
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^{42737} + 1)/3 
Verification status (*):  PRP 
Official Comment:  ECPP, generalized Lucas number, Wagstaff 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  M : Morain 
Decimal Digits:  12865 (log_{10} is 12864.641803437) 
Rank (*):  68228 (digit rank is 1) 
Entrance Rank (*):  32933 
Currently on list? (*):  short 
Submitted:  8/28/2007 13:19:44 CDT 
Last modified:  8/28/2007 13:27:29 CDT 
Database id:  82071 
Status Flags:  Verify 
Score (*):  33.2205 (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.
 Elliptic Curve Primality Proof (archivable *)
 Prime on list: no, rank 56
Subcategory: "ECPP"
(archival tag id 193533, tag last modified 20160620 16:50:35)  Generalized Lucas Number (archivable *)
 Prime on list: no, rank 24
Subcategory: "Generalized Lucas Number"
(archival tag id 193532, tag last modified 20160502 05:50:25)  Wagstaff (archivable *)
 Prime on list: yes, rank 2
Subcategory: "Wagstaff"
(archival tag id 193534, tag last modified 20140917 12:50:33)
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  82071 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"(2^42737+1)/3" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^42737+1)/3 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 2 Running N1 test using base 7 Running N1 test using base 13 Running N1 test using base 19 Running N+1 test using discriminant 29, base 2+sqrt(29) Running N+1 test using discriminant 29, base 3+sqrt(29) Running N+1 test using discriminant 29, base 5+sqrt(29) Running N+1 test using discriminant 29, base 6+sqrt(29) Running N+1 test using discriminant 29, base 8+sqrt(29) Running N+1 test using discriminant 29, base 9+sqrt(29) Calling N+1 BLS with factored part 0.98% and helper 0.15% (3.08% proof) (2^42737+1)/3 is Fermat and Lucas PRP! (414.8100s+0.0000s) [Elapsed time: 6.98333333333333 minutes]

modified  20070912 06:50:18 
created  20070828 13:20:30 
id  93262 

field  value 
prime_id  82071 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/pfgw o f q"(2^42737+1)/3" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 3771838 (2^42737+1)/3 has no small factor. [Elapsed time: 4.875 seconds]

modified  20070912 06:50:18 
created  20070828 13:22:01 
id  93263 

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
