  This paper presents a novel approach at the intersection of machine learning
and number theory, focusing on the classification of prime and non-prime
numbers. At the core of our research is the development of a highly sparse
encoding method, integrated with conventional neural network architectures.
This combination has shown promising results, achieving a recall of over 99\%
in identifying prime numbers and 79\% for non-prime numbers from an inherently
imbalanced sequential series of integers, while exhibiting rapid model
convergence before the completion of a single training epoch. We performed
training using $10^6$ integers starting from a specified integer and tested on
a different range of $2 \times 10^6$ integers extending from $10^6$ to $3
\times 10^6$, offset by the same starting integer. While constrained by the
memory capacity of our resources, which limited our analysis to a span of
$3\times10^6$, we believe that our study contribute to the application of
machine learning in prime number analysis. This work aims to demonstrate the
potential of such applications and hopes to inspire further exploration and
possibilities in diverse fields.
