"27288429267119080686...(1036580 other digits)...83679577406643267931"

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At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

Description:	"27288429267119080686...(1036580 other digits)...83679577406643267931"
Verification status (*):	Proven
Official Comment (*):	[none]
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	p384 : Booker, OpenPFGW
Decimal Digits:	1036620 (log₁₀ is 1036619.4359785)
Rank (*):	2091 (digit rank is 1)
Entrance Rank (*):	117
Currently on list? (*):	yes
Submitted:	5/20/2015 13:41:49 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	119933
Blob database id:	343
Status Flags:	Verify
Score (*):	46.7433 (normalized score 5.0334)

Description: (from blob table id=343)

23rd term of OEIS sequence A071580

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
Jeppe Stig Nielsen writes (15 May 2023): (report abuse)
The number, with its preceding sibling numbers, can be calculated in PARI/GP with:
k=[1, 1, 1, 1, 2, 10, 12, 10, 21, 25, 70, 670, 239, 2115, 586, 1619, 26800, 2505, 99019, 40903, 285641, 67166, 1852765];
p=vector(#k);for(i=1,#k,p[i]=k[i]*prod(j=1,i-1,p[j])+1);p
They can be written to a file with:
write("filename",p)
or:
s="";for(i=1,#p,s=Str(s,p[i],"\n"));write1("filename",s)
With PFGW, the file can serve as both a helper file and a file with holding primes to be checked. To prove each prime, one must have proved all the preceding primes first.

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions. We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.

field value

prime_id 119933

person_id 9

machine Using: Xeon 4c+4c 3.5GHz

what prime

notes Command: /home/caldwell/client/pfgw/pfgw64 -tc -hseq.txt p_119933.txt 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] No factoring at all, not even trivial division Primality testing 2728842926...6643267931 Reading factors from helper file seq.txt Running N-1 test using base 3 2728842926...6643267931 is prime! (31450.2640s+3.1532s) [Elapsed time: 8.74 hours] Helper File: 2 3 7 43 3613 65250781 5109197227031017 21753246920584523633819544186061 993727878334632126576336773629979379563850938567846991629270287 11755894002136302740698092312885392...(127 digits)...00689013689904800982674924371181051 38696292261050003201349366202173458...(253 digits)...65612511056495352491605949500793941 14332286189774870104317551696341424...(507 digits)...48270954885802908254115552768810741 73274698738389761006829658810761239...(1012 digits)...17826278006363479368035447079477379 47513886276367198914414824196589233...(2025 digits)...52999397072002049222212088477766671 62550149503686211463571726000111158...(4049 digits)...04776546108464953230305144998687549 10809508238138789559339950566292499...(8099 digits)...75659173185258697173561092166132459 19341930523721195833832714134170440...(16198 digits)...54330472845205587476819510909458401 34968143371009944807683195941346943...(32394 digits)...58669240772225458043089878397807691 48334357956367529955247336988597540...(64789 digits)...46392742738651127293944914382927403 96504715393810047476036000259169103...(129577 digits)...23085001554040350065811448388082023 65037292183782271055323708033539333...(259155 digits)...01341285413854538158678358327460183 99461233889495567276559497272528219...(518309 digits)...39606400333124353126433719371038957

modified 2020-07-07 22:30:17

created 2015-05-20 13:45:24

id 165557

field	value
prime_id	119933
person_id	9
machine	Using: Xeon 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/client/pfgw/pfgw64 -tc -hseq.txt p_119933.txt 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] No factoring at all, not even trivial division Primality testing 2728842926...6643267931 Reading factors from helper file seq.txt Running N-1 test using base 3 2728842926...6643267931 is prime! (31450.2640s+3.1532s) [Elapsed time: 8.74 hours] Helper File: 2 3 7 43 3613 65250781 5109197227031017 21753246920584523633819544186061 993727878334632126576336773629979379563850938567846991629270287 11755894002136302740698092312885392...(127 digits)...00689013689904800982674924371181051 38696292261050003201349366202173458...(253 digits)...65612511056495352491605949500793941 14332286189774870104317551696341424...(507 digits)...48270954885802908254115552768810741 73274698738389761006829658810761239...(1012 digits)...17826278006363479368035447079477379 47513886276367198914414824196589233...(2025 digits)...52999397072002049222212088477766671 62550149503686211463571726000111158...(4049 digits)...04776546108464953230305144998687549 10809508238138789559339950566292499...(8099 digits)...75659173185258697173561092166132459 19341930523721195833832714134170440...(16198 digits)...54330472845205587476819510909458401 34968143371009944807683195941346943...(32394 digits)...58669240772225458043089878397807691 48334357956367529955247336988597540...(64789 digits)...46392742738651127293944914382927403 96504715393810047476036000259169103...(129577 digits)...23085001554040350065811448388082023 65037292183782271055323708033539333...(259155 digits)...01341285413854538158678358327460183 99461233889495567276559497272528219...(518309 digits)...39606400333124353126433719371038957
modified	2020-07-07 22:30:17
created	2015-05-20 13:45:24
id	165557

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.