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.
Best Answer
The sum of the first 168 positive integers is $\frac{168^2+168}{2}=14196$, which is greater than answer (a). The sum of the first 168 primes must be even greater than that.