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# Two Primes Make One Square

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Age 7 to 11

Challenge Level

Flora had a challenge for her friends.

She asked, "Can you make square numbers by adding two prime numbers together?"

Ollie had a think.

"Well, let me see... I know that 4 = 2 + 2. That's a good start!"

**Have a go yourself. Try with the squares of the numbers from 4 to 20.**

Once you have had some initial ideas, take a look at how three more of Flora's friends started the problem:

Bailey said:

"I made the square numbers out of cubes and tried taking a prime number of cubes away and seeing if it left a prime number of cubes."

Dina said:

"I wondered whether noticing that 2 is the only even prime number was important."

Shameem said:

"I listed the prime numbers up to 100 and then I listed the squares of the numbers from 4 to 20."

Did you go about the task in the same way as any of these children?

What do you like about each method?

**Continue working on the problem. You might like to adopt Bailey's or Dina's or Shameem's approach.**

**Did you find any square numbers which cannot be made by adding two prime numbers together? Why or why not?**

You could print off this sheet which includes the problem and the three approaches.