Further extensions of the real numbers under Hurwitzs theorem states that there are four normed division algebras: the real numbers 
  
    
      
        
          R
        
      
    
    {\displaystyle \mathbb {R} }
  , the complex numbers 
  
    
      
        
          C
        
      
    
    {\displaystyle \mathbb {C} }
  , the quaternions 
  
    
      
        
          H
        
      
    
    {\displaystyle \mathbb {H} }
  , and the octonions 
  
    
      
        
          O
        
      
    
    {\displaystyle \mathbb {O} }
  .
In Knuths up-arrow notation, 2 ↑↑ 2 = 2 ↑↑↑ 2 = 4, and so forth, for any number of up arrows. By consequence, four is the only square one more than a prime number, specifically three. The sum of the first four prime numbers two + three + five + seven is the only sum of four consecutive prime numbers that yields an odd prime number, seventeen, which is the fourth super-prime. Four lies between the first proper pair of twin primes, three and five, which are the first two Fermat primes, like seventeen, which is the third.