
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^{29727} + 20273 
Verification status (*):  PRP 
Official Comment:  ECPP 
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  c18 : Luhn, Primo 
Decimal Digits:  8949 (log_{10} is 8948.7186811032) 
Rank (*):  72045 (digit rank is 1) 
Entrance Rank (*):  43814 
Currently on list? (*):  no 
Submitted:  7/28/2009 22:47:16 CDT 
Last modified:  7/28/2009 23:20:22 CDT 
Database id:  89447 
Status Flags:  Verify 
Score (*):  32.0957 (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 164
Subcategory: "ECPP"
(archival tag id 210480, tag last modified 20160620 16:50:35)
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  89447 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/TrialDiv/TrialDiv q 1 2 29727 20273 2>&1 [Elapsed time: 8.526 seconds]

modified  20111227 16:48:43 
created  20090728 22:48:01 
id  108262 

field  value 
prime_id  89447 
person_id  9 
machine  RedHat P4 P4 
what  prp 
notes  Command: /home/caldwell/client/pfgw tc q"2^29727+20273" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2^29727+20273 [N1/N+1, BrillhartLehmerSelfridge] Running N1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3584,21) to FFT(3584,20) Reduced from FFT(3584,20) to FFT(3584,19) Reduced from FFT(3584,19) to FFT(3584,18) Reduced from FFT(3584,18) to FFT(3584,17) 59464 bit request FFT size=(3584,17) Running N+1 test using discriminant 19, base 9+sqrt(19) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(3584,21) to FFT(3584,20) Reduced from FFT(3584,20) to FFT(3584,19) Reduced from FFT(3584,19) to FFT(3584,18) Reduced from FFT(3584,18) to FFT(3584,17) 59472 bit request FFT size=(3584,17) Calling N+1 BLS with factored part 0.08% and helper 0.07% (0.30% proof) 2^29727+20273 is Fermat and Lucas PRP! (45.4350s+0.1018s) [Elapsed time: 46.00 seconds]

modified  20090811 11:44:22 
created  20090728 22:53:01 
id  108263 

Query times: 0.0005 seconds to select prime, 0.0006 seconds to seek comments.
