Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth Perrin numbers.5 is the third Mersenne prime exponent of the form 
  
    
      
        
          2
          
            n
          
        
      
    
    {\displaystyle 2^{n}}
   − 
  
    
      
        1
      
    
    {\displaystyle 1}
  , which yields 
  
    
      
        31
      
    
    {\displaystyle 31}
  : the prime index of the third Mersenne prime and second double Mersenne prime 127, as well as the third double Mersenne prime exponent for the number 2,147,483,647, which is the largest value that a signed 32-bit integer field can hold.
The smallest of these, 
  
    
      
        
          
            
              g
            
          
          
            2
          
        
      
    
    {\displaystyle {\mathfrak {g}}_{2}}
  , can be represented in five-dimensional complex space and projected in the same number of dimensions as a ball rolling on top of another ball, whose motion is described in two-dimensional space.