The Fano index of a positive-dimensional Fano manifold 
is the largest positive integer 
for which 
in the Picard group
for a line bundle 
. It measures divisibility of the anticanonical class. The
Fano pseudoindex instead minimizes anticanonical
degrees over irreducible rational curves, and need not equal the index.
For 
, the index and pseudoindex
are both 
.
Each rational curve's anticanonical degree is divisible
by the index, so the index is at most the pseudoindex.
