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	31082^29499+29499^31082	138931	Hans Havermann	04/2021
5252	30573^30962-30962^30573	138876	Frank Doornink	05/2024
5253	2^461228+1870441	138844	Enzo Doria	05/2016
5254	2^461204-113675	138837	Enzo Doria	08/2014
5255	(397227*29^94935-19)/28	138837	Eric Chen	06/2025
5256	(2^461139-7)/47	138815	Lelio R Paula	08/2015
5257	(17*10^138812-521)/9	138813	Robert Price	04/2018
5258	3*10^138811-11	138812	Robert Price	07/2018
5259	29109^31088-31088^29109	138778	Frank Doornink	05/2024
5260	(28*10^138768+173)/3	138769	Robert Price	12/2019
5261	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
5262	(379*10^138737-1)/9	138739	Robert Price	02/2020
5263	(43*10^138648+101)/9	138649	Robert Price	11/2018
5264	2^460567-113541	138645	Enzo Doria	08/2014
5265	2^460539+224789	138637	Enzo Doria	07/2024
5266	(10^138622+161)/9	138622	Robert Price	09/2021
5267	7*10^138604+3	138605	Robert Price	08/2015
5268	(133*10^138600+17)/3	138602	Robert Price	11/2021
5269	33912^12203+12203^33912	138581	Hans Havermann	05/2021
5270	2^460330+69	138574	Lelio R Paula	09/2017
5271	(17*10^138569-77)/3	138570	Robert Price	08/2019
5272	31186^27725+27725^31186	138556	Hans Havermann	05/2021
5273	(41^85909-3^85909)/38	138552	Robert Price	09/2025
5274	(16*10^138545+89)/3	138546	Robert Price	03/2021
5275	39753^3056+3056^39753	138546	Hans Havermann	05/2021
5276	31282^26847+26847^31282	138545	Hans Havermann	05/2021
5277	6*10^138520-37	138521	Robert Price	02/2021
5280	2^460078-69581	138498	Enzo Doria	12/2015
5278	31830^22447+22447^31830	138498	Hans Havermann	05/2021
5279	Phi(237987,2^3)	138498	Henri Lifchitz	12/2025
5281	37384^5065+5065^37384	138492	Hans Havermann	05/2021
5282	28736^31055-31055^28736	138457	Frank Doornink	05/2024
5283	34774^9585+9585^34774	138456	Hans Havermann	05/2021
5284	10^138444-5001	138444	Robert Price	12/2021
5285	2^459768+1531	138404	Lelio R Paula	06/2012
5286	(266*10^138328-17)/3	138330	Robert Price	07/2020
5287	27200^31193-31193^27200	138328	Frank Doornink	01/2024
5288	2024^41836+2025	138319	Henri Lifchitz	01/2025
5289	28782^31019-31019^28782	138318	Frank Doornink	05/2024
5290	32963^15696+15696^32963	138306	Hans Havermann	05/2021
5291	2^459343-113611	138277	Enzo Doria	08/2014
5292	(28*10^138240+113)/3	138241	Robert Price	03/2020
5293	2^459199+1874393	138233	Enzo Doria	06/2016
5294	33339^14002+14002^33339	138230	Hans Havermann	05/2021
5295	30137^30860-30860^30137	138226	Frank Doornink	05/2024
5296	2^459063-345307	138192	Enzo Doria	06/2015
5297	2*10^138162-43	138163	Robert Price	04/2018
5298	2^458927-112747	138151	Enzo Doria	06/2014
5299	2^458927-69217	138151	Enzo Doria	11/2015
5300	30907^29458+29458^30907	138130	Hans Havermann	05/2021
5301	32882^15837+15837^32882	138094	Hans Havermann	05/2021
5302	39252^3295+3295^39252	138083	Hans Havermann	05/2021
5303	33789^12190+12190^33789	138062	Hans Havermann	06/2021
5304	555555*2^458524+1513	138036	Darren Bedwell	08/2009
5305	28095^31028-31028^28095	138033	Frank Doornink	05/2024
5306	30931^29002+29002^30931	138028	Hans Havermann	05/2021
5307	2^458465+2^32+1	138012	T. D. Noe	06/2007
5308	32206^19275+19275^32206	138003	Hans Havermann	05/2021
5309	2^458321-113053	137969	Enzo Doria	07/2014
5310	6^177298+323	137965	Riley Fisher	03/2023
5311	2^458298+79459	137962	Enzo Doria	06/2016
5312	30254^30789-30789^30254	137959	Frank Doornink	05/2024
5313	2^458248-21815	137947	Enzo Doria	07/2013
5314	2^458194+1876549	137931	Enzo Doria	07/2016
5315	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
5316	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
5317	(793*10^137887+53)/9	137889	Robert Price	01/2022
5318	2^457937+57	137853	Lelio R Paula	09/2017
5319	28714^30921-30921^28714	137849	Frank Doornink	05/2024
5320	(8*10^137845+13)/3	137846	Robert Price	06/2018
5321	2^457822+105	137819	Donovan Johnson	06/2006
5322	2^457754-113711	137798	Enzo Doria	09/2014
5323	11^132315-360	137792	Enzo Doria	09/2012
5324	(2^659318)%L(659318)	137787	Henri Lifchitz	05/2025
5325	32072^19689+19689^32072	137725	Hans Havermann	06/2021
5326	26529^31132-31132^26529	137720	Frank Doornink	03/2024
5327	44592^1225+1225^44592	137707	Hans Havermann	05/2021
5328	28986^30857-30857^28986	137690	Frank Doornink	05/2024
5329	2^457347-37	137676	Lelio R Paula	09/2017
5330	2^457322-2786393	137668	Enzo Doria	10/2015
5331	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
5332	Phi(699340M,10)	137664	Anonymous	03/2025
5333	34015^11134+11134^34015	137647	Hans Havermann	06/2021
5334	2^457240-59939	137643	Enzo Doria	10/2015
5335	(856*10^137633-1)/9	137635	Robert Price	03/2020
5336	36232^6289+6289^36232	137631	Hans Havermann	05/2021
5337	2^457120-21575	137607	Enzo Doria	07/2013
5338	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
5339	30963^27722+27722^30963	137564	Hans Havermann	04/2021
5340	33722^12003+12003^33722	137562	Hans Havermann	06/2021
5341	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
5342	41901^1918+1918^41901	137555	Hans Havermann	06/2021
5343	(7*10^137551-1)/3	137552	Robert Price	08/2022
5344	32930^15021+15021^32930	137539	Hans Havermann	05/2021
5345	31178^25785+25785^31178	137538	Hans Havermann	05/2021
5346	419^52446+52446^419	137525	Norbert Schneider	11/2020
5347	2^456813+214175	137515	Enzo Doria	10/2023
5348	2^456796-113513	137510	Enzo Doria	08/2014
5349	31788^21137+21137^31788	137485	Hans Havermann	04/2021
5350	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
5351	27151^31004-31004^27151	137466	Frank Doornink	01/2024
5352	2^456503-114361	137422	Enzo Doria	01/2015
5353	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
5354	30618^30618-5^5	137352	Serge Batalov	04/2024
5355	36248^6147+6147^36248	137332	Hans Havermann	05/2021
5356	31986^19651+19651^31986	137329	Hans Havermann	05/2021
5357	2^456167+22313	137320	Enzo Doria	09/2023
5358	31817^20656+20656^31817	137292	Hans Havermann	05/2021
5359	(37^87559-1)/3966428818030710150468	137289	Paul Vanderveen	06/2025
5360	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
5361	2^455922+76249	137247	Enzo Doria	05/2016
5362	31310^24171+24171^31310	137241	Hans Havermann	05/2021
5363	14^119741-119741^14	137239	Serge Batalov	04/2016
5364	35014^8297+8297^35014	137218	Hans Havermann	05/2021
5365	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
5367	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
5366	124^65536+57^65536	137195	Serge Batalov	03/2018
5368	2^455689+72677	137177	Enzo Doria	04/2016
5369	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
5370	31287^24128+24128^31287	137116	Hans Havermann	05/2021
5371	(37^87421-1)/36	137093	Robert Price	03/2012
5372	36233^6070+6070^36233	137077	Hans Havermann	05/2021
5373	(8*10^137073-17)/9	137073	Serge Batalov	11/2022
5374	38418^3697+3697^38418	137070	Hans Havermann	04/2021
5375	2^455323-57	137066	Lelio R Paula	09/2017
5376	(56*10^137019+583)/9	137020	Robert Price	08/2021
5377	25017^31148-31148^25017	136997	Frank Doornink	12/2023
5378	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
5379	2^455025-112723	136977	Enzo Doria	06/2014
5380	33876^11039+11039^33876	136959	Hans Havermann	05/2021
5381	(19860^32041-1)/(19860^179-1)	136943	Ryan Propper	11/2023
5382	(251^57059-1)/250	136921	Anonymous	04/2024
5383	35142^7873+7873^35142	136919	Hans Havermann	05/2021
5384	(4997*31^91805-1)/2	136918	Eric Chen	05/2024
5385	66*10^136894+7	136896	Robert Price	07/2020
5386	28766^30697-30697^28766	136875	Frank Doornink	05/2024
5387	2^454675-1777	136871	Yves Minet	10/2011
5388	31676^20931+20931^31676	136866	Hans Havermann	05/2021
5389	3*10^136829+29	136830	Robert Price	05/2018
5390	4*10^136813-57	136814	Robert Price	10/2018
5391	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
5392	fibonacci(654572)-2	136798	Jon Grantham	08/2023
5393	37359^4588+4588^37359	136795	Hans Havermann	05/2021
5394	2^454348-53	136773	Lelio R Paula	09/2017
5395	31^91680-2	136729	Lelio R Paula	05/2017
5396	2^454199-113697	136728	Enzo Doria	09/2014
5397	30785^27622+27622^30785	136725	Hans Havermann	05/2021
5398	32973^14014+14014^32973	136725	Hans Havermann	05/2021
5400	7*10^136716+69	136717	Robert Price	07/2019
5399	36002^6273+6273^36002	136717	Hans Havermann	05/2021
5401	6*10^136692+53	136693	Robert Price	05/2020
5402	Phi(568997,2)	136692	Henri Lifchitz	02/2026
5403	(13*10^136687+47)/3	136688	Robert Price	10/2018
5404	F(2*453976)%(2^453976)	136661	Henri Lifchitz	06/2025
5405	2^453935-2791357	136649	Enzo Doria	01/2016
5406	2^453906-69131	136640	Enzo Doria	11/2015
5407	33232^12915+12915^33232	136620	Hans Havermann	05/2021
5408	2^453791+1873913	136605	Enzo Doria	06/2016
5409	34166^9951+9951^34166	136592	Hans Havermann	05/2021
5410	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
5411	31102^24635+24635^31102	136587	Hans Havermann	05/2021
5412	580^49413+49413^580	136550	Norbert Schneider	02/2019
5413	2^453503-2788297	136519	Enzo Doria	11/2015
5414	34989^7958+7958^34989	136486	Hans Havermann	12/2020
5415	(2*10^136484+187)/9	136484	Robert Price	06/2022
5416	(5^653025)%L(653025)	136475	Henri Lifchitz	06/2025
5417	31007^25158+25158^31007	136452	Hans Havermann	11/2020
5418	2^453267-113827	136447	Enzo Doria	09/2014
5419	32234^17085+17085^32234	136435	Hans Havermann	12/2020
5420	2^453102+1877629	136398	Enzo Doria	08/2016
5421	31016^24981+24981^31016	136397	Hans Havermann	12/2020
5422	(62*10^136384-791)/9	136385	Robert Price	06/2019
5423	34171^9798+9798^34171	136382	Hans Havermann	12/2020
5424	(17*10^136354-113)/3	136355	Robert Price	06/2021
5425	32756^14541+14541^32756	136350	Hans Havermann	11/2020
5426	32205^17086+17086^32205	136313	Hans Havermann	12/2020
5427	(25*10^136303+161)/3	136304	Robert Price	09/2019
5428	35337^7196+7196^35337	136299	Hans Havermann	12/2020
5429	(182*10^136291+1)/3	136293	Robert Price	02/2020
5430	(88*10^136234+83)/9	136235	Robert Price	03/2022
5431	23*10^136225-7	136227	Robert Price	02/2020
5432	L(651821)	136223	Henri Lifchitz	09/2008
5433	25519^30908-30908^25519	136208	Frank Doornink	02/2024
5434	2^452460+77701	136205	Enzo Doria	05/2016
5435	2^452440-114755	136199	Enzo Doria	04/2015
5436	28625^30558-30558^28625	136190	Frank Doornink	05/2024
5437	32286^16489+16489^32286	136157	Hans Havermann	11/2020
5438	(47*10^136141+493)/9	136142	Robert Price	03/2019
5439	27140^30699-30699^27140	136108	Frank Doornink	01/2024
5440	Phi(199391,-5)	136098	Henri Lifchitz	12/2025
5441	40392^2339+2339^40392	136082	Hans Havermann	12/2020
5442	2*10^136057-43	136058	Robert Price	04/2018
5443	2^451971+21563	136057	Enzo Doria	08/2023
5444	(2^451956-5)/181	136051	Lelio R Paula	07/2015
5445	2^451947-22165	136050	Enzo Doria	07/2013
5446	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
5447	2^451787-21805	136002	Enzo Doria	07/2013
5448	2^451734-112817	135986	Enzo Doria	06/2014
5449	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
5450	2^451705-21879	135977	Enzo Doria	07/2013
5451	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
5452	2^451560-112349	135934	Enzo Doria	06/2014
5453	2^451530+45	135925	Lelio R Paula	08/2017
5454	26594^30719-30719^26594	135925	Frank Doornink	03/2024
5455	31622^19875+19875^31622	135922	Hans Havermann	11/2020
5456	(25*10^135906-73)/3	135907	Robert Price	09/2019
5457	2^451450-21743	135900	Enzo Doria	07/2013
5458	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
5459	35218^7199+7199^35218	135846	Hans Havermann	11/2020
5460	35661^6446+6446^35661	135844	Hans Havermann	11/2020
5461	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
5462	31869^18248+18248^31869	135801	Hans Havermann	12/2020
5463	(77*10^135789+157)/9	135790	Robert Price	05/2022
5464	Phi(286219,-3)	135763	Henri Lifchitz	12/2025
5465	2^450958+60529	135752	Enzo Doria	08/2023
5466	2^450805+65	135706	Lelio R Paula	08/2017
5467	10^135669+21	135670	Boyan Hu	12/2024
5468	30761^25728+25728^30761	135669	Hans Havermann	12/2020
5469	2*10^135663+69	135664	Robert Price	06/2020
5470	33962^9867+9867^33962	135651	Hans Havermann	11/2020
5471	34474^8605+8605^34474	135647	Hans Havermann	11/2020
5472	34501^8508+8508^34501	135583	Hans Havermann	12/2020
5473	35487^6614+6614^35487	135577	Hans Havermann	12/2020
5474	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
5475	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
5477	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
5476	Phi(193939,-5)	135557	Henri Lifchitz	12/2025
5478	(76*10^135553-49)/9	135554	Robert Price	07/2022
5479	5*3^284077+2^284077	135540	Jon Grantham	08/2023
5480	(844*10^135527-7)/9	135529	Robert Price	05/2021
5481	27191^30560-30560^27191	135517	Frank Doornink	01/2024
5482	40387^2260+2260^40387	135463	Hans Havermann	12/2020
5483	2^449944-113247	135447	Enzo Doria	07/2014
5484	Phi(70509,-1105)	135418	Henri Lifchitz	12/2025
5485	2^449770-113247	135395	Enzo Doria	07/2014
5486	2^449637-21471	135355	Enzo Doria	07/2013
5487	26061^30650-30650^26061	135351	Frank Doornink	03/2024
5488	2^449571-75	135335	Lelio R Paula	08/2017
5489	(14*10^135301-53)/3	135302	Robert Price	12/2018
5490	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
5491	(13*10^135279+437)/9	135280	Robert Price	04/2018
5492	2^449330-35	135262	Lelio R Paula	08/2017
5493	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
5494	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
5495	(13*10^135184-43)/3	135185	Robert Price	11/2018
5496	2^449049-115309	135178	Enzo Doria	07/2015
5497	(10^135174+191)/3	135174	Robert Price	02/2018
5498	2^449030-15	135172	Lelio R Paula	08/2017
5499	(157*10^135151-1)/3	135153	Robert Price	01/2022
5500	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022

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Probable Primes Top 10000

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