The way I see it Mochizuki's work could turn out to be like Maxwell's theory of electromagnetism. It could give us a definitive theory on the nature of prime numbers, but first someone needs to come and understand and solve it. A 'solution' of a differential equation system would be a formula, a 'solution' of Mochizuki's system would be an algorithm. Many new algorithms could come out of this, and one of them could be an algorithm for prime factorization.
But: I'm not a mathematician, so maybe I'm just fantasizing right now.
Comments
The claimed proof doesnt directly help us in factoring primes. At least not now. It has more to do with "structure" of primes.
The way I see it Mochizuki's work could turn out to be like Maxwell's theory of electromagnetism. It could give us a definitive theory on the nature of prime numbers, but first someone needs to come and understand and solve it. A 'solution' of a differential equation system would be a formula, a 'solution' of Mochizuki's system would be an algorithm. Many new algorithms could come out of this, and one of them could be an algorithm for prime factorization.
But: I'm not a mathematician, so maybe I'm just fantasizing right now.