Never ask a girl her age

Number Theory Level 3

One day, I had a boring date. But just then:

I asked her, "What's your age by the way?"

She replied, "Oh, it's a two digit prime number which when added to a square, forms a new perfect square.

I said, "Ok, but there are many prime numbers like that!"

She replied, "The first 2 digits of the square of my age form a perfect square, and the last digit of the square of my age is equal to the first digit of my age."

That's some interesting conversation now. What was the minimum age of the girl?


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