Answer: The number which Fran is thinking about is 82 or 93.
Explanation:
A two-digit number can be written as:
a*10 + b
Where a and b are single-digit numbers.
We know that:
"the first digit is 6 more than the second digit"
then:
a = b + 6
And we know that the second digit is a prime number.
Then we can have:
b = 2
b = 3
b = 5
b = 7
Now let's try with these different options.
if b = 2, then:
a = 2 + 6 = 8
Then the number is:
8*10 + 2 = 82
If b = 3, then:
a = 3 + 6 = 9
Then the number is:
9*10 + 3 = 93
if b = 5, then:
a = 5 + 6 = 11
But a needs to be a single-digit number, then b can not be 5 or larger.
Then the only two possible numbers are:
82 and 93.
So the number which Fran is thinking about is 82 or 93.