
The nth Prime Page will now find any of the first 2,623,557,157,654,233 primes or
π( x) for x up to 100,000,000,000,000,000.
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:  (2^{3539} + 1)/3 
Verification status (*):  PRP 
Official Comment:  First titanic by ECPP, generalized Lucas number, Wagstaff 
Proofcode(s): (*):  M : Morain 
Decimal Digits:  1065 (log_{10} is 1064.86803340011) 
Rank (*):  109308 (digit rank is 8) 
Entrance Rank (*):  838 
Currently on list? (*):  short 
Submitted:  1989 
Last modified:  1989 
Database id:  54344 
Status Flags:  Verify 
Score (*):  25.4686 (normalized score 0) 

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.
 Generalized Lucas Number (archivable *)
 Prime on list: no, rank 97
Subcategory: "Generalized Lucas Number"
(archival tag id 181330, tag last modified 20160502 05:50:25)  * old special cases (deprecated *)
 Prime on list: no, rank 1
Subcategory: "* old special cases"
(archival tag id 181329, tag last modified 20050603 13:39:34)  Elliptic Curve Primality Proof (archivable *)
 Prime on list: no, rank 869
Subcategory: "ECPP"
(archival tag id 181331, tag last modified 20160620 16:50:35)  Wagstaff (archivable *)
 Prime on list: yes, rank 9
Subcategory: "Wagstaff"
(archival tag id 181332, tag last modified 20140917 12:50:33)
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  54344 
person_id  9 
machine  Linux PII 200 
what  prp 
notes  PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N1 test using base 2 Primality testing (2^3539+1)/3 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 5 Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) Running N+1 test using discriminant 13, base 3+sqrt(13) Running N+1 test using discriminant 13, base 6+sqrt(13) Running N+1 test using discriminant 13, base 8+sqrt(13) Calling N+1 BLS with factored part 2.69% and helper 1.33% (9.44% proof) (2^3539+1)/3 is Fermat and Lucas PRP! (46.500000 seconds) 
modified  20030325 11:23:04 
created  20030103 23:43:33 
id  60765 

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
