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 ?
7251	2^360706-458903	108584	Enzo Doria	04/2015
7252	31112^3087+3087^31112	108567	Hans Havermann	11/2020
7253	2^360641-113185	108564	Enzo Doria	07/2014
7254	(29*10^108559-71)/3	108560	Robert Price	07/2021
7256	2^360618+75019	108557	Enzo Doria	04/2016
7255	2^360618+2025	108557	Henri Lifchitz	01/2025
7257	2^360607-216367	108554	Harrison Mesh	06/2022
7258	29^74228+556	108551	Eric Chen	06/2025
7259	(14*10^108545-221)/9	108546	Robert Price	04/2018
7260	(44*10^108544-233)/9	108545	Robert Price	01/2019
7261	3*5^155286+2	108541	Lelio R Paula	11/2014
7262	7^128422+4	108530	Lelio R Paula	11/2014
7263	7^128421-80	108529	Lelio R Paula	03/2017
7264	2^360497+53807	108521	Yves Minet	07/2010
7265	2^360468-4559	108512	Yves Minet	03/2019
7266	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
7267	2^360366+1459	108481	Lelio R Paula	09/2011
7268	2^360364-1499	108481	Yves Minet	05/2013
7269	25662^16871+16871^25662	108477	Hans Havermann	10/2020
7270	25009^21748+21748^25009	108475	Hans Havermann	10/2020
7271	14^94642-23	108472	Lelio R Paula	05/2017
7272	(197*10^108446-11)/3	108448	Robert Price	03/2020
7273	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
7274	4*10^108412+9	108413	Robert Price	05/2015
7275	(259*10^108409-1)/3	108411	Robert Price	12/2020
7276	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
7277	133^51042-132	108406	Norbert Schneider	02/2019
7278	2^360093-351103	108399	Enzo Doria	06/2015
7279	2^360042+723	108384	Lelio R Paula	01/2012
7280	85^56164-2	108364	Lelio R Paula	10/2013
7281	2^359937-29323	108352	Enzo Doria	07/2015
7282	22^80712-23	108350	Anonymous	09/2024
7283	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
7284	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
7285	2^359898-19997	108341	Enzo Doria	06/2013
7286	(2^359886+2122)/2	108337	Stefano Morozzi	09/2020
7287	2*5^154948-7	108305	Lelio R Paula	11/2014
7288	10^108303+13	108304	Lelio R Paula	02/2017
7289	10^108303-207959	108303	Patrick De Geest	03/2017
7290	7*10^108300+69	108301	Robert Price	07/2019
7291	198^47155-47155^198	108300	Norman Luhn	09/2024
7292	2^359730+753	108290	Lelio R Paula	12/2011
7293	(8*10^108273+13)/3	108274	Robert Price	06/2018
7294	2^359650-19797	108266	Enzo Doria	06/2013
7295	(47*10^108261+259)/9	108262	Robert Price	03/2022
7296	91^55259-90^55259	108255	Robert Price	07/2015
7297	10^108251+85749	108252	Patrick De Geest	02/2021
7298	10^108251-50000000001	108251	Robert Price	12/2020
7299	10^108251-252081	108251	Patrick De Geest	02/2021
7300	4*10^108238-71	108239	Robert Price	12/2018
7301	3^226845+68	108233	Lelio R Paula	03/2017
7302	31836^2509+2509^31836	108227	Hans Havermann	10/2020
7303	5^154822-12866	108216	Enzo Doria	05/2014
7304	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
7305	2^359454-177	108207	Lelio R Paula	12/2011
7306	(19*10^108184+191)/3	108185	Robert Price	05/2019
7307	6^139022-59	108181	Lelio R Paula	02/2017
7308	(19*10^108176-43)/3	108177	Robert Price	05/2019
7309	2^359352-179	108176	Lelio R Paula	12/2011
7310	2^359338-1858781	108172	Enzo Doria	04/2016
7311	12^100230-97	108167	Lelio R Paula	03/2017
7312	27028^10043+10043^27028	108163	Hans Havermann	11/2020
7313	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
7314	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
7315	26583^11702+11702^26583	108147	Hans Havermann	11/2020
7316	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
7317	6^138956-59	108129	Lelio R Paula	02/2017
7318	2^359184+30285	108126	Lelio R Paula	04/2017
7319	13^97059+10	108119	Lelio R Paula	03/2017
7320	2^359137-81	108112	Lelio R Paula	12/2011
7322	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
7321	2^359110-11655	108103	Lelio R Paula	04/2017
7323	2^359069-933075	108091	Paul Bourdelais	06/2021
7324	26227^13222+13222^26227	108090	Hans Havermann	10/2020
7325	8*6^138875+5	108067	Lelio R Paula	11/2014
7326	2^358987-216919	108066	Enzo Doria	05/2014
7327	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
7328	39^67918-67918^39	108062	Norbert Schneider	02/2017
7329	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
7330	25282^18767+18767^25282	108040	Hans Havermann	11/2020
7331	2^358785-16933	108006	Enzo Doria	05/2013
7332	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
7333	6^138770-77	107985	Lelio R Paula	02/2017
7334	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
7335	10^107976+19	107977	Lelio R Paula	02/2017
7336	10^107976-202103	107976	Patrick De Geest	03/2017
7337	2^358684+75781	107975	Enzo Doria	04/2016
7338	24928^21411+21411^24928	107955	Hans Havermann	10/2020
7339	99^54094+2	107952	Lelio R Paula	06/2013
7340	(2^358583-9)/391	107942	Lelio R Paula	12/2013
7341	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
7342	2^358538+55	107931	Lelio R Paula	12/2011
7343	2^358517-109009	107925	Enzo Doria	03/2014
7344	26395^12258+12258^26395	107914	Hans Havermann	10/2020
7345	3^226159+104	107906	Lelio R Paula	03/2017
7346	7*10^107870+39	107871	Robert Price	01/2023
7347	2^358310-11655	107863	Lelio R Paula	03/2017
7348	(68*10^107852-329)/9	107853	Robert Price	03/2021
7349	2^358275-112987	107852	Enzo Doria	07/2014
7350	3^226038+4	107848	Tyler NeSmith	01/2021
7351	2^358233-20005	107839	Enzo Doria	06/2013
7352	2^358194+175	107828	Lelio R Paula	12/2011
7353	107^53125-106	107812	Norbert Schneider	12/2016
7354	(25*10^107804+161)/3	107805	Robert Price	09/2019
7355	3^225922-2	107793	Lelio R Paula	10/2013
7356	12^99874-95	107783	Lelio R Paula	03/2017
7357	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
7358	2^358030-171	107778	Lelio R Paula	12/2011
7359	11^103488-4170	107772	Enzo Doria	12/2012
7360	2^357930-4547	107748	Yves Minet	03/2019
7361	2^357911-20089	107742	Enzo Doria	06/2013
7362	2^357885+12857	107735	Yves Minet	07/2010
7363	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
7364	7^127473+40	107728	Lelio R Paula	03/2017
7365	5*2^357850+9	107725	Lelio R Paula	09/2014
7366	2^357786-291191	107705	Enzo Doria	06/2015
7367	28907^5320+5320^28907	107705	Hans Havermann	10/2020
7368	18^85798-23	107700	Lelio R Paula	04/2017
7369	3*10^107697+61	107698	Robert Price	09/2020
7370	(14*10^107694-83)/3	107695	Robert Price	12/2018
7371	2^357688-1854269	107675	Enzo Doria	09/2015
7372	2^357671-112225	107670	Enzo Doria	06/2014
7373	34323^1370+1370^34323	107662	Hans Havermann	11/2020
7374	2^357618-21005	107654	Enzo Doria	06/2013
7375	2^357615-17505	107653	Enzo Doria	05/2013
7376	26350^12171+12171^26350	107649	Hans Havermann	11/2020
7377	(30^72871-1)/29	107638	Robert Price	12/2011
7378	25021^20026+20026^25021	107631	Hans Havermann	11/2020
7379	2^357521+1870217	107625	Enzo Doria	05/2016
7380	2^357477-1203	107612	Lelio R Paula	03/2017
7381	26008^13693+13693^26008	107583	Hans Havermann	10/2020
7382	25432^16991+16991^25432	107583	Hans Havermann	10/2020
7383	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
7384	5^153894-18	107568	Lelio R Paula	02/2017
7385	2^357324-69059	107566	Enzo Doria	11/2015
7386	467^40296+40296^467	107563	Norbert Schneider	03/2019
7387	29446^4495+4495^29446	107559	Hans Havermann	10/2020
7388	(8*10^107556-149)/3	107557	Robert Price	12/2021
7389	2^357283-869688105	107553	Lelio R Paula	01/2017
7390	2^357280-16805	107552	Enzo Doria	05/2013
7391	10^107547+481719	107548	Patrick De Geest	03/2017
7392	10^107547-47	107547	Lelio R Paula	02/2017
7393	(23*10^107540+37)/3	107541	Robert Price	02/2022
7394	17^87396-32	107537	Lelio R Paula	04/2017
7395	(746*10^107505+1)/9	107507	Robert Price	03/2020
7396	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
7397	2^357081+107	107493	Lelio R Paula	12/2011
7398	2^357058-3911	107486	Yves Minet	04/2017
7399	3^225274+64	107484	Lelio R Paula	03/2017
7400	5*10^107482-57	107483	Robert Price	03/2021
7401	18^85619-95	107476	Lelio R Paula	04/2017
7402	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
7403	3^225248-130	107471	Lelio R Paula	03/2017
7404	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
7405	27029^9448+9448^27029	107450	Hans Havermann	11/2020
7406	2^356935-18085	107449	Enzo Doria	05/2013
7407	55396^87+87^55396	107442	Hans Havermann	10/2020
7408	(14*10^107439-137)/3	107440	Robert Price	04/2021
7409	164^48505-48505^164	107432	Norman Luhn	09/2024
7410	10^107409+37	107410	Lelio R Paula	02/2017
7411	10^107409-329633	107409	Patrick De Geest	03/2017
7412	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
7413	2^356787-109027	107404	Enzo Doria	04/2014
7414	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
7415	3*10^107389+77	107390	Robert Price	09/2018
7416	(11*10^107385+61)/9	107386	Tyler Busby	01/2023
7417	5^153622-42	107378	Lelio R Paula	02/2017
7418	2^356699-97305	107378	Lelio R Paula	03/2017
7419	13129^26072-26072^13129	107371	Norbert Schneider	09/2022
7420	2^356654+85	107364	Lelio R Paula	11/2011
7421	2^356641-19921	107360	Enzo Doria	06/2013
7422	5*10^107355+11	107356	Robert Price	08/2019
7423	2^356623-465	107355	Lelio R Paula	03/2017
7424	19^83945-92	107345	Lelio R Paula	02/2017
7425	25491^16246+16246^25491	107337	Hans Havermann	11/2020
7426	10^107334+28149	107335	Patrick De Geest	03/2017
7427	10^107334-83	107334	Lelio R Paula	02/2017
7428	2^356518+885	107323	Lelio R Paula	03/2017
7429	(59*10^107322+391)/9	107323	Robert Price	03/2021
7430	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
7431	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
7432	2^356442-114713	107300	Enzo Doria	04/2015
7433	2^356425+72257	107295	Enzo Doria	04/2016
7434	2^356351-112237	107273	Enzo Doria	06/2014
7436	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
7435	2^356322+74539	107264	Enzo Doria	04/2016
7437	2^356274+1874479	107250	Enzo Doria	06/2016
7438	24606^22819+22819^24606	107241	Hans Havermann	10/2020
7439	(2^356243+3686)/2	107240	Stefano Morozzi	09/2020
7440	20^82422-93	107234	Lelio R Paula	02/2017
7441	2^356157-20365	107214	Enzo Doria	06/2013
7442	8*10^107209+99	107210	Robert Price	03/2021
7443	2^356129-18949	107206	Enzo Doria	05/2013
7444	(15^91163-1)/13873078234414574	107200	Paul Vanderveen	06/2025
7445	2^356100-109587	107197	Enzo Doria	04/2014
7446	2*10^107173-37	107174	Robert Price	11/2021
7447	(2^355978+3262)/2	107160	Stefano Morozzi	02/2021
7448	(31*2^355970+1)/5	107159	Lelio R Paula	03/2014
7449	2^355968-64875	107158	Lelio R Paula	01/2017
7450	2^355952+1870321	107153	Enzo Doria	05/2016
7451	27069^9088+9088^27069	107152	Hans Havermann	11/2020
7452	2^355915-117	107142	Lelio R Paula	11/2011
7453	(16*10^107140+77)/3	107141	Robert Price	03/2019
7454	24628^22369+22369^24628	107124	Hans Havermann	11/2020
7455	(19*2^355838-1)/15	107119	Lelio R Paula	03/2014
7456	3^224495-8	107112	Lelio R Paula	12/2013
7457	3*10^107096+23	107097	Robert Price	03/2022
7458	25077^18632+18632^25077	107086	Hans Havermann	10/2020
7459	7^126691-44	107067	Lelio R Paula	03/2017
7460	4^177830-8243	107065	Mike Oakes	02/2011
7461	(509*10^107057+13)/9	107059	Robert Price	05/2022
7462	2^355604+214051	107048	Enzo Doria	10/2023
7463	(2^355562+1702)/2	107035	Stefano Morozzi	09/2020
7464	10^107028+3593037	107029	Paul Bourdelais	10/2021
7465	10^107028-43301	107028	Alfred Reich	08/2024
7466	2^355524-21237	107024	Enzo Doria	06/2013
7468	(10223*2^355515+1)/4855	107022	Lelio R Paula	07/2014
7467	24843^20320+20320^24843	107022	Hans Havermann	10/2020
7469	2^355494-19901	107015	Enzo Doria	06/2013
7470	2^355454-869688105	107003	Lelio R Paula	01/2017
7471	4*10^106997+13	106998	Robert Price	02/2021
7472	(8*10^106985-629)/9	106985	Robert Price	01/2022
7473	2^355366+54615	106976	Lelio R Paula	01/2017
7474	(31*2^355346-1)/1563	106969	Lelio R Paula	03/2014
7475	2^355275-19861	106949	Enzo Doria	06/2013
7476	27503^7738+7738^27503	106949	Hans Havermann	11/2020
7477	(85*10^106943+77)/9	106944	Robert Price	07/2022
7478	(9179*2^355234-1)/1915	106937	Lelio R Paula	05/2015
7479	4*10^106914-93	106915	Robert Price	07/2020
7480	(151^49069-1)/90910031243271150	106904	Paul Vanderveen	06/2025
7481	4*10^106892-3	106893	Robert Price	10/2015
7482	(66^58741+1)/67	106881	Paul Bourdelais	08/2017
7483	2^355001+335931	106866	Enzo Doria	08/2024
7484	2^354946-3	106850	M. Frind & P. Underwood	08/2002
7485	(2^354945+3134)/2	106849	Stefano Morozzi	09/2020
7486	(46^64384+1)/(46^128+1)	106843	Martin Hopf	12/2023
7487	2^354873-18693	106828	Enzo Doria	05/2013
7488	(2^354831+3186)/2	106815	Stefano Morozzi	09/2020
7490	2^354828+4257	106814	Lelio R Paula	01/2017
7489	25216^17217+17217^25216	106814	Hans Havermann	10/2020
7491	(2^354799+1218)/2	106805	Stefano Morozzi	09/2020
7492	436^40459+40459^436	106791	Norbert Schneider	03/2019
7493	(21^80761+1)/22	106783	Paul Bourdelais	03/2010
7494	(115*10^106772-7)/9	106774	Robert Price	02/2020
7495	2^354640-354640+1	106758	Robert Price	10/2014
7496	(2^354603+2606)/2	106746	Stefano Morozzi	09/2020
7497	2^354585+95	106741	Lelio R Paula	10/2011
7498	(206*10^106737+1)/9	106739	Robert Price	04/2022
7499	2^354553+189	106732	Lelio R Paula	10/2011
7500	(8*10^106729-71)/9	106729	Serge Batalov	11/2022

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Probable Primes Top 10000

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