## Monday, January 14, 2013

### Odd Semi-prime Property

Let N = pq be any odd semiprime. Let 's' be the ceiling of square root of 'N'.

If 's' is even then there exist odd 'l' and k = l + 2 such that (s^2 - k^2) < N < (s^2 - l^2) else

If 's' is odd then there exist even 'l' and k = l + 2 such that (s^2 - k^2) < N < (s^2 - l^2)

Let r = q + Δ,

where 'Δ' is very small +ve integer compared to 'p' & 'q'

When 2l + 4 < p then pr will be less than and nearer to (s^2 + l^2) and p(r + 1) will be greater than and nearer to (s^2 + k^2)

When 2l + 4 > p then pr will be greater than and nearer to (s^2 + l^2) and depends upon 2p, p(r + 1) will be either greater or lesser than and nearer to (s^2 + k^2)

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