G2.2 If the sum of 25 consecutive positive integers is the product of 3 prime numbers, what is the minimum sum of these 3 prime numbers?
Let the smallest positive integer be $x$. We use the formula: $S(n)=\frac{n}{2}[2 a+(n-1) d]$. $\frac{25}{2}(2 x+24 \times 1)=25(x+12)=5 \times 5 \times(x+12)=$ product of 3 prime numbers The minimum prime for $x+12$ is 13 . The minimum sum of these 3 prime numbers is 23 .