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 ?
7501	(23*10^109113+61)/3	109114	Robert Price	01/2022
7502	2*10^109100-49	109101	Robert Price	09/2020
7503	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
7504	65^60167-64^60167	109078	Robert Price	08/2013
7505	Phi(63393,-1105)	109075	Henri Lifchitz	12/2025
7506	7*3^228589-2	109066	Lelio R Paula	09/2014
7507	24874^24243+24243^24874	109063	Hans Havermann	11/2020
7508	(17*10^109059-161)/9	109060	Robert Price	02/2021
7509	29158^5495+5495^29158	109050	Hans Havermann	11/2020
7510	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
7511	2*7^129008+9	109025	Lelio R Paula	11/2014
7512	88*10^109022+7	109024	Robert Price	03/2020
7513	28194^7337+7337^28194	108985	Hans Havermann	10/2020
7514	(5*10^108960+91)/3	108961	Robert Price	04/2018
7515	2^361957+76367	108960	Enzo Doria	05/2016
7516	(11*29^74504-245655)/28	108955	Eric Chen	06/2025
7517	2^361873-1411	108935	Yves Minet	01/2013
7518	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
7519	216^216^216+91^91^91	108917	Henri Lifchitz	03/2025
7520	47^65132-65132^47	108908	Norman Luhn	09/2024
7521	115^52842-114	108892	Norbert Schneider	07/2018
7522	13^97745-24	108883	Lelio R Paula	03/2017
7523	(2^361696+2562)/2	108882	Stefano Morozzi	09/2020
7524	17^88475+8	108864	Lelio R Paula	04/2017
7525	2^361567+51	108843	Lelio R Paula	01/2012
7526	2^361563-109501	108842	Enzo Doria	04/2014
7527	12^100852+83	108838	Lelio R Paula	03/2017
7528	2^361497+767	108822	Lelio R Paula	01/2012
7529	L(520691)/78103651/1057002731/42794551909	108791	Serge Batalov	07/2024
7530	28019^7630+7630^28019	108785	Hans Havermann	10/2020
7531	24723^24758-24758^24723	108765	Norbert Schneider	11/2020
7532	2^361280-112349	108757	Enzo Doria	06/2014
7533	2^361271-5955	108754	Lelio R Paula	04/2017
7534	12^100757+19	108736	Lelio R Paula	03/2017
7535	25368^19333+19333^25368	108735	Hans Havermann	11/2020
7536	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
7537	2^361153-111546435	108718	Paul Bourdelais	10/2021
7538	14^94849-61	108710	Lelio R Paula	05/2017
7539	27267^9700+9700^27267	108708	Hans Havermann	11/2020
7540	(19^85009-5^85009)/14	108705	Robert Price	07/2013
7541	24832^23853+23853^24832	108704	Hans Havermann	11/2020
7542	27502^8963+8963^27502	108701	Hans Havermann	11/2020
7543	(130^51419-1)/129	108695	Anonymous	06/2024
7544	25807^16278+16278^25807	108689	Hans Havermann	11/2020
7545	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
7546	2^360973+1299	108664	Lelio R Paula	04/2017
7547	24^78728+23	108662	Anonymous	09/2024
7548	2^360959-109101	108660	Enzo Doria	04/2014
7549	6*5^155454+7	108659	Lelio R Paula	11/2014
7550	10^108656+79	108657	Lelio R Paula	02/2017
7551	10^108656-50001	108656	Patrick De Geest	03/2017
7552	2^360918-35	108648	Lelio R Paula	01/2012
7553	4*10^108646-47	108647	Robert Price	10/2021
7554	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
7555	3*10^108624-49	108625	Robert Price	07/2018
7556	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
7557	(134*10^108610+7)/3	108612	Robert Price	02/2020
7558	2*10^108609+29	108610	Robert Price	02/2021
7559	(10^108604+7)/71/191	108600	Alfred Reich	06/2021
7560	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
7561	2^360706-458903	108584	Enzo Doria	04/2015
7562	31112^3087+3087^31112	108567	Hans Havermann	11/2020
7563	2^360641-113185	108564	Enzo Doria	07/2014
7564	(29*10^108559-71)/3	108560	Robert Price	07/2021
7566	2^360618+75019	108557	Enzo Doria	04/2016
7565	2^360618+2025	108557	Henri Lifchitz	01/2025
7567	2^360607-216367	108554	Harrison Mesh	06/2022
7568	29^74228+556	108551	Eric Chen	06/2025
7569	(14*10^108545-221)/9	108546	Robert Price	04/2018
7570	(44*10^108544-233)/9	108545	Robert Price	01/2019
7571	3*5^155286+2	108541	Lelio R Paula	11/2014
7572	7^128422+4	108530	Lelio R Paula	11/2014
7573	7^128421-80	108529	Lelio R Paula	03/2017
7574	2^360497+53807	108521	Yves Minet	07/2010
7575	2^360468-4559	108512	Yves Minet	03/2019
7576	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
7577	2^360366+1459	108481	Lelio R Paula	09/2011
7578	2^360364-1499	108481	Yves Minet	05/2013
7579	25662^16871+16871^25662	108477	Hans Havermann	10/2020
7580	25009^21748+21748^25009	108475	Hans Havermann	10/2020
7581	14^94642-23	108472	Lelio R Paula	05/2017
7582	(197*10^108446-11)/3	108448	Robert Price	03/2020
7583	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
7584	4*10^108412+9	108413	Robert Price	05/2015
7585	(259*10^108409-1)/3	108411	Robert Price	12/2020
7586	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
7587	133^51042-132	108406	Norbert Schneider	02/2019
7588	2^360093-351103	108399	Enzo Doria	06/2015
7589	2^360042+723	108384	Lelio R Paula	01/2012
7590	85^56164-2	108364	Lelio R Paula	10/2013
7591	2^359937-29323	108352	Enzo Doria	07/2015
7592	22^80712-23	108350	Anonymous	09/2024
7593	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
7594	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
7595	2^359898-19997	108341	Enzo Doria	06/2013
7596	(2^359886+2122)/2	108337	Stefano Morozzi	09/2020
7597	2*5^154948-7	108305	Lelio R Paula	11/2014
7598	10^108303+13	108304	Lelio R Paula	02/2017
7599	10^108303-207959	108303	Patrick De Geest	03/2017
7600	7*10^108300+69	108301	Robert Price	07/2019
7601	198^47155-47155^198	108300	Norman Luhn	09/2024
7602	2^359730+753	108290	Lelio R Paula	12/2011
7603	(8*10^108273+13)/3	108274	Robert Price	06/2018
7604	2^359650-19797	108266	Enzo Doria	06/2013
7605	(47*10^108261+259)/9	108262	Robert Price	03/2022
7606	91^55259-90^55259	108255	Robert Price	07/2015
7607	10^108251+85749	108252	Patrick De Geest	02/2021
7608	10^108251-50000000001	108251	Robert Price	12/2020
7609	10^108251-252081	108251	Patrick De Geest	02/2021
7610	4*10^108238-71	108239	Robert Price	12/2018
7611	3^226845+68	108233	Lelio R Paula	03/2017
7612	31836^2509+2509^31836	108227	Hans Havermann	10/2020
7613	5^154822-12866	108216	Enzo Doria	05/2014
7614	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
7615	2^359454-177	108207	Lelio R Paula	12/2011
7616	(19*10^108184+191)/3	108185	Robert Price	05/2019
7617	6^139022-59	108181	Lelio R Paula	02/2017
7618	(19*10^108176-43)/3	108177	Robert Price	05/2019
7619	2^359352-179	108176	Lelio R Paula	12/2011
7620	2^359338-1858781	108172	Enzo Doria	04/2016
7621	12^100230-97	108167	Lelio R Paula	03/2017
7622	27028^10043+10043^27028	108163	Hans Havermann	11/2020
7623	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
7624	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
7625	26583^11702+11702^26583	108147	Hans Havermann	11/2020
7626	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
7627	6^138956-59	108129	Lelio R Paula	02/2017
7628	2^359184+30285	108126	Lelio R Paula	04/2017
7629	13^97059+10	108119	Lelio R Paula	03/2017
7630	2^359137-81	108112	Lelio R Paula	12/2011
7632	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
7631	2^359110-11655	108103	Lelio R Paula	04/2017
7633	2^359069-933075	108091	Paul Bourdelais	06/2021
7634	26227^13222+13222^26227	108090	Hans Havermann	10/2020
7635	8*6^138875+5	108067	Lelio R Paula	11/2014
7636	2^358987-216919	108066	Enzo Doria	05/2014
7637	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
7638	39^67918-67918^39	108062	Norbert Schneider	02/2017
7639	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
7640	25282^18767+18767^25282	108040	Hans Havermann	11/2020
7641	(918^36457-1)/917	108014	Tom Wu	08/2025
7642	2^358785-16933	108006	Enzo Doria	05/2013
7643	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
7644	6^138770-77	107985	Lelio R Paula	02/2017
7645	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
7646	10^107976+19	107977	Lelio R Paula	02/2017
7647	10^107976-202103	107976	Patrick De Geest	03/2017
7648	2^358684+75781	107975	Enzo Doria	04/2016
7649	24928^21411+21411^24928	107955	Hans Havermann	10/2020
7650	99^54094+2	107952	Lelio R Paula	06/2013
7651	(2^358583-9)/391	107942	Lelio R Paula	12/2013
7652	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
7653	2^358538+55	107931	Lelio R Paula	12/2011
7654	2^358517-109009	107925	Enzo Doria	03/2014
7655	26395^12258+12258^26395	107914	Hans Havermann	10/2020
7656	3^226159+104	107906	Lelio R Paula	03/2017
7657	7*10^107870+39	107871	Robert Price	01/2023
7658	2^358310-11655	107863	Lelio R Paula	03/2017
7659	(68*10^107852-329)/9	107853	Robert Price	03/2021
7660	2^358275-112987	107852	Enzo Doria	07/2014
7661	3^226038+4	107848	Tyler NeSmith	01/2021
7662	2^358233-20005	107839	Enzo Doria	06/2013
7663	2^358194+175	107828	Lelio R Paula	12/2011
7664	107^53125-106	107812	Norbert Schneider	12/2016
7665	(25*10^107804+161)/3	107805	Robert Price	09/2019
7666	3^225922-2	107793	Lelio R Paula	10/2013
7667	12^99874-95	107783	Lelio R Paula	03/2017
7668	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
7669	2^358030-171	107778	Lelio R Paula	12/2011
7670	11^103488-4170	107772	Enzo Doria	12/2012
7671	2^357930-4547	107748	Yves Minet	03/2019
7672	2^357911-20089	107742	Enzo Doria	06/2013
7673	2^357885+12857	107735	Yves Minet	07/2010
7674	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
7675	7^127473+40	107728	Lelio R Paula	03/2017
7676	5*2^357850+9	107725	Lelio R Paula	09/2014
7677	2^357786-291191	107705	Enzo Doria	06/2015
7678	28907^5320+5320^28907	107705	Hans Havermann	10/2020
7679	18^85798-23	107700	Lelio R Paula	04/2017
7680	3*10^107697+61	107698	Robert Price	09/2020
7681	(14*10^107694-83)/3	107695	Robert Price	12/2018
7682	2^357688-1854269	107675	Enzo Doria	09/2015
7683	2^357671-112225	107670	Enzo Doria	06/2014
7684	34323^1370+1370^34323	107662	Hans Havermann	11/2020
7685	2^357618-21005	107654	Enzo Doria	06/2013
7686	2^357615-17505	107653	Enzo Doria	05/2013
7687	26350^12171+12171^26350	107649	Hans Havermann	11/2020
7689	(30^72871-1)/29	107638	Robert Price	12/2011
7688	Phi(72871,5#)	107638	Henri Lifchitz	12/2025
7690	25021^20026+20026^25021	107631	Hans Havermann	11/2020
7691	2^357521+1870217	107625	Enzo Doria	05/2016
7692	2^357477-1203	107612	Lelio R Paula	03/2017
7693	26008^13693+13693^26008	107583	Hans Havermann	10/2020
7694	25432^16991+16991^25432	107583	Hans Havermann	10/2020
7695	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
7696	5^153894-18	107568	Lelio R Paula	02/2017
7697	2^357324-69059	107566	Enzo Doria	11/2015
7698	467^40296+40296^467	107563	Norbert Schneider	03/2019
7699	29446^4495+4495^29446	107559	Hans Havermann	10/2020
7700	(8*10^107556-149)/3	107557	Robert Price	12/2021
7701	2^357283-869688105	107553	Lelio R Paula	01/2017
7702	2^357280-16805	107552	Enzo Doria	05/2013
7703	10^107547+481719	107548	Patrick De Geest	03/2017
7704	10^107547-47	107547	Lelio R Paula	02/2017
7705	(23*10^107540+37)/3	107541	Robert Price	02/2022
7706	17^87396-32	107537	Lelio R Paula	04/2017
7707	(746*10^107505+1)/9	107507	Robert Price	03/2020
7708	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
7709	2^357081+107	107493	Lelio R Paula	12/2011
7710	2^357058-3911	107486	Yves Minet	04/2017
7711	3^225274+64	107484	Lelio R Paula	03/2017
7712	5*10^107482-57	107483	Robert Price	03/2021
7713	18^85619-95	107476	Lelio R Paula	04/2017
7714	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
7715	3^225248-130	107471	Lelio R Paula	03/2017
7716	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
7717	27029^9448+9448^27029	107450	Hans Havermann	11/2020
7718	2^356935-18085	107449	Enzo Doria	05/2013
7719	55396^87+87^55396	107442	Hans Havermann	10/2020
7720	(14*10^107439-137)/3	107440	Robert Price	04/2021
7721	164^48505-48505^164	107432	Norman Luhn	09/2024
7722	10^107409+37	107410	Lelio R Paula	02/2017
7723	10^107409-329633	107409	Patrick De Geest	03/2017
7724	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
7725	2^356787-109027	107404	Enzo Doria	04/2014
7726	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
7727	3*10^107389+77	107390	Robert Price	09/2018
7728	(11*10^107385+61)/9	107386	Tyler Busby	01/2023
7729	5^153622-42	107378	Lelio R Paula	02/2017
7730	2^356699-97305	107378	Lelio R Paula	03/2017
7731	13129^26072-26072^13129	107371	Norbert Schneider	09/2022
7732	2^356654+85	107364	Lelio R Paula	11/2011
7733	2^356641-19921	107360	Enzo Doria	06/2013
7734	5*10^107355+11	107356	Robert Price	08/2019
7735	2^356623-465	107355	Lelio R Paula	03/2017
7736	19^83945-92	107345	Lelio R Paula	02/2017
7737	25491^16246+16246^25491	107337	Hans Havermann	11/2020
7738	10^107334+28149	107335	Patrick De Geest	03/2017
7739	10^107334-83	107334	Lelio R Paula	02/2017
7740	2^356518+885	107323	Lelio R Paula	03/2017
7741	(59*10^107322+391)/9	107323	Robert Price	03/2021
7742	(3*2^356506-1)/467	107317	Lelio R Paula	03/2014
7743	(2^356468+1162)/2	107308	Stefano Morozzi	09/2020
7744	2^356442-114713	107300	Enzo Doria	04/2015
7745	2^356425+72257	107295	Enzo Doria	04/2016
7746	2^356351-112237	107273	Enzo Doria	06/2014
7748	(6^137845-11)/5	107264	Paul Bourdelais	11/2011
7747	2^356322+74539	107264	Enzo Doria	04/2016
7749	2^356274+1874479	107250	Enzo Doria	06/2016
7750	24606^22819+22819^24606	107241	Hans Havermann	10/2020

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Probable Primes Top 10000

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