I am a two digit prime number.
The sum of my digits is prime.
I am the lowest number that I could be.
Which number am I?

I am twice the square of an odd prime.
I am half of a square number.
Which number am I?

I am the square of a prime.
If I was one higher I would be prime.
If I was one lower I would be prime.
Which number am I?

Take half of me away to get a prime.
Add on half of me to get
the square of a prime.
Which number am I?

I am the product of two primes.
The total of my digits is prime.
I am the lowest number that I could be.
Which number am I?

I am the product of two primes.
The sum of my digits
is the cube of a prime.
Which number am I?