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	30137^30860-30860^30137	138226	Frank Doornink	05/2024
5252	2^459063-345307	138192	Enzo Doria	06/2015
5253	2*10^138162-43	138163	Robert Price	04/2018
5254	2^458927-112747	138151	Enzo Doria	06/2014
5255	2^458927-69217	138151	Enzo Doria	11/2015
5256	30907^29458+29458^30907	138130	Hans Havermann	05/2021
5257	32882^15837+15837^32882	138094	Hans Havermann	05/2021
5258	39252^3295+3295^39252	138083	Hans Havermann	05/2021
5259	33789^12190+12190^33789	138062	Hans Havermann	06/2021
5260	555555*2^458524+1513	138036	Darren Bedwell	08/2009
5261	28095^31028-31028^28095	138033	Frank Doornink	05/2024
5262	30931^29002+29002^30931	138028	Hans Havermann	05/2021
5263	2^458465+2^32+1	138012	T. D. Noe	06/2007
5264	32206^19275+19275^32206	138003	Hans Havermann	05/2021
5265	2^458321-113053	137969	Enzo Doria	07/2014
5266	6^177298+323	137965	Riley Fisher	03/2023
5267	2^458298+79459	137962	Enzo Doria	06/2016
5268	30254^30789-30789^30254	137959	Frank Doornink	05/2024
5269	2^458248-21815	137947	Enzo Doria	07/2013
5270	2^458194+1876549	137931	Enzo Doria	07/2016
5271	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
5272	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
5273	(793*10^137887+53)/9	137889	Robert Price	01/2022
5274	2^457937+57	137853	Lelio R Paula	09/2017
5275	28714^30921-30921^28714	137849	Frank Doornink	05/2024
5276	(8*10^137845+13)/3	137846	Robert Price	06/2018
5277	2^457822+105	137819	Donovan Johnson	06/2006
5278	2^457754-113711	137798	Enzo Doria	09/2014
5279	11^132315-360	137792	Enzo Doria	09/2012
5280	(2^659318)%L(659318)	137787	Henri Lifchitz	05/2025
5281	32072^19689+19689^32072	137725	Hans Havermann	06/2021
5282	26529^31132-31132^26529	137720	Frank Doornink	03/2024
5283	44592^1225+1225^44592	137707	Hans Havermann	05/2021
5284	28986^30857-30857^28986	137690	Frank Doornink	05/2024
5285	2^457347-37	137676	Lelio R Paula	09/2017
5286	2^457322-2786393	137668	Enzo Doria	10/2015
5287	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
5288	Phi(699340M,10)	137664	Anonymous	03/2025
5289	34015^11134+11134^34015	137647	Hans Havermann	06/2021
5290	2^457240-59939	137643	Enzo Doria	10/2015
5291	(856*10^137633-1)/9	137635	Robert Price	03/2020
5292	36232^6289+6289^36232	137631	Hans Havermann	05/2021
5293	2^457120-21575	137607	Enzo Doria	07/2013
5294	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
5295	30963^27722+27722^30963	137564	Hans Havermann	04/2021
5296	33722^12003+12003^33722	137562	Hans Havermann	06/2021
5297	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
5298	41901^1918+1918^41901	137555	Hans Havermann	06/2021
5299	(7*10^137551-1)/3	137552	Robert Price	08/2022
5300	32930^15021+15021^32930	137539	Hans Havermann	05/2021
5301	31178^25785+25785^31178	137538	Hans Havermann	05/2021
5302	419^52446+52446^419	137525	Norbert Schneider	11/2020
5303	2^456813+214175	137515	Enzo Doria	10/2023
5304	2^456796-113513	137510	Enzo Doria	08/2014
5305	31788^21137+21137^31788	137485	Hans Havermann	04/2021
5306	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
5307	27151^31004-31004^27151	137466	Frank Doornink	01/2024
5308	2^456503-114361	137422	Enzo Doria	01/2015
5309	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
5310	30618^30618-5^5	137352	Serge Batalov	04/2024
5311	36248^6147+6147^36248	137332	Hans Havermann	05/2021
5312	31986^19651+19651^31986	137329	Hans Havermann	05/2021
5313	2^456167+22313	137320	Enzo Doria	09/2023
5314	31817^20656+20656^31817	137292	Hans Havermann	05/2021
5315	(37^87559-1)/3966428818030710150468	137289	Paul Vanderveen	06/2025
5316	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
5317	2^455922+76249	137247	Enzo Doria	05/2016
5318	31310^24171+24171^31310	137241	Hans Havermann	05/2021
5319	14^119741-119741^14	137239	Serge Batalov	04/2016
5320	35014^8297+8297^35014	137218	Hans Havermann	05/2021
5321	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
5323	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
5322	124^65536+57^65536	137195	Serge Batalov	03/2018
5324	2^455689+72677	137177	Enzo Doria	04/2016
5325	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
5326	31287^24128+24128^31287	137116	Hans Havermann	05/2021
5327	(37^87421-1)/36	137093	Robert Price	03/2012
5328	36233^6070+6070^36233	137077	Hans Havermann	05/2021
5329	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
5330	38418^3697+3697^38418	137070	Hans Havermann	04/2021
5331	2^455323-57	137066	Lelio R Paula	09/2017
5332	(56*10^137019+583)/9	137020	Robert Price	08/2021
5333	25017^31148-31148^25017	136997	Frank Doornink	12/2023
5334	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
5335	2^455025-112723	136977	Enzo Doria	06/2014
5336	33876^11039+11039^33876	136959	Hans Havermann	05/2021
5337	(19860^32041-1)/(19860^179-1)	136943	Ryan Propper	11/2023
5338	(251^57059-1)/250	136921	Anonymous	04/2024
5339	35142^7873+7873^35142	136919	Hans Havermann	05/2021
5340	(4997*31^91805-1)/2	136918	Eric Chen	05/2024
5341	66*10^136894+7	136896	Robert Price	07/2020
5342	28766^30697-30697^28766	136875	Frank Doornink	05/2024
5343	2^454675-1777	136871	Yves Minet	10/2011
5344	31676^20931+20931^31676	136866	Hans Havermann	05/2021
5345	3*10^136829+29	136830	Robert Price	05/2018
5346	4*10^136813-57	136814	Robert Price	10/2018
5347	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
5348	fibonacci(654572)-2	136798	Jon Grantham	08/2023
5349	37359^4588+4588^37359	136795	Hans Havermann	05/2021
5350	2^454348-53	136773	Lelio R Paula	09/2017
5351	31^91680-2	136729	Lelio R Paula	05/2017
5352	2^454199-113697	136728	Enzo Doria	09/2014
5353	30785^27622+27622^30785	136725	Hans Havermann	05/2021
5354	32973^14014+14014^32973	136725	Hans Havermann	05/2021
5356	7*10^136716+69	136717	Robert Price	07/2019
5355	36002^6273+6273^36002	136717	Hans Havermann	05/2021
5357	6*10^136692+53	136693	Robert Price	05/2020
5358	Phi(568997,2)	136692	Henri Lifchitz	02/2026
5359	(13*10^136687+47)/3	136688	Robert Price	10/2018
5360	F(2*453976)%(2^453976)	136661	Henri Lifchitz	06/2025
5361	2^453935-2791357	136649	Enzo Doria	01/2016
5362	2^453906-69131	136640	Enzo Doria	11/2015
5363	33232^12915+12915^33232	136620	Hans Havermann	05/2021
5364	2^453791+1873913	136605	Enzo Doria	06/2016
5365	34166^9951+9951^34166	136592	Hans Havermann	05/2021
5366	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
5367	31102^24635+24635^31102	136587	Hans Havermann	05/2021
5368	580^49413+49413^580	136550	Norbert Schneider	02/2019
5369	2^453503-2788297	136519	Enzo Doria	11/2015
5370	34989^7958+7958^34989	136486	Hans Havermann	12/2020
5371	(2*10^136484+187)/9	136484	Robert Price	06/2022
5372	(5^653025)%L(653025)	136475	Henri Lifchitz	06/2025
5373	31007^25158+25158^31007	136452	Hans Havermann	11/2020
5374	2^453267-113827	136447	Enzo Doria	09/2014
5375	32234^17085+17085^32234	136435	Hans Havermann	12/2020
5376	2^453102+1877629	136398	Enzo Doria	08/2016
5377	31016^24981+24981^31016	136397	Hans Havermann	12/2020
5378	(62*10^136384-791)/9	136385	Robert Price	06/2019
5379	34171^9798+9798^34171	136382	Hans Havermann	12/2020
5380	(17*10^136354-113)/3	136355	Robert Price	06/2021
5381	32756^14541+14541^32756	136350	Hans Havermann	11/2020
5382	32205^17086+17086^32205	136313	Hans Havermann	12/2020
5383	(25*10^136303+161)/3	136304	Robert Price	09/2019
5384	35337^7196+7196^35337	136299	Hans Havermann	12/2020
5385	(182*10^136291+1)/3	136293	Robert Price	02/2020
5386	(88*10^136234+83)/9	136235	Robert Price	03/2022
5387	23*10^136225-7	136227	Robert Price	02/2020
5388	L(651821)	136223	Henri Lifchitz	09/2008
5389	25519^30908-30908^25519	136208	Frank Doornink	02/2024
5390	2^452460+77701	136205	Enzo Doria	05/2016
5391	2^452440-114755	136199	Enzo Doria	04/2015
5392	28625^30558-30558^28625	136190	Frank Doornink	05/2024
5393	32286^16489+16489^32286	136157	Hans Havermann	11/2020
5394	(47*10^136141+493)/9	136142	Robert Price	03/2019
5395	27140^30699-30699^27140	136108	Frank Doornink	01/2024
5396	Phi(199391,-5)	136098	Henri Lifchitz	12/2025
5397	40392^2339+2339^40392	136082	Hans Havermann	12/2020
5398	2*10^136057-43	136058	Robert Price	04/2018
5399	2^451971+21563	136057	Enzo Doria	08/2023
5400	(2^451956-5)/181	136051	Lelio R Paula	07/2015
5401	2^451947-22165	136050	Enzo Doria	07/2013
5402	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
5403	2^451787-21805	136002	Enzo Doria	07/2013
5404	2^451734-112817	135986	Enzo Doria	06/2014
5405	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
5406	2^451705-21879	135977	Enzo Doria	07/2013
5407	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
5408	2^451560-112349	135934	Enzo Doria	06/2014
5409	2^451530+45	135925	Lelio R Paula	08/2017
5410	26594^30719-30719^26594	135925	Frank Doornink	03/2024
5411	31622^19875+19875^31622	135922	Hans Havermann	11/2020
5412	(25*10^135906-73)/3	135907	Robert Price	09/2019
5413	2^451450-21743	135900	Enzo Doria	07/2013
5414	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
5415	35218^7199+7199^35218	135846	Hans Havermann	11/2020
5416	35661^6446+6446^35661	135844	Hans Havermann	11/2020
5417	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
5418	31869^18248+18248^31869	135801	Hans Havermann	12/2020
5419	(77*10^135789+157)/9	135790	Robert Price	05/2022
5420	Phi(286219,-3)	135763	Henri Lifchitz	12/2025
5421	2^450958+60529	135752	Enzo Doria	08/2023
5422	2^450805+65	135706	Lelio R Paula	08/2017
5423	10^135669+21	135670	Boyan Hu	12/2024
5424	30761^25728+25728^30761	135669	Hans Havermann	12/2020
5425	2*10^135663+69	135664	Robert Price	06/2020
5426	33962^9867+9867^33962	135651	Hans Havermann	11/2020
5427	34474^8605+8605^34474	135647	Hans Havermann	11/2020
5428	34501^8508+8508^34501	135583	Hans Havermann	12/2020
5429	35487^6614+6614^35487	135577	Hans Havermann	12/2020
5430	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
5431	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
5433	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
5432	Phi(193939,-5)	135557	Henri Lifchitz	12/2025
5434	(76*10^135553-49)/9	135554	Robert Price	07/2022
5435	5*3^284077+2^284077	135540	Jon Grantham	08/2023
5436	(844*10^135527-7)/9	135529	Robert Price	05/2021
5437	27191^30560-30560^27191	135517	Frank Doornink	01/2024
5438	40387^2260+2260^40387	135463	Hans Havermann	12/2020
5439	2^449944-113247	135447	Enzo Doria	07/2014
5440	Phi(70509,-1105)	135418	Henri Lifchitz	12/2025
5441	2^449770-113247	135395	Enzo Doria	07/2014
5442	2^449637-21471	135355	Enzo Doria	07/2013
5443	26061^30650-30650^26061	135351	Frank Doornink	03/2024
5444	2^449571-75	135335	Lelio R Paula	08/2017
5445	(14*10^135301-53)/3	135302	Robert Price	12/2018
5446	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
5447	(13*10^135279+437)/9	135280	Robert Price	04/2018
5448	2^449330-35	135262	Lelio R Paula	08/2017
5449	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
5450	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
5451	(13*10^135184-43)/3	135185	Robert Price	11/2018
5452	2^449049-115309	135178	Enzo Doria	07/2015
5453	(10^135174+191)/3	135174	Robert Price	02/2018
5454	2^449030-15	135172	Lelio R Paula	08/2017
5455	(157*10^135151-1)/3	135153	Robert Price	01/2022
5456	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
5457	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
5458	(37*10^135099+251)/9	135100	Robert Price	09/2021
5459	32221^15586+15586^32221	135095	Hans Havermann	12/2020
5460	2^448762-351401	135091	Enzo Doria	07/2015
5461	2*10^135083-43	135084	Robert Price	04/2018
5462	31357^20278+20278^31357	135056	Hans Havermann	12/2020
5463	32242^15445+15445^32242	135055	Hans Havermann	12/2020
5464	k(198476)	135054	Robert Price	07/2020
5465	32461^14470+14470^32461	135053	Hans Havermann	12/2020
5466	31353^20288+20288^31353	135045	Hans Havermann	12/2020
5467	5*10^135019+77	135020	Robert Price	12/2018
5468	(10^135011+719)/9	135011	Serge Batalov	12/2014
5469	(197*10^134978+7)/3	134980	Robert Price	12/2020
5470	2^448386-2786261	134978	Enzo Doria	03/2016
5471	26480^30517-30517^26480	134975	Frank Doornink	03/2024
5472	(73*10^134939+143)/9	134940	Robert Price	07/2019
5473	33957^9392+9392^33957	134903	Hans Havermann	12/2020
5474	2^448122+20809	134899	Enzo Doria	08/2023
5475	2^448113-113949	134896	Enzo Doria	11/2014
5476	30958^22755+22755^30958	134887	Hans Havermann	12/2020
5477	2^447888-2786639	134828	Enzo Doria	03/2016
5478	2^447870-396765	134823	Enzo Doria	07/2013
5479	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
5480	2^447766-21791	134791	Enzo Doria	07/2013
5481	(19*10^134786-49)/3	134787	Robert Price	05/2019
5482	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
5483	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
5484	2^447552-1019	134727	Yves Minet	02/2014
5485	(2*10^134720-41)/3	134720	Robert Price	02/2018
5486	(25*10^134695-97)/9	134696	Robert Price	01/2022
5487	2^447437-113569	134692	Enzo Doria	08/2014
5488	2^447426-65	134689	Lelio R Paula	08/2017
5489	2^447357-2797573	134668	Enzo Doria	04/2016
5490	2^447278+93	134645	Lelio R Paula	08/2017
5491	33193^11370+11370^33193	134623	Hans Havermann	12/2020
5492	30736^23979+23979^30736	134619	Hans Havermann	11/2020
5493	2^447094-113193	134589	Enzo Doria	07/2014
5494	3^282041-9934	134568	Enzo Doria	05/2014
5495	2^447019-109039	134567	Enzo Doria	04/2014
5496	31376^19437+19437^31376	134561	Hans Havermann	12/2020
5497	2^446990-22041	134558	Enzo Doria	07/2013
5498	123^64370+122	134528	Karsten Bonath	04/2018
5499	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5500	31251^20158+20158^31251	134519	Hans Havermann	11/2020

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Probable Primes Top 10000

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