Aleksey Vladimirovich wrote:My God, now I got how wrong I was
...
I thought solving of this problem by Winston's approach would request some fancy and very slow algorithm, but I was so wrong. Results talk for themselves.
Thank you guys for steering me to the right solution and your patience! You rock, guys!

And isn't it much more fun when you work out the solution for yourself? That's why we DON'T just hand out answers here.

And well done.

Winston

Isn't it funny how there's always time and money enough to do it WRONG?
Articles by Winston can be found here

fred rosenberger wrote: . . . I haven't done the math to figure out the complexity of each algorithm, . . .

Iterating the series of numbers to find their prime factors, multiplied by time to multiply those factors. At worst, quadratic, but for large numbers it may approach nlogn complexity.