Generating a given number of consecutive numbers all of which are composites is easy. For example the following is a sequence of 100 consecutive composite numbers:
These numbers are huge. The first number of the sequence is around 9.4259 × 10 ^ 159. A smaller solution can be found by using "primorials" instead of factorials. Primorial is the product of all primes less than or equal to a given number. If we use primorials the first number is reduced to:
>> prod(primes(101)) + 2
>> ans =
2.3286e+38
Although, this is a significant size reduction, the smallest possible 100 consecutive composites series, is still way less than that. The smallest 100 consecutive composites series,starts with 370262, that is:
if we define the set 'C' as the smallest consecutive 'n' composite numbers, the function 'f(n)' as the smallest element in 'C', and 'F' is the set that contains all f(x)'s for x = 1,2,3...n, write the function S(n), which is the sum of all elements of F.
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