Let
a
1
>
a
2
>
⋯
>
a
n
{a_1} > {a_2} > \cdots > {a_n}
be a finite sequence of positive integers. R. L. Graham has conjectured that
max
i
,
j
{
a
i
/
(
a
i
,
a
j
)
}
⩾
n
{\max _{i,j}}\left \{ {{a_i}/({a_i},{a_j})} \right \} \geqslant n
. We verify this conjecture in case at least one of the
α
i
{\alpha _i}
’s is prime.