Actually, there are plenty of those. The oldest might be this well-known formula by Euler: n^2 - n + 41 gives a prime for all positive integers smaller than 41.
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There are infinitely many rays.
7 times (number of weeks)
There is no such formula; there are infinitely many number between them.
Prime factorization is the result of expressing a number as the product of its prime factors. It will assist you in finding the GCF and LCM of any given number set.
There is no formula that will specifically give you a prime number and no non-prime number. Therefore, several large numbers are tested to see if they are primes, until a prime number is found.