Finding the largest prime factor
The names of the function and parameters inner n current don't mean anything; I suggest testFactor num factor instead.  I'd also swap the two parameters so that the one that varies more (the candidate factor) appears last — this is a convention to facilitate currying.

Switching the order of the cases lets you avoid nesting conditions.

let largestPrimeFactor (number:int64) =
    let rec testFactor num factor =
        if factor * factor &gt; num then
            num
        else if num % factor = 0L then
            testFactor (num / factor) factor
        else if factor = 2L then
            testFactor num 3L
        else 
            testFactor num (factor + 2L)
    testFactor number 2L