[Cryptography] Has quantum cryptanalysis actually achieved anything?

[Stephan Neuhaus]

On 2/20/25 08:57, Jon Callas wrote:
> As a factoid, the special forms that 15 and 21 have is that they're 2^n-1 * 2^n+1 -- so a string of 1 bits times a high bit, a bunch of zero bits, and then the low bit.

Hi Jon

I've just noticed this: While 15 does indeed have this form (as 
(4-1)(4+1)), I can't make 21 work. It's 3x7, which would be (4-1)(8-1), 
but that doesn't conform to your idea of "string of 1 bits, a bunch of 
zero bits, plus a 1 bit". I can't even make it work by relaxing the 
requirements to "(2^n + 1) x (2^m - 1)". If you want to write 21 as (n - 
k)(n + k) for some integers n and k, then n = 5 and k = 2.

Did I misunderstand something here?

Fun

Stephan