  New condition Re>Re_th_min=124 of linear (exponential) instability of the
Hagen-Poisseuille (HP) with respect to extremely small by magnitude
axially-symmetric disturbances of the tangential component of the velocity
field is obtained. For this, disturbances must necessarily have quasi-periodic
longitude variability (not representable as a Fourier series or integral) along
the pipe axis that complies with experimental data and differs from the usually
considered idealized case of pure periodic disturbances for which HP flow is
stable for arbitrary large Reynolds numbers Re. Obtained minimal threshold
Reynolds number is related to the spatial structure of disturbances (having two
radial modes with non-commensurable longitudinal periods) in which irrational
value p=1.58 of the ratio of the two longitudinal periods is close to the value
of the "golden ratio" equal to 1.618.
