[math-fun] A prime factor factory

Given any prime p, we can look at all the prime factors of 2p+1, and then perform the same process (double, add 1, find all prime factors) with those primes, and so on; must the process eventually stabilize? E.g.: 2 -> 5 -> 11 -> 23 -> 47 -> 95=5*19 19 -> 39=3*13 3 -> 7 -> 15=3*5 13 -> 27=3*3*3 Done. I looked at a variant where one uses 2p-1 instead of 2p+1; it appears to lead to closure a lot more rapidly. For the 2p-1 version, I was able to check in my head that all primes under 100 lead to closure; for the 2p+1 version, I wasn’t able to do this. Jim Propp