We answer an open problem raised by Chen-Zhang in 2008 and prove that, for any minimal projective 3-fold X of general type with the geometric genus p(g)(X) >= 5, the 4-canonical map phi(4,X) is non-birational if and only if X is birationally equivalent to a fibration, onto a curve, of which the general fiber is a minimal surface of general type with (c(1)(2), p(g)) = (1, 2). The statement does not hold for those with the geometric genus p(g) (X) <= 4 according to our examples.
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