# Destination Sherlock Holmes #3

Number Theory Level 3

Suppose $$a, b, c, d, e, f, g, h, i$$ are 9 consecutive prime numbers and $$h, i, j, k, l$$ are 5 consecutive prime numbers whose individual summations are same i.e. $$\sum_{("a" to "i")} = \sum_{("h" to "l")}$$. Guess this unique number (i.e. the summation) if the number can be represented as $$a^2 + {(a-1)}^{2}$$ and as $$b * c$$.

Other problem of this set is here.

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