Number Theory Challenge: Identifying Prime Numbers

To determine which number is a prime number, we must individually verify each of the options provided.

• Check $57$:
• Divisibility by 2: $57$ is odd, so not divisible.
• Divisibility by 3: Sum of digits $5 + 7 = 12$, divisible by 3, hence 57 is divisible by 3.
• Conclusion: $57$ is not a prime number.
• Check $58$:
• Divisibility by 2: $58$ is even, hence divisible by 2.
• Conclusion: $58$ is not a prime number.
• Check $55$:
• Divisibility by 2: $55$ is odd, not divisible by 2.
• Divisibility by 3: Sum of digits $5 + 5 = 10$, not divisible by 3.
• Divisibility by 5: Ends with 5, divisible by 5.
• Conclusion: $55$ is not a prime number.
• Check $60$:
• Divisibility by 2: $60$ is even, hence divisible by 2.
• Conclusion: $60$ is not a prime number.

After evaluating all options, none of the provided numbers is a prime number. It appears there may be a misunderstanding in the problem or typo, as no addtional information is given to explain an alternative solution.

Thus, none of the above numbers are prime, and we should conclude there is either a mistake in the given problem or choices.