Of precisely five different conjugacy classes of maximal subgroups of 
  
    
      
        
          
            M
          
          
            11
          
        
      
    
    {\displaystyle \mathrm {M} _{11}}
  , one is the almost simple symmetric group 
  
    
      
        
          
            S
          
          
            5
          
        
      
    
    {\displaystyle \mathrm {S} _{5}}
   (of order 5!
Every odd number greater than 
  
    
      
        1
      
    
    {\displaystyle 1}
   is the sum of at most five prime numbers, and every odd number greater than 
  
    
      
        5
      
    
    {\displaystyle 5}
   is conjectured to be expressible as the sum of three prime numbers. Helfgott has provided a proof of the latter, also known as the odd Goldbach conjecture, that is already widely acknowledged by mathematicians as it still undergoes peer-review.