Let n=p⋅q (p < q) and Δ=∣p−q∣, where p,q are odd integers, then, it is hypothesized that factorizing this composite n will take O(1) time once the steady state value is reached for any Δ
Nearby in the stack
in
zone0
of some observation deck (od) with specific dial settings. We also introduce a new factorization approach by looking for
Δ
in different
Δ
sieve zones. Once
Δ
is found and
n
is already given, one can easily find the factors of this composite n from any one of the following quadratic equations:
p2+pΔ−n=0
or
q2−qΔ−n=0
. The new factorization approach does not rely on congruence of squares or any special properties of n, p or q and is only based on sieving the
Δ
. In addition, some other new factorization approaches are also discussed. Finally, a new trapdoor function is presented which is leveraged to encrypt and decrypt a message with different keys. The most fascinating part of the discovery is how addition is used in factorization of a semiprime number by making it yield the difference of its prime factors.