# world records in mathematics

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## Mathematics Subject Classification

### Largest number factored?

What do you mean by "the largest composite number factored"?? Here is a larger one:

2^20000000000000

which can be easily factored...

A

### Re: Largest number factored?

I need to come up with a clearer but still concise way to express this. If you gave me 2^20000000000000 written out in its base 10 digits and asked me to factor it, I think I would first try dividing it by 2. Then again. And again. At some point I would start to suspect that there about 20000000000000 more divisions by 2 to perform, but I would actually have to go through the process to confirm this. But since you've already told me it's 2^20000000000000, I don't have to go through all that. That's not the way it works with the RSA messages. Sure, someone chose the two primes and multiplied them together. But he's not going to just hand over the primes to anyone. It's a similar situation with most of the Fermat numbers. We know the base 2 logarithm of 2^2^20000000000000 + 1 but we have no idea what odd numbers to multiply to get the same number, or if maybe that is a prime itself, and there probably isn't someone who could just hand us the appropriate numbers.

### Re: Largest number factored?

Sure, I understand how factoring works. My only point is that the category 'largest composite number factored' doesn't really make sense, unless you further qualify these composite numbers as Fermat numbers, Mersenne numbers or RSA numbers.

Alvaro

### Re: Largest number factored?

It should be any composite number for which the team doing the factoring was not privy to what the answer should be before carrying out the calculations.

John