How did the mark scheme even start off that highlighted part????? huh

[coarse steppe]

They used a few small numbers as examples and noticed that odd primes can be written as the difference of two consecutive squares

Then, from there, 1/2 (p+1) and 1/2 (p-1) will be consecutive integers as p is odd

Then finding the difference between them gives you p

I know it's a bit of a stretch, but that's why its a challenge question I guess

here is my video that offers an slightly different approach: https://www.youtube.com/watch?v=lH8cKUZSRes starting at 9:16

hope that helps

[coarse steppe]

they're essentially just two consecutive integers

p is odd

so if you take p and add one, take p and subtract one and divide by 2, you'll get two consecutive integers