Why do mathematicians like prime numbers?

Could you please elaborate on the fascination that mathematicians hold for prime numbers? Is it because of their unique properties, such as being divisible only by 1 and themselves, that make them stand out in the realm of numbers? Or is it the fact that they play a pivotal role in cryptography, allowing for secure data transmission? Additionally, could you discuss the significance of prime numbers in fields such as cryptography, algorithms, and number theory, and how they continue to captivate the minds of mathematicians worldwide?