Talk:Primorial numbers: Difference between revisions

:Our edits clashed! In the article I have rephrased the usage of "exponential" to note that it is the task that is growing exponentially (n = 10^i for i = 1, 2, 3, ...) so that even for a linear exercise, the work would grow exponentially. But here there is a further growth factor beyond the linear, because the number size is growing faster than linear, because n is growing... The supposition being that a multiply is linear in (number of digits) given that the multiplicand is one (embolismic) digit only. Except, we know that sooner or later, its digit count will grow. The unit of "sizeness" is not always obvious or convenient. To calculate Primorial(n) the task size is obviously determined by the value of n, from which is deduced log(n) for the number of digits both of n itself and Primorial(n) and one argues about the time for a multiply with those sizes of digit strings, and then perhaps the integration of those times so as to reach n from 1. All of which depends on n. But, since digit string length is so important, one might choose to talk about log(n) as being the unit of size. In the factoring of numbers, for example, I (and Prof. Knuth) speak of n and sqrt(n), but, with ever larger n, it seems now it is fashionable to use log(n) as the unit, and speak of "polynomial time in N" or similar, when N is actually log(n)