
Re: Request for help with short argument
Posted:
Nov 14, 2012 8:29 PM


Thanks for looking at it, trj.
I need to think about your point  initially not sure I get your point properly, so I might be confused.
I am visualising each n as in the centre of a stretch of p_nmany numbers for each given pn.
So n2, n1, n, n+1, n+2 for multiples of 5 then n3, n2, n1, n, n+1, n+2, n+3 for multiples of 7 and so on.
Do the probabilities _need_ to be independent of each other in the sense you mean? Surely if we look at a range of numbers n, and test each one like this, it remains true that 3/5 of the total n in the range will be in the neighbourhood of a multiple of 5 that is not n1 or n+1, while 3/5 . 5/7 of those n will be in the neighbourhood both of a multiple of 5 not at n1 or n+1 and at the same time in the neighbourhood of a a multiple of 7 not at n1 or n+1 either?
I agree it is probably at this point in the argument that I am overlooking something.

