155816

I started off by listing the prime numbers from 1 to 9: 2, 3, 5 and 7. After I listed the numbers I crossed out the even prime number(s): 2. Clue number one it tells me it should be a palindromic number, so the number at the end should be the first digit as well (and possibly the second). Thanks to clue number five I knew that the number should not be over 500 therefore eliminating 7 and 5. I then knew the number had to be 3_3 or 333 but then realised the difference between the largest and smallest number must be five, from clue 3, and decided it could not be 333. So I did 3+5 which equals 8. I came to the conclusion that the answer was 383 but I wanted to check whether it would add up to 14 (3+3+8), which clue 4 mentions. The numbers did add up to 14 meaning the answer is 383.