  A number $m$ is said to be a $\textit{de Polignac number}$, if infinitely
many pairs of consecutive primes exist, such that $m$ can be written as the
difference of those consecutive prime numbers. Recently in [ W. D. Banks:
Consecutive primes and IP sets, arXiv:2403.10637.], using arguments from the
Ramsey theory, W. D. Banks proved that the collection of $\textit{de Polignac
number}$ is an $IP^\star$ set (Though his original statement is relatively
weaker, an iterative application of pigeonhole principle/ theory of
ultrafilters shows that this statement is sufficient to conclude the set is
$IP^\star$). As a consequence, we have this collection as an additively
syndetic set. In this article, we show that this collection is also a
multiplicative syndetic set. In our proof, we use combinatorial arguments and
the tools from the algebra of the Stone-\v{C}ech compactification of discrete
semigroups (for details see [N. Hindman, and D. Strauss: Algebra in the
Stone-\v{C}ech Compactification: Theory and Applications, second edition, de
Gruyter, Berlin,2012.]).
