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Published 2011
This question has been very well answered - thank you to everyone who sent us solutions.
D, J and M from Year 5 and B, H and He from Year 4 at St. Nicolas CE Junior School, Newbury explain how they tackled it:
"We listed the prime numbers up to 100 and then we listed the squares of the numbers between 4 and 20. Then we started working out the answers by adding two prime numbers together to make the squares until we reached 400. We found out that two squares were impossible to make. When we had an odd square number, we had to have a number that adds on to 2 to make the square number and sometimes this number wouldn't be prime. For example, to make 121 with two primes, one of the primes has to be 2, and 119 is not prime.
Our results were:
25 = 2 + 23 | 36 = 13 + 23 | 49 = 2 + 47 | 64 = 17 + 47 |
81 = 2 + 79 | 100 = 3 + 97 | 121 impossible | 144 = 47 + 97 |
169 + 2 167 | 196 = 29 + 167 | 225 = 2 + 223 | 256 = 89 + 167 |
289 impossible | 324 = 101 + 223 | 361 = 2 + 359 | 400 = 41 + 359 |