Playing with Powers of 2

Let \(P\left( x \right) \) be the sum of the digits of \(x\). We define \(T\left( x\right) \) as applying \(P\left( x \right) \) to the number \(x\), and then to the result (repeatedly), until the outcome is a single digit. For example, \(T\left( 249 \right) :\quad P(249)=15,\quad P(15)=6\) so \(T\left( 249 \right) =6\).

Let \(T({ 2 }^{ 2016 })=N\). Find the least possible value for \(x>1\) that satisfy \({ 2 }^{ P(x) }\equiv N \pmod x \).

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