
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^{226749}  1)^{2}  2 
Verification status (*):  Proven 
Official Comment:  
Proofcode(s): (*):  p103 : Harvey, MultiSieve, OpenPFGW 
Decimal Digits:  136517 (log_{10} is 136516.500973624) 
Rank (*):  32742 (digit rank is 1) 
Entrance Rank (*):  284 
Currently on list? (*):  no 
Submitted:  1/11/2005 14:48:56 CDT 
Last modified:  1/11/2005 14:48:56 CDT 
Removed (*):  9/21/2009 09:18:54 CDT 
Database id:  73109 
Status Flags:  none 
Score (*):  40.513 (normalized score 0.0401) 

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  73109 
person_id  9 
machine  Linux P4 2.8GHz 
what  prime 
notes  Command: /home/caldwell/client/pfgw f tc q"(2^2267491)^22" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^2267491)^22 [N1/N+1, BrillhartLehmerSelfridge] trial factoring to 47524042 Running N1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) Reduced from FFT(57344,17) to FFT(57344,16) 907004 bit request FFT size=(57344,16) Running N1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) Reduced from FFT(57344,17) to FFT(57344,16) 907004 bit request FFT size=(57344,16) Running N1 test using base 19 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) Reduced from FFT(57344,17) to FFT(57344,16) 907004 bit request FFT size=(57344,16) Running N+1 test using discriminant 29, base 1+sqrt(29) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) Reduced from FFT(57344,17) to FFT(57344,16) 907012 bit request FFT size=(57344,16) Running N+1 test using discriminant 29, base 2+sqrt(29) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) Reduced from FFT(57344,17) to FFT(57344,16) 907012 bit request FFT size=(57344,16) Running N+1 test using discriminant 29, base 3+sqrt(29) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(57344,20) to FFT(57344,19) Reduced from FFT(57344,19) to FFT(57344,18) Reduced from FFT(57344,18) to FFT(57344,17) Reduced from FFT(57344,17) to FFT(57344,16) 907012 bit request FFT size=(57344,16) Calling N+1 BLS with factored part 50.01% and helper 0.00% (150.03% proof) (2^2267491)^22 is prime! (81666.6389s+0.0387s)

modified  20050117 11:11:49 
created  20050111 14:53:00 
id  78121 

Query times: 0.0004 seconds to select prime, 0.0009 seconds to seek comments.
