u/OkExtension7564

For those who would like to take a break from the main problem or look at it from a different perspective, I propose a similar hypothesis:

Conjecture (Division by the smallest divisor): If we take any prime number p > 2, multiply it by 3, add 2, and continue this process until we get a composite number, and when we get a composite number, we divide it by the smallest prime divisor until we get a prime number again, then we will eventually get into a cycle of length 19: 5 → 17 → 53 → 23 → 71 → 43 → 131 → 79 → 239 → 719 → 127 → 383 → 1151 → 691 → 83 → 251 → 151 → 13 → 41 → 5