I sat an exam 2 months ago and the question paper contains the problem:
Given that there are 168 primes below 1000. Then the sum of all primes
below 1000 is
(a) 11555 (b) 76127 (c) 57298 (d) 81722
My attempt to solve it: We know that below 1000 there are 167 odd primes and 1 even prime (2), so the sum has to be odd, leaving only the first two numbers. Then I tried to use the formula “Every prime can be written in of the form 6n−1,6n+1 except 2 and 3.”, but I got stuck at that.
The sum of the first 168 positive integers is 1682+1682=14196, which is greater than answer (a). The sum of the first 168 primes must be even greater than that.