To find two-digit prime numbers, you need to identify numbers between 10 and 99 that are only divisible by 1 and themselves.
Here's a step-by-step approach:
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List Two-Digit Numbers: Start with the range of two-digit numbers (10-99).
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Eliminate Even Numbers: Exclude all even numbers because they are divisible by 2. This significantly reduces the list.
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Eliminate Multiples of 5: Remove any numbers ending in 0 or 5 (except for 5 itself, but it's not a two-digit number).
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Check Divisibility by Remaining Primes: Starting with the next prime number, 3, check if the remaining numbers are divisible by 3, 7. If a number is divisible by any of these primes, eliminate it. Since the square root of 99 is less than 10, you only need to check divisibility up to 7.
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The Remaining Numbers are Prime: The numbers that remain after these eliminations are two-digit prime numbers.
Here's the list of all two-digit prime numbers:
11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Therefore, there are 21 two-digit prime numbers.
