
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:  258317 · 2^{5450519} + 1 
Verification status (*):  Proven 
Official Comment:  
Proofcode(s): (*):  g414 : Gilvey, Srsieve, PrimeGrid, PrimeSierpinski, LLR, Proth.exe 
Decimal Digits:  1640776 (log_{10} is 1640775.12308943) 
Rank (*):  44 (digit rank is 1) 
Entrance Rank (*):  12 
Currently on list? (*):  short 
Submitted:  7/27/2008 12:42:32 CDT 
Last modified:  7/31/2008 08:45:08 CDT 
Database id:  85350 
Status Flags:  none 
Score (*):  48.1517 (normalized score 83.3549) 

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  85350 
person_id  9 
machine  RedHat P4 P4 
what  trial_divided 
notes  Command: /home/caldwell/client/TrialDiv/TrialDiv q 258317 2 5450519 1 2>&1 [Elapsed time: 11.263 seconds]

modified  20111227 16:48:46 
created  20080727 12:52:02 
id  100153 

field  value 
prime_id  85350 
person_id  9 
machine  RedHat P4 P4 
what  prime 
notes  Command: /home/caldwell/client/pfgw t q"258317*2^5450519+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 258317*2^5450519+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(786432,19) to FFT(786432,18) Reduced from FFT(786432,18) to FFT(786432,17) Reduced from FFT(786432,17) to FFT(786432,16) 10901082 bit request FFT size=(786432,16) Calling BrillhartLehmerSelfridge with factored part 100.00% 258317*2^5450519+1 is prime! (330726.1657s+0.0039s) [Elapsed time: 3.83 days]

modified  20080912 14:12:35 
created  20080727 12:53:01 
id  100154 

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