Prime challenge

Number Theory Level pending

Given are five different prime numbers \(A, B, C, D\) and \(E\) that satisfy the following conditions

\(A + B + D = E\)

\(3 \times B < E + 10\)

\(C + B = A\)

\(2 \times A + C = E - 1\)

What is the value of \(E\)?

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