price	12/2018
5429	3^226845+68	108233	Lelio R Paula	03/2017
5430	31836^2509+2509^31836	108227	Hans Havermann	10/2020
5431	5^154822-12866	108216	Enzo Doria	05/2014
5432	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
5433	2^359454-177	108207	Lelio R Paula	12/2011
5434	(19*10^108184+191)/3	108185	Robert Price	05/2019
5435	6^139022-59	108181	Lelio R Paula	02/2017
5436	(19*10^108176-43)/3	108177	Robert Price	05/2019
5437	2^359352-179	108176	Lelio R Paula	12/2011
5438	2^359338-1858781	108172	Enzo Doria	04/2016
5439	12^100230-97	108167	Lelio R Paula	03/2017
5440	27028^10043+10043^27028	108163	Hans Havermann	11/2020
5441	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
5442	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
5443	26583^11702+11702^26583	108147	Hans Havermann	11/2020
5444	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
5445	6^138956-59	108129	Lelio R Paula	02/2017
5446	2^359184+30285	108126	Lelio R Paula	04/2017
5447	13^97059+10	108119	Lelio R Paula	03/2017
5448	2^359137-81	108112	Lelio R Paula	12/2011
5450	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
5449	2^359110-11655	108103	Lelio R Paula	04/2017
5451	2^359069-933075	108091	Paul Bourdelais	06/2021
5452	26227^13222+13222^26227	108090	Hans Havermann	10/2020
5453	8*6^138875+5	108067	Lelio R Paula	11/2014
5454	2^358987-216919	108066	Enzo Doria	05/2014
5455	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
5456	39^67918-67918^39	108062	Norbert Schneider	02/2017
5457	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
5458	25282^18767+18767^25282	108040	Hans Havermann	11/2020
5459	2^358785-16933	108006	Enzo Doria	05/2013
5460	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
5461	6^138770-77	107985	Lelio R Paula	02/2017
5462	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
5463	10^107976+19	107977	Lelio R Paula	02/2017
5464	10^107976-202103	107976	Patrick De Geest	03/2017
5465	2^358684+75781	107975	Enzo Doria	04/2016
5466	24928^21411+21411^24928	107955	Hans Havermann	10/2020
5467	99^54094+2	107952	Lelio R Paula	06/2013
5468	(2^358583-9)/391	107942	Lelio R Paula	12/2013
5469	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
5470	2^358538+55	107931	Lelio R Paula	12/2011
5471	2^358517-109009	107925	Enzo Doria	03/2014
5472	26395^12258+12258^26395	107914	Hans Havermann	10/2020
5473	3^226159+104	107906	Lelio R Paula	03/2017
5474	7*10^107870+39	107871	Robert Price	01/2023
5475	2^358310-11655	107863	Lelio R Paula	03/2017
5476	(68*10^107852-329)/9	107853	Robert Price	03/2021
5477	2^358275-112987	107852	Enzo Doria	07/2014
5478	3^226038+4	107848	Tyler NeSmith	01/2021
5479	2^358233-20005	107839	Enzo Doria	06/2013
5480	2^358194+175	107828	Lelio R Paula	12/2011
5481	107^53125-106	107812	Norbert Schneider	12/2016
5482	(25*10^107804+161)/3	107805	Robert Price	09/2019
5483	3^225922-2	107793	Lelio R Paula	10/2013
5484	12^99874-95	107783	Lelio R Paula	03/2017
5485	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
5486	2^358030-171	107778	Lelio R Paula	12/2011
5487	11^103488-4170	107772	Enzo Doria	12/2012
5488	2^357930-4547	107748	Yves Minet	03/2019
5489	2^357911-20089	107742	Enzo Doria	06/2013
5490	2^357885+12857	107735	Yves Minet	07/2010
5491	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
5492	7^127473+40	107728	Lelio R Paula	03/2017
5493	5*2^357850+9	107725	Lelio R Paula	09/2014
5494	2^357786-291191	107705	Enzo Doria	06/2015
5495	28907^5320+5320^28907	107705	Hans Havermann	10/2020
5496	18^85798-23	107700	Lelio R Paula	04/2017
5497	3*10^107697+61	107698	Robert Price	09/2020
5498	(14*10^107694-83)/3	107695	Robert Price	12/2018
5499	2^357688-1854269	107675	Enzo Doria	09/2015
5500	2^357671-112225	107670	Enzo Doria	06/2014

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