The book introduces innovative approaches to conjectures and established knowledge in the realm of prime numbers. It explores how famous mathematicians like Sophie Germain and Mersenne, among others, conceptualized prime numbers Not only does the text clarify Fermat's Little Theorem, but it also offers an explanation for the existence of pseudoprimes. Furthermore, it sheds light on the effectiveness of the Lucas-Lehmer algorithm in discovering Mersenne Primes. By elucidating fundamental concepts, the book provides fresh insights into the study of prime numbers within Number Theory. While its primary audience consists of enthusiasts and mathematicians in search of new patterns and analytical methodologies for prime numbers, the book is designed to be accessible to a broader audience. With over 70 explanatory figures and clear prose, it appeals to anyone intrigued by the intricate world of prime numbers.