Irrational 3.0
Write and then concatenate the prime numbers in increasing sequence
Is this number rational or irrational?
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1 solution
Show that the fraction is not periodic. Using Dirichlet's theorem, if x and y are coprimes, then the there are infinite primes in the x k + y series, where k = 0 , 1 , 2 , 3 , … . If the fraction is periodic and the lenght of the periodic is t , then because the 1 0 2 t k + 1 primes the periodic would contain only 0 's.