So, what I'll add tonight, as well as answering questions between now and Sunday, is the code to calculate (For any size) the difference between BigN and n for known RSA numbers. At that scale, you will see a Revelation. The difference is a VERY smooth number in every case.

Smooth numbers feature in the settings for a search in the general number field sieve.

Before this evening, have a look at large products, and the difference between n and BigN. The difference is the same as for n-1 and BigN-1, which you would find in [-f,1]

>>8719

>>8720

This way of thinking.

>>8729

Now.

I got caught up at an AA meeting.

I'm going to tell you how the non-trivial method works.

BigN - n for the product of two large primes does not look that smooth.

The following may be why the solution is not public.

If you multiply c by small primes, the smoothness of BigN-n increase.

Once the size of the product of small primes is larger than the root of c, when that product is multiplied by c, there is enough information to imply n.

Everything discussed so far is related to this.

Who would have thought you need to make c bigger?

It works because the number of combinations of factors and appearances in a column increases non-linearly. I.e. the more small factors introduced increase the number of combinations by more than the count of new factors.

I will demonstrate how this works.

This is how the non-trivial Lookup works.

>>8732

Take some time to let it sink in.

It's all about increasing the amount of information until there is enough to let the grid do the work.

We know how to look up any number.

We know the big oh complexity of finding the square root increases by at most log q. This is the biggest operation in the steps. This determines big oh overall.

The number of combinations (And column appearances) grows much faster as we add small primes, ergo (Architect reference) there is a point where the number of factors gives up the answer. The maximum required is the root of c for the product of these added factors.

The solution remains log q in big oh, where q is the length of c in bits.

>>8733

It's about the number of times a number appears in a column. If the factors of a number are unique, the combinations of na in cell 1 increase dramatically.

The appearances of the new c appears many times more in the column.

It will seem counter intuitive.

That is perhaps why this isn't known publicly.

>>8733

Lets say you take the first fifteen primes and multiple c to make c'.

You would focus on the column with e',d' and c'.

There is a very fast to do this.

It would not make enough sense if we didn't build to this.

I will show you.

>>8739

Avoid the use of two, use odd primes.

In the early work I experimented with squares and cubes of 5.

>>8743

Use large numbers if you can, do you have access to BigInteger?