Computational attempt at verifying a number theoretic conjecture of mine
Conjecture
, and F(N) be the set of all prime factors of N.
where P(E) is the power set of E. Let
If p is a prime number, then
Goal
Computationally verify this conjecture for as many of the first prime numbers as possible.
Results of the first attempt
Within 5 iterations, the conjecture was verified for all of the first 2595 prime numbers.
Update
It turned out that a similar proposition had a simple proof:
This says that for any prime number p, we can find a set C. But it is not necessarily that this set or the corresponding multiple of p will be generated by our process.