Some Problems on the Prime Factors of Consecutive Integers

@inproceedings{Lanes2004SomePO,
title={Some Problems on the Prime Factors of Consecutive Integers},
author={P Lanes and J. L. Selfridge},
year={2004}
}

One would expect that v o(n) > oo as n -> oo but we are very far from being able to prove this . We can only show that vo(n) > 1 for n > 17 . In fact we can show the following result : vo(n) > 1 for all n except n = 1, 2, 3, 4, 7, 8, 16 . It is easy to see that vo(n) = 1 for the above values of n . In general if k > 1 then v(n ; k) < 1 for Ice + 3k > n 3 . In fact for k > n we have v(n ; k) = 1 if and only if n + k is a prime . Clearly vo(n) = 1 implies n = p' . Assume first p odd . v o(n) = 1… CONTINUE READING