Difficulty to Hash Validation Correlation
Difficulty is not the same as target hash (target in short).

They are inversely related, so minimal possible difficulty (of 1) gives maximal target, by definition given as (https://en.bitcoin.it/wiki/Target): 


  0x00000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
  
  Because Bitcoin stores the target as a floating-point type, this is
  truncated:
  
  0x00000000FFFF0000000000000000000000000000000000000000000000000000


The current difficulty is calculated as maximal target divided by the current target. For example (https://en.bitcoin.it/wiki/Difficulty):


  0x00000000FFFF0000000000000000000000000000000000000000000000000000 /
  0x00000000000404CB000000000000000000000000000000000000000000000000 
  = 16307.420938523983


So in your example the Difficulty = 1,347,001,430,558.57 would give the current target of:


  current_target = 
  0x00000000FFFF0000000000000000000000000000000000000000000000000000 /
  1,347,001,430,558.57


If you calculate this (take care as one number is hexadecimal and other decimal), the comparison should give that this current_target is higher than the mined hash of: 


  0x000000000000000000cf3620d570d08d1799a1cafbbfae512fdba2124665eca0


EDIT: Pen and paper calculation gives me that the current target is around:


  0x000000000000000000FFFF000000000000000000000000000000000000000000


How I got this. 1,347,001,430,558.57 is around 1.225 * (16^10). As the target is in base 16, this means that dividing by 1 * (16^10) is like shifting the digits 10 places to the right. To get precise result after digits shifting I should divide by 1.225, but I ignored this in this pen and paper calculation.

EDIT2: To be even more precise I take 16/1.225 is around 13 (D in hex), so the target is around:


  0x000000000000000000D000000000000000000000000000000000000000000000