A statement about Rsa2048.

Assuming there are only two prime factors of equal length
in rsa2048 these two primes below would represent the
smallest possible and largest possible prime factors.

The smallest factor of 309 digits---
The range --
from
100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010459
to sqrt(rsa2048)

The largest factor of 309 digits---
The range --
from
sqrt(rsa2048)
too --
251959084756578934940271832400483985714292821262040320277771378360436620207075955562640185258807844069182906412495150821892985591491761845028084891200728449926873928072877767359714183472702618963750149718246911650776133798590957000973304597488084284017974291006424586918171951187461215151726546322822168673523

Knowing this and assuming the two factors are
of equal length, neither one of these two primes
could ever represent one of the factors in rsa2048.

I have a simple proof.

Dan
.

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