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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!

Filed under: Exploration 11 Comments