How old is Amy?

The sum of the digits must be prime, so one digit must be odd and one digit must be even (since the sum of the digits cannot be 2, since the digits of 11 are not prime). Since 2 is the only even prime, one of the digits is 2.

Furthermore, 2 must be the first digit, otherwise the number would be even (and thus not prime). Therefore the options are:

23, which works, since 2 is prime, 3 is prime, $2+3=5$ is prime, and 23 is prime

25, which itself is not prime

27, which itself is not prime (nor is the sum of its digits)

Thus, Amy is 23 years old.

11 also is a super prime.

I put 32, which technically works, but nope, it just HAS to be 23. What is this, AP Multiple Choice, we gotta pick the BEST answer, not one of the other correct answer??

Let $p =\overline{ab}$ be the super prime. The digits a and b must be prime, so digit candidates are 2, 3, 5, 7 The digit sum a+b (which is at least 4) must be prime too, so because b must be odd, a will be even, so a must be 2. Three candidates remain: 23, 25, 27 of which 23 is the only prime.

The actual definition of Super prime is not the one given in the problem. A super prime number is any prime number that occupies a prime number position in a numerical index. Say you have 5 spots numbered 1, 2, 3, 4, 5. You then fill those spots with the first prime numbers; 2, 3, 5, 7, 11. Because 3, 5, and 11 occupy the "prime" spots, they are super prime. Essentially the second, third, fifth, seventh, eleventh, etc etc prime numbers in order are super prime. So, Lets examine the conditions given in the problem. First off, forget the true definition of super prime. Since this problem neglected the true definition, we can only use the rules given in the statement. It states that the number is superprime, but never states that the number itself is a prime number. It then goes on to provide its own definition of super prime. "both digits are prime, and the sum of its digits are prime." So by the rules of the problem, the only conditions we need to meet are that both digits are prime and that the sum of both digits is prime. 23 and 32 work!

The very first thing mentioned about the number is that is the two-digit superPRIME. Amy then says "well it's PRIME, but what's so super about it". John explains "It is PRIME, so are both its digits and so is the sum of both its digits". Thus we are looking for a PRIME number both of whose digits are themselves PRIME and which add together to make a prime. The only even prime is two, and one is not considered to be a prime, so the digits cannot add up to two. Thus, since the digits add up to an odd number (to be prime) two must be one of those digits, necessarily the first as otherwise the original number would not be prime. This gives us three theoretical possibilities for the second digit - 3, 5 and 7 are the only odd single digit primes. 25 = 5 x 5 and 27 = 3 x 3 x 3, so both of those are ruled out. Therefore 23, which is prime is correct - and a check reveals that 2 and 3 are both prime and 2 + 3 = 5 which is also prime. The reason for the capitalisation of the word Prime in the preamble to this solution is the sheer number of comments I have seen on other solutions that indicate failure to observe the actual requirements of the problem, so I thought I would emphasise them.

2 is a prime and 3 is a prime , their sum is 5 (also a prime)

The first and second digit is all prime numbers. Then, the first prime number is 2. The second prime number is 3. So 23.

i think this is a stupid question. there are a lot of possibilities.

the possibilities are:

-11 (provided 1 is prime)

• 23

-32

-25

-52

therefore, there is NO concrete answer

Amy has a two digit age. For two prime numbers to have a prime sum, there must be one even digit, as two odd numbers is even, and even numbers are never prime (aside from 2). Since 2 is the only even prime, it must be in the number. It must also be in the ten's place since otherwise, the number is even. 23 is the only odd number starting with 2, and it fits the description. Thus, Amy is 23.

2 is prime, 3 is prime, and 2+3=5 which is also prime

The problem claims that it is a two digit number that is the superprime.

Then Amy says"Well it's PRIME, but what makes it so super". This infers that the number is a prime. John then explains and lays down the conditions of a number being a superPRIME(excluding the one already mentioned, that the number itself is a prime) "Both its digits are prime as is the sum of its digits!". So the conditions are:

1.It is a two digit number

2.The number is prime(many people have missed this) .

3.Both it's digits are prime(One is not considered to be prime due to the fundamental theorem of arithmetic).

4.The sum of it's digits is prime

It is true that there is a real definition of superprime that is not the one mentioned in the problem, but we need to use these conditions for this problem.

Now, seeing as we are not meant to guess Amy's age using the picture, but rather use maths, we can then proceed:

One digit must be odd and the other even, as all primes but two are odd as a sum of two is impossible to obtain(11 is not a superprime. Check condition 3). Therefore two, the only even prime, is the even digit and also the first digit, to ensure the number is prime. The options are then as follows:

21.(Not prime)

1. (Sastisfies all conditions.)

2. (Not prime)

3. (Not prime)

4. (Digits not prime)

Therefore 23 is the answer.