**

**The magnitude of the unknown factor is between 5.0e+150 and 2.0e+205 A lot of numbers to crunch, but I feel it could be made into an even smaller pool of numbers.

2.21128× 10^259

1.10564× 10^108

**

**

It is difficult to discern what is the goal of the computations, other than that it has to do with computing integer factors of a product. Can NSolve of polynomials be used for this purpose? I have no reason to believe that would be a possibility. And you have not provided a reason to suspect that it might be applicable (as best i can tell). So I'll say, provisionally, that it's a stretch.

Thanks Daniel. Sorry for my late reply.

The computations work, but are the goal of the computations correct?

I mean it looks good and all, but what I am trying to do is factor large RSA numbers. The last one was a 2048 bit one. Mathematica gave me the values that would be close to zero in my equation. I claim that the smaller semiPrime factor will occur on the graph of the equation where y equals zero.

So did Mathematica give a correct number where the equation equals zero? And if that number is correct does my hypothesis of where the smaller SemiPrime factor occurs hold true? How do I use Mathematica to confirm?

I need advice on how to crunch numbers with Mathematica. Someone helped me before and used the monitor class. I want to see the process as the computer computation occurs. In the console Mathematica will indicate processing in the menu bar, but I need assurance it is doing something and how far along the process is.

In my posts, this one and previous, I have tried brute force the semiPrimes smallest factor after I estimate where it occurs. I will provide and example here as a notebook. I have criticism that it is trivial, that my attempts are futile because 10^37 is still to large to crunch. But I took the error of the equation I used to estimate the value and I feel it is close and that it is useful because it significantly reduced the number of values to try.

Either way I want to crunch large numbers. Anyone have any tips or resources?

4.08615746000780408833983218761558688141378368019671197 × 10^37

If you look at Rohit’s post on this thread if you could find the error of 41350 for the smaller factor that is actually 41227 it would be a better way to factor.

Mathematica can find x in 2 seconds, but then it takes brute force to solve exactly. I am no expert in programming in Mathematica. It runs the calculation but does not give me an indication what is going on. These calculations could take weeks.

I have gotten an estimate for a 2048 bit number but until I can brute force it I can’t see if I am correct. See my discussion list on my profile for latest attempts.

I am not advertising, but I can post all info in one post. Go to www.scienceforums.net Mathematics Simple Yet Interesting page8 to see all my work as it relates to this post.

The bounty of factoring the 2048 bit SemiPrime is over but this work is critical to Prime distribution and the factorization problem.

Could someone point me to tutorials on how to crunch numbers in Mathematica?

Factor an unfactored RSA number by estimating the smaller factor on the graph then brute forcing the sample values.

On the graph as x approaches zero, x is the smaller Prime factor. But there is a margin of error so we test values between 5 and zero. From left to right and with any luck we will find the smaller Prime factor.

Refer to the first graph of the attached notebook for the estimate.

https://community.wolfram.com/groups/-/m/t/3066471

Solve does not agree with

The middle equation crosses the x-axis at zero where x is 41227 the smaller Prime factor of pnp

Clear[x, pnp]; pnp = 2564855351;
eqn = ((pnp - (Sqrt[(x^2*pnp^4 + 2*pnp*x^5) + x^8])/pnp^4 - (1 - (x^2/(2*pnp)))*(pnp^2/x^2)));

Solve[eqn == 0 && x >= 0, x, Reals] // N
(* {{x -> 41350.98025}, {x -> 6.387801493*10^11}} *)