# Why are they primes?

Logic Level 4

$2 \div 3\div 5 \div 7 \div 11 \div 13 \div 17 \div 19$

The value of the expression above is equal to $$\dfrac{2}{4849845}$$.

If I added a pair of parentheses like $2 \div 3\div 5 \div 7 \div 11 \div 13 \div (17 \div 19) ,$ the resultant number will not be the same as the original number.

If I'm allowed to add any number of parentheses to the original expression above, how many distinct values can the resultant number take?

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