sentences:  To put it algebraically, given an exponent "a", a Higgs prime "Hp""n" satisfies
  
  where Φ("x") is Euler's totient function.For squares, the first few Higgs primes are 2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 43, 47, ... .So, for example, 13 is a Higgs prime because the square of the product of the smaller Higgs primes is 5336100, and divided by 12 this is 444675.