11 and 13.
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The first five two-digit prime numbers are 11, 13, 17, 19, and 23.
There are only two prime numbers that are consecutive numbers, 2 and 3. Their product is 2 x 3 = 6. The first prime numbers are 2, 3, 5, and 7 and the only two consecutive prime numbers whose product is a single digit are 2 and 3. (The next two consecutive prime numbers, 3 and 5, have a two-digit product.)
2, 3, 5, And 7 are the first 4 prime numbers
2, 3, 5, and 7 are the only one-digit prime numbers.
73 is the largest 2 digit number that is both prime and has prime numbers for both of its digits.