Has anyone ever invented a magic trick for convincing an audience that a magician has the ability to factor large integers in his head? This would be a great trick, I think.

That's one of the toughest nuts to crack--most modern cryptography is based on the difficulty of even high speed computers being able to factor large numbers.

So, for the right audience, if you could figure out a way to give the illusion that you are able to do that, it would be an impressive feat indeed.

I suppose you would have to force the large number in some way; but how to do it in a non-tedious manner is beyond me. I think that for this to play, you'd also have to be able to repeat on demand at least once or twice more.

Nice idea.

Larry Becker's "One In A Million" might be a good place to start.

I've run into John Horton Conway at conferences. Conway admits that he likes to learn (and perform) "show off" stunts like the common (and easy) day-for-any-date bit.
Dr. Conway also does more difficult mental calculations, like mentally calculating the date of Easter for any given year...or the phase of the moon for any given date.
I last saw him two years ago and he told me he had been working on factoring. He was skilled enough and confident enough to take on any four-digit number. ("I've only just recently begun to work on this," he explained.)
"Without thinking about it, give me any four-digit number," he said to me.
I ignored his instructions and gave him the product of a large two-digit prime and a smaller two-digit prime. I remember coming up with the result quickly enough that I didn't think he would know that I had "engineered" my "random" four-digit number. Well...not only did he immediately give me the factors, but I suspect he knew that I hadn't picked my number randomly. "It's harder for me when I'm given a number with more small prime factors," he said in a knowing tone.

Al

Can you describe "One in a Million" by Larry Becker? I couldn't find it in an internet search.

I've thought of a general method but I don't have the details: Force a number somehow from the audience. Then factor it (by memorization).

Any ideas on how to force it?

Alan Jackson has a great trick called "Diabolical Divisors" in Apocalypse that would fit the bill. It's also hidden without title at the end of the "Another 'Combination'" section of Mathematical Wizardry. All the spectator needs is a calculator.

It's a multi-phase routine in which you ask the spectator for various 2- or 3-digit numbers, have them enter that number 2 or 3 times (to get results such as 414141 or 517517). Each time you do this, you're able to determine progressively larger and larger factors for them quickly. The spectator can verify the divisors you give by dividing them in their calculator.

Technically, this is more of a divisors trick than a true factor trick, but most of the numbers you're able to give in this routine are indeed prime factors (there are also a couple of odd non-primes involved that the audience could easily assume were prime if they don't think about it too much).



Add-a-No might be a good approach here.

Good advice, Scott. Perform that and a couple, or three, others from my book, and you definitely will be considered to be a mathematical genius. HL.

You mean like pretending your iPhone has a quantum computer app - then doing the standard add-a-number bit?