Question 95
for a positive integer $n$, denote by $S_n$ The sum of the $n$ LEAST PRIMES: $S_1 = 2$, $S_2 = 2+3=5$, $S_3 = 2+3+5=10$, and so on. Determine Two Consecutive Terms of the Sequence $S_1, S_2, S_3, \ldots$ Can be perfect squares. (V. Sharich) for each natural $n$ Let's denote by $S_n$ the amount of the first $n$ prime numbers: $S_1 = 2$, $S_2 = 2+3 = 5$, $S_3 = 2+3+5 = 10$, .... can two consecutive members of the sequence ($S_n$) turn out to be squares of natural numbers? (V. Sharic)