It might seem like that based on the definition, but read the whole article and you'll find it's the other way around. Mill's number is shown to exist be showi

It might seem like that based on the definition, but read the whole article and you'll find it's the other way around. Mill's number is shown to exist be showing that primes in certain ranges exist, and then building the number (somewhat like constructing a number from its decimal expansion). So you don't use Mill's number to construct prime numbers, you use prime numbers to construct Mill's number.