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	26231^14718+14718^26231	109327	Hans Havermann	10/2020
7252	25461^19672+19672^25461	109326	Hans Havermann	10/2020
7253	4*10^109316-63	109317	Robert Price	10/2018
7254	2^363120+3	109311	Donovan Johnson	04/2006
7255	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
7256	2^363042-114641	109287	Enzo Doria	04/2015
7257	2^363020-112793	109280	Enzo Doria	06/2014
7258	(8732^27889-1)/(8732^167-1)	109256	Ryan Propper	11/2023
7259	(85*10^109253+203)/9	109254	Robert Price	09/2020
7260	24990^23431+23431^24990	109202	Hans Havermann	10/2020
7261	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
7262	(2^362716+1282)/2	109189	Stefano Morozzi	01/2021
7263	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
7264	25060^22737+22737^25060	109180	Hans Havermann	10/2020
7265	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
7266	5^156181+38	109166	Lelio R Paula	02/2017
7267	(2^362623+3618)/2	109161	Stefano Morozzi	09/2020
7268	25138^21993+21993^25138	109157	Hans Havermann	10/2020
7269	4*10^109142+91	109143	Robert Price	08/2018
7270	3^228750+68	109142	Lelio R Paula	03/2017
7271	(2^362561+786)/2	109142	Stefano Morozzi	09/2020
7272	578*29^74623+7	109132	Eric Chen	06/2025
7273	(23*10^109113+61)/3	109114	Robert Price	01/2022
7274	2*10^109100-49	109101	Robert Price	09/2020
7275	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
7276	65^60167-64^60167	109078	Robert Price	08/2013
7277	7*3^228589-2	109066	Lelio R Paula	09/2014
7278	24874^24243+24243^24874	109063	Hans Havermann	11/2020
7279	(17*10^109059-161)/9	109060	Robert Price	02/2021
7280	29158^5495+5495^29158	109050	Hans Havermann	11/2020
7281	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
7282	2*7^129008+9	109025	Lelio R Paula	11/2014
7283	88*10^109022+7	109024	Robert Price	03/2020
7284	28194^7337+7337^28194	108985	Hans Havermann	10/2020
7285	(5*10^108960+91)/3	108961	Robert Price	04/2018
7286	2^361957+76367	108960	Enzo Doria	05/2016
7287	(11*29^74504-245655)/28	108955	Eric Chen	06/2025
7288	2^361873-1411	108935	Yves Minet	01/2013
7289	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
7290	216^216^216+91^91^91	108917	Henri Lifchitz	03/2025
7291	47^65132-65132^47	108908	Norman Luhn	09/2024
7292	115^52842-114	108892	Norbert Schneider	07/2018
7293	13^97745-24	108883	Lelio R Paula	03/2017
7294	(2^361696+2562)/2	108882	Stefano Morozzi	09/2020
7295	17^88475+8	108864	Lelio R Paula	04/2017
7296	2^361567+51	108843	Lelio R Paula	01/2012
7297	2^361563-109501	108842	Enzo Doria	04/2014
7298	12^100852+83	108838	Lelio R Paula	03/2017
7299	2^361497+767	108822	Lelio R Paula	01/2012
7300	L(520691)/78103651/1057002731/42794551909	108791	Serge Batalov	07/2024
7301	28019^7630+7630^28019	108785	Hans Havermann	10/2020
7302	24723^24758-24758^24723	108765	Norbert Schneider	11/2020
7303	2^361280-112349	108757	Enzo Doria	06/2014
7304	2^361271-5955	108754	Lelio R Paula	04/2017
7305	12^100757+19	108736	Lelio R Paula	03/2017
7306	25368^19333+19333^25368	108735	Hans Havermann	11/2020
7307	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
7308	2^361153-111546435	108718	Paul Bourdelais	10/2021
7309	14^94849-61	108710	Lelio R Paula	05/2017
7310	27267^9700+9700^27267	108708	Hans Havermann	11/2020
7311	(19^85009-5^85009)/14	108705	Robert Price	07/2013
7312	24832^23853+23853^24832	108704	Hans Havermann	11/2020
7313	27502^8963+8963^27502	108701	Hans Havermann	11/2020
7314	(130^51419-1)/129	108695	Anonymous	06/2024
7315	25807^16278+16278^25807	108689	Hans Havermann	11/2020
7316	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
7317	2^360973+1299	108664	Lelio R Paula	04/2017
7318	24^78728+23	108662	Anonymous	09/2024
7319	2^360959-109101	108660	Enzo Doria	04/2014
7320	6*5^155454+7	108659	Lelio R Paula	11/2014
7321	10^108656+79	108657	Lelio R Paula	02/2017
7322	10^108656-50001	108656	Patrick De Geest	03/2017
7323	2^360918-35	108648	Lelio R Paula	01/2012
7324	4*10^108646-47	108647	Robert Price	10/2021
7325	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
7326	3*10^108624-49	108625	Robert Price	07/2018
7327	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
7328	(134*10^108610+7)/3	108612	Robert Price	02/2020
7329	2*10^108609+29	108610	Robert Price	02/2021
7330	(10^108604+7)/71/191	108600	Alfred Reich	06/2021
7331	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
7332	2^360706-458903	108584	Enzo Doria	04/2015
7333	31112^3087+3087^31112	108567	Hans Havermann	11/2020
7334	2^360641-113185	108564	Enzo Doria	07/2014
7335	(29*10^108559-71)/3	108560	Robert Price	07/2021
7337	2^360618+75019	108557	Enzo Doria	04/2016
7336	2^360618+2025	108557	Henri Lifchitz	01/2025
7338	2^360607-216367	108554	Harrison Mesh	06/2022
7339	29^74228+556	108551	Eric Chen	06/2025
7340	(14*10^108545-221)/9	108546	Robert Price	04/2018
7341	(44*10^108544-233)/9	108545	Robert Price	01/2019
7342	3*5^155286+2	108541	Lelio R Paula	11/2014
7343	7^128422+4	108530	Lelio R Paula	11/2014
7344	7^128421-80	108529	Lelio R Paula	03/2017
7345	2^360497+53807	108521	Yves Minet	07/2010
7346	2^360468-4559	108512	Yves Minet	03/2019
7347	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
7348	2^360366+1459	108481	Lelio R Paula	09/2011
7349	2^360364-1499	108481	Yves Minet	05/2013
7350	25662^16871+16871^25662	108477	Hans Havermann	10/2020
7351	25009^21748+21748^25009	108475	Hans Havermann	10/2020
7352	14^94642-23	108472	Lelio R Paula	05/2017
7353	(197*10^108446-11)/3	108448	Robert Price	03/2020
7354	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
7355	4*10^108412+9	108413	Robert Price	05/2015
7356	(259*10^108409-1)/3	108411	Robert Price	12/2020
7357	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
7358	133^51042-132	108406	Norbert Schneider	02/2019
7359	2^360093-351103	108399	Enzo Doria	06/2015
7360	2^360042+723	108384	Lelio R Paula	01/2012
7361	85^56164-2	108364	Lelio R Paula	10/2013
7362	2^359937-29323	108352	Enzo Doria	07/2015
7363	22^80712-23	108350	Anonymous	09/2024
7364	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
7365	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
7366	2^359898-19997	108341	Enzo Doria	06/2013
7367	(2^359886+2122)/2	108337	Stefano Morozzi	09/2020
7368	2*5^154948-7	108305	Lelio R Paula	11/2014
7369	10^108303+13	108304	Lelio R Paula	02/2017
7370	10^108303-207959	108303	Patrick De Geest	03/2017
7371	7*10^108300+69	108301	Robert Price	07/2019
7372	198^47155-47155^198	108300	Norman Luhn	09/2024
7373	2^359730+753	108290	Lelio R Paula	12/2011
7374	(8*10^108273+13)/3	108274	Robert Price	06/2018
7375	2^359650-19797	108266	Enzo Doria	06/2013
7376	(47*10^108261+259)/9	108262	Robert Price	03/2022
7377	91^55259-90^55259	108255	Robert Price	07/2015
7378	10^108251+85749	108252	Patrick De Geest	02/2021
7379	10^108251-50000000001	108251	Robert Price	12/2020
7380	10^108251-252081	108251	Patrick De Geest	02/2021
7381	4*10^108238-71	108239	Robert Price	12/2018
7382	3^226845+68	108233	Lelio R Paula	03/2017
7383	31836^2509+2509^31836	108227	Hans Havermann	10/2020
7384	5^154822-12866	108216	Enzo Doria	05/2014
7385	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
7386	2^359454-177	108207	Lelio R Paula	12/2011
7387	(19*10^108184+191)/3	108185	Robert Price	05/2019
7388	6^139022-59	108181	Lelio R Paula	02/2017
7389	(19*10^108176-43)/3	108177	Robert Price	05/2019
7390	2^359352-179	108176	Lelio R Paula	12/2011
7391	2^359338-1858781	108172	Enzo Doria	04/2016
7392	12^100230-97	108167	Lelio R Paula	03/2017
7393	27028^10043+10043^27028	108163	Hans Havermann	11/2020
7394	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
7395	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
7396	26583^11702+11702^26583	108147	Hans Havermann	11/2020
7397	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
7398	6^138956-59	108129	Lelio R Paula	02/2017
7399	2^359184+30285	108126	Lelio R Paula	04/2017
7400	13^97059+10	108119	Lelio R Paula	03/2017
7401	2^359137-81	108112	Lelio R Paula	12/2011
7403	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
7402	2^359110-11655	108103	Lelio R Paula	04/2017
7404	2^359069-933075	108091	Paul Bourdelais	06/2021
7405	26227^13222+13222^26227	108090	Hans Havermann	10/2020
7406	8*6^138875+5	108067	Lelio R Paula	11/2014
7407	2^358987-216919	108066	Enzo Doria	05/2014
7408	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
7409	39^67918-67918^39	108062	Norbert Schneider	02/2017
7410	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
7411	25282^18767+18767^25282	108040	Hans Havermann	11/2020
7412	2^358785-16933	108006	Enzo Doria	05/2013
7413	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
7414	6^138770-77	107985	Lelio R Paula	02/2017
7415	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
7416	10^107976+19	107977	Lelio R Paula	02/2017
7417	10^107976-202103	107976	Patrick De Geest	03/2017
7418	2^358684+75781	107975	Enzo Doria	04/2016
7419	24928^21411+21411^24928	107955	Hans Havermann	10/2020
7420	99^54094+2	107952	Lelio R Paula	06/2013
7421	(2^358583-9)/391	107942	Lelio R Paula	12/2013
7422	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
7423	2^358538+55	107931	Lelio R Paula	12/2011
7424	2^358517-109009	107925	Enzo Doria	03/2014
7425	26395^12258+12258^26395	107914	Hans Havermann	10/2020
7426	3^226159+104	107906	Lelio R Paula	03/2017
7427	7*10^107870+39	107871	Robert Price	01/2023
7428	2^358310-11655	107863	Lelio R Paula	03/2017
7429	(68*10^107852-329)/9	107853	Robert Price	03/2021
7430	2^358275-112987	107852	Enzo Doria	07/2014
7431	3^226038+4	107848	Tyler NeSmith	01/2021
7432	2^358233-20005	107839	Enzo Doria	06/2013
7433	2^358194+175	107828	Lelio R Paula	12/2011
7434	107^53125-106	107812	Norbert Schneider	12/2016
7435	(25*10^107804+161)/3	107805	Robert Price	09/2019
7436	3^225922-2	107793	Lelio R Paula	10/2013
7437	12^99874-95	107783	Lelio R Paula	03/2017
7438	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
7439	2^358030-171	107778	Lelio R Paula	12/2011
7440	11^103488-4170	107772	Enzo Doria	12/2012
7441	2^357930-4547	107748	Yves Minet	03/2019
7442	2^357911-20089	107742	Enzo Doria	06/2013
7443	2^357885+12857	107735	Yves Minet	07/2010
7444	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
7445	7^127473+40	107728	Lelio R Paula	03/2017
7446	5*2^357850+9	107725	Lelio R Paula	09/2014
7447	2^357786-291191	107705	Enzo Doria	06/2015
7448	28907^5320+5320^28907	107705	Hans Havermann	10/2020
7449	18^85798-23	107700	Lelio R Paula	04/2017
7450	3*10^107697+61	107698	Robert Price	09/2020
7451	(14*10^107694-83)/3	107695	Robert Price	12/2018
7452	2^357688-1854269	107675	Enzo Doria	09/2015
7453	2^357671-112225	107670	Enzo Doria	06/2014
7454	34323^1370+1370^34323	107662	Hans Havermann	11/2020
7455	2^357618-21005	107654	Enzo Doria	06/2013
7456	2^357615-17505	107653	Enzo Doria	05/2013
7457	26350^12171+12171^26350	107649	Hans Havermann	11/2020
7458	(30^72871-1)/29	107638	Robert Price	12/2011
7459	25021^20026+20026^25021	107631	Hans Havermann	11/2020
7460	2^357521+1870217	107625	Enzo Doria	05/2016
7461	2^357477-1203	107612	Lelio R Paula	03/2017
7462	26008^13693+13693^26008	107583	Hans Havermann	10/2020
7463	25432^16991+16991^25432	107583	Hans Havermann	10/2020
7464	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
7465	5^153894-18	107568	Lelio R Paula	02/2017
7466	2^357324-69059	107566	Enzo Doria	11/2015
7467	467^40296+40296^467	107563	Norbert Schneider	03/2019
7468	29446^4495+4495^29446	107559	Hans Havermann	10/2020
7469	(8*10^107556-149)/3	107557	Robert Price	12/2021
7470	2^357283-869688105	107553	Lelio R Paula	01/2017
7471	2^357280-16805	107552	Enzo Doria	05/2013
7472	10^107547+481719	107548	Patrick De Geest	03/2017
7473	10^107547-47	107547	Lelio R Paula	02/2017
7474	(23*10^107540+37)/3	107541	Robert Price	02/2022
7475	17^87396-32	107537	Lelio R Paula	04/2017
7476	(746*10^107505+1)/9	107507	Robert Price	03/2020
7477	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
7478	2^357081+107	107493	Lelio R Paula	12/2011
7479	2^357058-3911	107486	Yves Minet	04/2017
7480	3^225274+64	107484	Lelio R Paula	03/2017
7481	5*10^107482-57	107483	Robert Price	03/2021
7482	18^85619-95	107476	Lelio R Paula	04/2017
7483	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
7484	3^225248-130	107471	Lelio R Paula	03/2017
7485	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
7486	27029^9448+9448^27029	107450	Hans Havermann	11/2020
7487	2^356935-18085	107449	Enzo Doria	05/2013
7488	55396^87+87^55396	107442	Hans Havermann	10/2020
7489	(14*10^107439-137)/3	107440	Robert Price	04/2021
7490	164^48505-48505^164	107432	Norman Luhn	09/2024
7491	10^107409+37	107410	Lelio R Paula	02/2017
7492	10^107409-329633	107409	Patrick De Geest	03/2017
7493	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
7494	2^356787-109027	107404	Enzo Doria	04/2014
7495	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
7496	3*10^107389+77	107390	Robert Price	09/2018
7497	(11*10^107385+61)/9	107386	Tyler Busby	01/2023
7498	5^153622-42	107378	Lelio R Paula	02/2017
7499	2^356699-97305	107378	Lelio R Paula	03/2017
7500	13129^26072-26072^13129	107371	Norbert Schneider	09/2022

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Probable Primes Top 10000

(301822 PRPs in the top)