Pillai and Brauer proved that for
m≧17 we can find blocks
B
m
of
m consecutive integers such that no element in the block is pairwise prime with each of the other elements. The following basic
generalization is proved: For each
d>1 there is a number
G(d) such that for every
m≧
G(d) there exist infinitely many blocks
B
m
of
m consecutive integers, such that for each
r∈
B
m
there exists
s∈
B
m
, (
r,s)≧
d.