Balanced prime

<p>In <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, a balanced prime is a <a href="/facts/Prime_number/L20FLkgn">prime number</a> with equal-sized <a href="/facts/Prime_gap/quWSv5NR">prime gaps</a> above and below it, so that it is equal to the <a href="/facts/Arithmetic_mean/L3Pv333o">arithmetic mean</a> of the nearest primes above and below. Or to put it <a href="/facts/Algebra/nMdqczjo">algebraically</a>, the 
  
    
      
        n
      
    
    {\displaystyle n}
  
th prime number 
  
    
      
        
          p
          
            n
          
        
      
    
    {\displaystyle p_{n}}
  
 is a balanced prime if
</p>

p
          
            n
          
        
        =
        
          
            
              
                p
                
                  n
                  −
                  1
                
              
              +
              
                p
                
                  n
                  +
                  1
                
              
            
            2
          
        
        .
      
    
    {\displaystyle p_{n}={{p_{n-1}+p_{n+1}} \over 2}.}

<p>For example, 53 is the sixteenth prime; the fifteenth and seventeenth primes, 47 and 59, add up to 106, and half of that is 53; thus 53 is a balanced prime.
</p>

Balanced prime open-in-new

Balanced prime