  While the one-Cooper pair problem is now a textbook exercise, the energy of
two pairs of electrons with opposite spins and zero total momentum has not been
derived yet, the exact handling of Pauli blocking between bound pairs being not
that easy for N=2 already. The two-Cooper pair problem however is quite
enlightening to understand the very peculiar role played by the Pauli exclusion
principle in superconductivity. Pauli blocking is known to drive the change
from 1 to $N$ pairs, but no precise description of this continuous change has
been given so far. Using Richardson procedure, we here show that Pauli blocking
increases the free part of the two-pair ground state energy, but decreases the
binding part when compared to two isolated pairs - the excitation gap to break
a pair however increasing from one to two pairs. When extrapolated to the dense
BCS regime, the decrease of the pair binding while the gap increases strongly
indicates that, at odd with common belief, the average pair binding energy
cannot be of the order of the gap.
