# 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?

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

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