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 ?
6501	2^363120+3	109311	Donovan Johnson	04/2006
6502	(10^109297-1)/9	109297	Paul Bourdelais, Harvey Dubner	04/2007
6503	2^363042-114641	109287	Enzo Doria	04/2015
6504	2^363020-112793	109280	Enzo Doria	06/2014
6505	(8732^27889-1)/(8732^167-1)	109256	Ryan Propper	11/2023
6506	(85*10^109253+203)/9	109254	Robert Price	09/2020
6507	24990^23431+23431^24990	109202	Hans Havermann	10/2020
6508	(2^362746+3738)/2	109198	Stefano Morozzi	09/2020
6509	(2^362716+1282)/2	109189	Stefano Morozzi	01/2021
6510	(67607*2^362695+1)/70499	109183	Lelio R Paula	07/2014
6511	25060^22737+22737^25060	109180	Hans Havermann	10/2020
6512	(9*2^362644+1)/5	109167	Lelio R Paula	03/2014
6513	5^156181+38	109166	Lelio R Paula	02/2017
6514	(2^362623+3618)/2	109161	Stefano Morozzi	09/2020
6515	25138^21993+21993^25138	109157	Hans Havermann	10/2020
6516	4*10^109142+91	109143	Robert Price	08/2018
6517	3^228750+68	109142	Lelio R Paula	03/2017
6518	(2^362561+786)/2	109142	Stefano Morozzi	09/2020
6519	(23*10^109113+61)/3	109114	Robert Price	01/2022
6520	2*10^109100-49	109101	Robert Price	09/2020
6521	(10223*2^362376+1)/9	109090	Lelio R Paula	07/2014
6522	65^60167-64^60167	109078	Robert Price	08/2013
6523	7*3^228589-2	109066	Lelio R Paula	09/2014
6524	24874^24243+24243^24874	109063	Hans Havermann	11/2020
6525	(17*10^109059-161)/9	109060	Robert Price	02/2021
6526	29158^5495+5495^29158	109050	Hans Havermann	11/2020
6527	(78557*2^362188+1)/189	109033	Lelio R Paula	07/2014
6528	2*7^129008+9	109025	Lelio R Paula	11/2014
6529	88*10^109022+7	109024	Robert Price	03/2020
6530	28194^7337+7337^28194	108985	Hans Havermann	10/2020
6531	(5*10^108960+91)/3	108961	Robert Price	04/2018
6532	2^361957+76367	108960	Enzo Doria	05/2016
6533	2^361873-1411	108935	Yves Minet	01/2013
6534	(24737*2^361857+1)/35	108933	Lelio R Paula	07/2014
6535	47^65132-65132^47	108908	Norman Luhn	09/2024
6536	115^52842-114	108892	Norbert Schneider	07/2018
6537	13^97745-24	108883	Lelio R Paula	03/2017
6538	(2^361696+2562)/2	108882	Stefano Morozzi	09/2020
6539	17^88475+8	108864	Lelio R Paula	04/2017
6540	2^361567+51	108843	Lelio R Paula	01/2012
6541	2^361563-109501	108842	Enzo Doria	04/2014
6542	12^100852+83	108838	Lelio R Paula	03/2017
6543	2^361497+767	108822	Lelio R Paula	01/2012
6544	L(520691)/78103651/1057002731/42794551909	108791	Serge Batalov	07/2024
6545	28019^7630+7630^28019	108785	Hans Havermann	10/2020
6546	24723^24758-24758^24723	108765	Norbert Schneider	11/2020
6547	2^361280-112349	108757	Enzo Doria	06/2014
6548	2^361271-5955	108754	Lelio R Paula	04/2017
6549	12^100757+19	108736	Lelio R Paula	03/2017
6550	25368^19333+19333^25368	108735	Hans Havermann	11/2020
6551	(2^361195+3618)/2	108731	Stefano Morozzi	09/2020
6552	2^361153-111546435	108718	Paul Bourdelais	10/2021
6553	14^94849-61	108710	Lelio R Paula	05/2017
6554	27267^9700+9700^27267	108708	Hans Havermann	11/2020
6555	(19^85009-5^85009)/14	108705	Robert Price	07/2013
6556	24832^23853+23853^24832	108704	Hans Havermann	11/2020
6557	27502^8963+8963^27502	108701	Hans Havermann	11/2020
6558	(130^51419-1)/129	108695	Anonymous	06/2024
6559	25807^16278+16278^25807	108689	Hans Havermann	11/2020
6560	(11*2^361027+1)/40463	108677	Lelio R Paula	03/2014
6561	2^360973+1299	108664	Lelio R Paula	04/2017
6562	24^78728+23	108662	Anonymous	09/2024
6563	2^360959-109101	108660	Enzo Doria	04/2014
6564	6*5^155454+7	108659	Lelio R Paula	11/2014
6565	10^108656+79	108657	Lelio R Paula	02/2017
6566	10^108656-50001	108656	Patrick De Geest	03/2017
6567	2^360918-35	108648	Lelio R Paula	01/2012
6568	4*10^108646-47	108647	Robert Price	10/2021
6569	(11*2^360886-1)/7	108638	Lelio R Paula	03/2014
6570	3*10^108624-49	108625	Robert Price	07/2018
6571	(2^360831+666)/2	108621	Stefano Morozzi	09/2020
6572	(134*10^108610+7)/3	108612	Robert Price	02/2020
6573	2*10^108609+29	108610	Robert Price	02/2021
6574	(10^108604+7)/71/191	108600	Alfred Reich	06/2021
6575	(2^360742+3222)/2	108594	Stefano Morozzi	09/2020
6576	2^360706-458903	108584	Enzo Doria	04/2015
6577	31112^3087+3087^31112	108567	Hans Havermann	11/2020
6578	2^360641-113185	108564	Enzo Doria	07/2014
6579	(29*10^108559-71)/3	108560	Robert Price	07/2021
6580	2^360618+75019	108557	Enzo Doria	04/2016
6581	2^360607-216367	108554	Harrison Mesh	06/2022
6582	(14*10^108545-221)/9	108546	Robert Price	04/2018
6583	(44*10^108544-233)/9	108545	Robert Price	01/2019
6584	3*5^155286+2	108541	Lelio R Paula	11/2014
6585	7^128422+4	108530	Lelio R Paula	11/2014
6586	7^128421-80	108529	Lelio R Paula	03/2017
6587	2^360497+53807	108521	Yves Minet	07/2010
6588	2^360468-4559	108512	Yves Minet	03/2019
6589	(2^360451+578)/2	108507	Stefano Morozzi	09/2020
6590	2^360366+1459	108481	Lelio R Paula	09/2011
6591	2^360364-1499	108481	Yves Minet	05/2013
6592	25662^16871+16871^25662	108477	Hans Havermann	10/2020
6593	25009^21748+21748^25009	108475	Hans Havermann	10/2020
6594	14^94642-23	108472	Lelio R Paula	05/2017
6595	(197*10^108446-11)/3	108448	Robert Price	03/2020
6596	(2^360229+1290)/2	108440	Stefano Morozzi	01/2021
6597	4*10^108412+9	108413	Robert Price	05/2015
6598	(259*10^108409-1)/3	108411	Robert Price	12/2020
6599	(2^360122+1194)/2	108408	Stefano Morozzi	09/2020
6600	133^51042-132	108406	Norbert Schneider	02/2019
6601	2^360093-351103	108399	Enzo Doria	06/2015
6602	2^360042+723	108384	Lelio R Paula	01/2012
6603	85^56164-2	108364	Lelio R Paula	10/2013
6604	2^359937-29323	108352	Enzo Doria	07/2015
6605	22^80712-23	108350	Anonymous	09/2024
6606	(2^359922+1762)/2	108348	Stefano Morozzi	09/2020
6607	(2^359903+758)/2	108342	Stefano Morozzi	09/2020
6608	2^359898-19997	108341	Enzo Doria	06/2013
6609	(2^359886+2122)/2	108337	Stefano Morozzi	09/2020
6610	2*5^154948-7	108305	Lelio R Paula	11/2014
6611	10^108303+13	108304	Lelio R Paula	02/2017
6612	10^108303-207959	108303	Patrick De Geest	03/2017
6613	7*10^108300+69	108301	Robert Price	07/2019
6614	198^47155-47155^198	108300	Norman Luhn	09/2024
6615	2^359730+753	108290	Lelio R Paula	12/2011
6616	(8*10^108273+13)/3	108274	Robert Price	06/2018
6617	2^359650-19797	108266	Enzo Doria	06/2013
6618	(47*10^108261+259)/9	108262	Robert Price	03/2022
6619	91^55259-90^55259	108255	Robert Price	07/2015
6620	10^108251+85749	108252	Patrick De Geest	02/2021
6621	10^108251-50000000001	108251	Robert Price	12/2020
6622	10^108251-252081	108251	Patrick De Geest	02/2021
6623	4*10^108238-71	108239	Robert Price	12/2018
6624	3^226845+68	108233	Lelio R Paula	03/2017
6625	31836^2509+2509^31836	108227	Hans Havermann	10/2020
6626	5^154822-12866	108216	Enzo Doria	05/2014
6627	(9*2^359480+1)/5	108215	Lelio R Paula	03/2014
6628	2^359454-177	108207	Lelio R Paula	12/2011
6629	(19*10^108184+191)/3	108185	Robert Price	05/2019
6630	6^139022-59	108181	Lelio R Paula	02/2017
6631	(19*10^108176-43)/3	108177	Robert Price	05/2019
6632	2^359352-179	108176	Lelio R Paula	12/2011
6633	2^359338-1858781	108172	Enzo Doria	04/2016
6634	12^100230-97	108167	Lelio R Paula	03/2017
6635	27028^10043+10043^27028	108163	Hans Havermann	11/2020
6636	(25*2^359297-1)/137	108159	Lelio R Paula	03/2014
6637	(2^359262-509203)/9	108148	Lelio R Paula	12/2013
6638	26583^11702+11702^26583	108147	Hans Havermann	11/2020
6639	(3^226648-8)/352715633	108131	Lelio R Paula	12/2013
6640	6^138956-59	108129	Lelio R Paula	02/2017
6641	2^359184+30285	108126	Lelio R Paula	04/2017
6642	13^97059+10	108119	Lelio R Paula	03/2017
6643	2^359137-81	108112	Lelio R Paula	12/2011
6645	(15185*2^359105-1)/567	108103	Lelio R Paula	05/2015
6644	2^359110-11655	108103	Lelio R Paula	04/2017
6646	2^359069-933075	108091	Paul Bourdelais	06/2021
6647	26227^13222+13222^26227	108090	Hans Havermann	10/2020
6648	8*6^138875+5	108067	Lelio R Paula	11/2014
6649	2^358987-216919	108066	Enzo Doria	05/2014
6650	(2^358977+2714)/2	108063	Stefano Morozzi	09/2020
6651	39^67918-67918^39	108062	Norbert Schneider	02/2017
6652	24^78283-1*78283^24	108048	Dylan Delgado	12/2019
6653	25282^18767+18767^25282	108040	Hans Havermann	11/2020
6654	2^358785-16933	108006	Enzo Doria	05/2013
6655	(2^358783+5)/33383	108000	Lelio R Paula	12/2013
6656	6^138770-77	107985	Lelio R Paula	02/2017
6657	(2^358727-1017)/94178479	107980	Lelio R Paula	12/2013
6658	10^107976+19	107977	Lelio R Paula	02/2017
6659	10^107976-202103	107976	Patrick De Geest	03/2017
6660	2^358684+75781	107975	Enzo Doria	04/2016
6661	24928^21411+21411^24928	107955	Hans Havermann	10/2020
6662	99^54094+2	107952	Lelio R Paula	06/2013
6663	(2^358583-9)/391	107942	Lelio R Paula	12/2013
6664	(2^358562+838)/2	107938	Stefano Morozzi	02/2021
6665	2^358538+55	107931	Lelio R Paula	12/2011
6666	2^358517-109009	107925	Enzo Doria	03/2014
6667	26395^12258+12258^26395	107914	Hans Havermann	10/2020
6668	3^226159+104	107906	Lelio R Paula	03/2017
6669	7*10^107870+39	107871	Robert Price	01/2023
6670	2^358310-11655	107863	Lelio R Paula	03/2017
6671	(68*10^107852-329)/9	107853	Robert Price	03/2021
6672	2^358275-112987	107852	Enzo Doria	07/2014
6673	3^226038+4	107848	Tyler NeSmith	01/2021
6674	2^358233-20005	107839	Enzo Doria	06/2013
6675	2^358194+175	107828	Lelio R Paula	12/2011
6676	107^53125-106	107812	Norbert Schneider	12/2016
6677	(25*10^107804+161)/3	107805	Robert Price	09/2019
6678	3^225922-2	107793	Lelio R Paula	10/2013
6679	12^99874-95	107783	Lelio R Paula	03/2017
6680	(2^358042+3042)/2	107782	Stefano Morozzi	09/2020
6681	2^358030-171	107778	Lelio R Paula	12/2011
6682	11^103488-4170	107772	Enzo Doria	12/2012
6683	2^357930-4547	107748	Yves Minet	03/2019
6684	2^357911-20089	107742	Enzo Doria	06/2013
6685	2^357885+12857	107735	Yves Minet	07/2010
6686	(248587#+9289)/(71327111512899)	107733	Makoto Morimoto	06/2019
6687	7^127473+40	107728	Lelio R Paula	03/2017
6688	5*2^357850+9	107725	Lelio R Paula	09/2014
6689	2^357786-291191	107705	Enzo Doria	06/2015
6690	28907^5320+5320^28907	107705	Hans Havermann	10/2020
6691	18^85798-23	107700	Lelio R Paula	04/2017
6692	3*10^107697+61	107698	Robert Price	09/2020
6693	(14*10^107694-83)/3	107695	Robert Price	12/2018
6694	2^357688-1854269	107675	Enzo Doria	09/2015
6695	2^357671-112225	107670	Enzo Doria	06/2014
6696	34323^1370+1370^34323	107662	Hans Havermann	11/2020
6697	2^357618-21005	107654	Enzo Doria	06/2013
6698	2^357615-17505	107653	Enzo Doria	05/2013
6699	26350^12171+12171^26350	107649	Hans Havermann	11/2020
6700	(30^72871-1)/29	107638	Robert Price	12/2011
6701	25021^20026+20026^25021	107631	Hans Havermann	11/2020
6702	2^357521+1870217	107625	Enzo Doria	05/2016
6703	2^357477-1203	107612	Lelio R Paula	03/2017
6704	26008^13693+13693^26008	107583	Hans Havermann	10/2020
6705	25432^16991+16991^25432	107583	Hans Havermann	10/2020
6706	(2^357371+3726)/2	107580	Stefano Morozzi	09/2020
6707	5^153894-18	107568	Lelio R Paula	02/2017
6708	2^357324-69059	107566	Enzo Doria	11/2015
6709	467^40296+40296^467	107563	Norbert Schneider	03/2019
6710	29446^4495+4495^29446	107559	Hans Havermann	10/2020
6711	(8*10^107556-149)/3	107557	Robert Price	12/2021
6712	2^357283-869688105	107553	Lelio R Paula	01/2017
6713	2^357280-16805	107552	Enzo Doria	05/2013
6714	10^107547+481719	107548	Patrick De Geest	03/2017
6715	10^107547-47	107547	Lelio R Paula	02/2017
6716	(23*10^107540+37)/3	107541	Robert Price	02/2022
6717	17^87396-32	107537	Lelio R Paula	04/2017
6718	(746*10^107505+1)/9	107507	Robert Price	03/2020
6719	(2^357125+1730)/2	107506	Stefano Morozzi	09/2020
6720	2^357081+107	107493	Lelio R Paula	12/2011
6721	2^357058-3911	107486	Yves Minet	04/2017
6722	3^225274+64	107484	Lelio R Paula	03/2017
6723	5*10^107482-57	107483	Robert Price	03/2021
6724	18^85619-95	107476	Lelio R Paula	04/2017
6725	(2^357013+2526)/2	107472	Stefano Morozzi	09/2020
6726	3^225248-130	107471	Lelio R Paula	03/2017
6727	(5*2^356961+1)/143	107455	Lelio R Paula	03/2014
6728	27029^9448+9448^27029	107450	Hans Havermann	11/2020
6729	2^356935-18085	107449	Enzo Doria	05/2013
6730	55396^87+87^55396	107442	Hans Havermann	10/2020
6731	(14*10^107439-137)/3	107440	Robert Price	04/2021
6732	164^48505-48505^164	107432	Norman Luhn	09/2024
6733	10^107409+37	107410	Lelio R Paula	02/2017
6734	10^107409-329633	107409	Patrick De Geest	03/2017
6735	(2^356799+3134)/2	107407	Stefano Morozzi	09/2020
6736	2^356787-109027	107404	Enzo Doria	04/2014
6737	(2^356767+78557)/5	107397	Lelio R Paula	12/2013
6738	3*10^107389+77	107390	Robert Price	09/2018
6739	(11*10^107385+61)/9	107386	Tyler Busby	01/2023
6740	5^153622-42	107378	Lelio R Paula	02/2017
6741	2^356699-97305	107378	Lelio R Paula	03/2017
6742	13129^26072-26072^13129	107371	Norbert Schneider	09/2022
6743	2^356654+85	107364	Lelio R Paula	11/2011
6744	2^356641-19921	107360	Enzo Doria	06/2013
6745	5*10^107355+11	107356	Robert Price	08/2019
6746	2^356623-465	107355	Lelio R Paula	03/2017
6747	19^83945-92	107345	Lelio R Paula	02/2017
6748	25491^16246+16246^25491	107337	Hans Havermann	11/2020
6749	10^107334+28149	107335	Patrick De Geest	03/2017
6750	10^107334-83	107334	Lelio R Paula	02/2017

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Probable Primes Top 10000

(295921 PRPs in the top)