So you have a semiprime n
n = p*q where p < q
A curious fact about bases is that if a number x ends with a zero in base y, then x is divisible by y. Therefor, if we where to represent n in all bases from 2 to n, then n would only end with a zero in base p, q and n.
Bellow is n represented in all the bases from n and downwards:
- The first entry is n in base n
- The second entry is base q. In base q, n would end with a zero and the first digit would be digit number p
- The third entry is the point where we go from 2 to 3 digits. I don't know what x is
- The forth entry is base p. For some reason, if n is a semiprime then the second digit will be digit number (q-p)
- Between the first and the second entry, the first digit is going to increment in a curve that is very flat at the beginning, and very steep towards the end
Can anyone explain why the second digit of n represented in base p is equal to q-p?