How can a student prove the ABC hypothesis using prime numbers, quantum mechanics and creative imagination?

The ABC conjecture states that for three mutually prime numbers A, B, and C satisfying the relation A + B = C, the product of the prime divisors A, B, and C is usually not much less than C. The theorem is very simple to formulate, but extremely difficult to prove. Some five hundred pages have been spent by some of the most eminent mathematicians in the Western world trying to find a proof - but the result is anything but ambiguous and difficult to verify. Meanwhile, any student with advanced training in the exact sciences can understand and prove the ABC hypothesis, relying on creative imagination based on the synthesis of school knowledge, including physics and chemistry. Prime numbers have a huge research potential, they play a unifying role in understanding the world around us. And this is important for education.