Divisible by this year? v2015 (Part 1: Happy New Year!)

Number Theory Level 4

Let \(a_{1}\), \(a_{2}\), \(a_{3}\), \(\dots\), \(a_{2013}\), and \(a_{2014}\) be \(2014\) positive distinct prime integers where \(a_i < a_{i + 1}\) for all positive integer \(i < 2014\)

Find the least possible value of \(a_1\) if

\[{ { a }_{1 } }^{ 2}+ { { a }_{2 } }^{ 2}+{ { a }_{3 } }^{ 2} + \dots + { { a }_{2013 } }^{ 2}+ { { a }_{2014 } }^{ 2}\]

is divisible by \(2015\)

Please show your solutions! Thanks!!!

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