Wild About Math! Making Math fun and accessible

Interesting relationship among primes

Many properties of primes are very difficult to determine and prove. Here's an exploration that's within reach of many of us:

What is interesting about the difference of the squares of most any two primes? In other words, what is interesting about p₁²-p₂² for most primes p₁ and p₂? When does this property hold? Prove your assertion.

I got the idea for this puzzle/exploration from Standup Maths and adapted it to make it harder!