
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:
field (help)  value 
Description:  ((((((2521008887^{3} + 80)^{3} + 12)^{3} + 450)^{3} + 894)^{3} + 3636)^{3} + 70756)^{3} + 97220 
Verification status (*):  PRP 
Official Comment:  ECPP, Mills' prime 
Unofficial Comments:  This prime has 2 user comments below. 
Proofcode(s): (*):  FE1 : Morain, FastECPP 
Decimal Digits:  20562 (log_{10} is 20561.2431617196) 
Rank (*):  63305 (digit rank is 1) 
Entrance Rank (*):  22561 
Currently on list? (*):  short 
Submitted:  6/5/2006 15:32:01 CDT 
Last modified:  7/7/2006 10:39:35 CDT 
Database id:  77907 
Status Flags:  Verify 
Score (*):  34.6719 (normalized score 0.0001) 

Archival tags:
There are certain forms classed as
archivable: these prime may (at times)
remain on this list even if they do not make
the Top 5000 proper. Such primes are tracked with archival
tags.
 Mills' prime (tolerated *)
 Prime on list: no, rank 1
Subcategory: "Mills' prime"
(archival tag id 192157, tag last modified 20090212 20:01:29)  Elliptic Curve Primality Proof (archivable *)
 Prime on list: yes, rank 17
Subcategory: "ECPP"
(archival tag id 192156, tag last modified 20170604 14:20:21)
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.
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  77907 
person_id  9 
machine  WinXP P4 2.2GHz By K 
what  prp 
notes  Command: pfgw.exe n f tc q"(((((((2521008881+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220" 2>&1 PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing (((((((2521008881+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220 [N1/N+1, BrillhartLehmerSelfridge] trial factoring to 6252599 Running N1 test using base 3 Running N1 test using base 5 Running N1 test using base 11 Running N+1 test using discriminant 19, base 1+sqrt(19) Calling N1 BLS with factored part 0.05% and helper 0.03% (0.17% proof) (((((((2521008881+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220 is Fermat and Lucas PRP! (351.7329s+0.0394s) [Elapsed time: 356 seconds]

modified  20060714 06:27:04 
created  20060605 15:58:09 
id  84439 

field  value 
prime_id  77907 
person_id  9 
machine  GenToo P3 400MHz 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f q"((((((2521008887^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] ((((((2521008887^3+80)^3+.........^3+3636)^3+70756 1/1
trial factoring to 6252599 ((((((2521008887^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220 has no small factor. [Elapsed time: 10.931 seconds]

modified  20060714 06:27:03 
created  20060707 10:39:24 
id  85237 

Query times: 0.0003 seconds to select prime, 0.0006 seconds to seek comments.
