In particular, five is the first congruent number, since it is the length of the hypotenuse of the smallest integer-sided right triangle.Five is the second Fermat prime of the form 
  
    
      
        
          2
          
            
              2
              
                n
              
            
          
        
      
    
    {\displaystyle 2^{2^{n}}}
  + 
  
    
      
        1
      
    
    {\displaystyle 1}
  , and more generally the second Sierpiński number of the first kind, 
  
    
      
        
          n
          
            n
          
        
      
    
    {\displaystyle n^{n}}
  + 
  
    
      
        1
      
    
    {\displaystyle 1}
  .
There are exclusively twelve complex aperiotopes in 
  
    
      
        
          
            C
          
          
            n
          
        
      
    
    {\displaystyle \mathbb {C} ^{n}}
   complex spaces of dimensions 
  
    
      
        n
      
    
    {\displaystyle n}
   ⩾ 
  
    
      
        5
      
    
    {\displaystyle 5}
  , with fifteen in 
  
    
      
        
          
            C
          
          
            4
          
        
      
    
    {\displaystyle \mathbb {C} ^{4}}
   and sixteen in 
  
    
      
        
          
            C
          
          
            3
          
        
      
    
    {\displaystyle \mathbb {C} ^{3}}
  ; alongside complex polytopes in 
  
    
      
        
          
            C
          
          
            5
          
        
      
    
    {\displaystyle \mathbb {C} ^{5}}
   and higher under simplex, hypercubic and orthoplex groups, the latter with van Oss polytopes.