Why Search for these Huge Primes?

Hi there,

I'm writing a story and one of my characters is a mathematician. He is looking for the next Mersenne Prime (yes, I'll be mentioning GIMPS). Another character, who knows little about math and is a "practical person" asks him, "What's the point?"

How can my character respond about a practical reason for searching for Mersenne prime? So far I would mention the following - the world record, searching for that lucrative prize-winning prime, the finding of perfect numbers, but I'd really like to be able to point to a really practical application. I am NOT a mathematician and don't understand a lot about it - I chose Mersenne primes because 2^n-1 is simple enough for me to comprehend! I know that large prime numbers are used in certain encryption applications, but I don't know whether Mersenne primes specifically would be useful for this purpose.

Does anyone have any ideas as to how my character should respond?

Thank you! :)
Susan

[Wacky]

Originally Posted by Susan

I know that large prime numbers are used in certain encryption applications

When numbers are used for encryption, they obscure the "message" only because the number actually used is one of a very large set of possible numbers. That way, if an eavesdropper obtains the encrypted message, even though they know the math to be used to decrypt it, they cannot do so because they don't know the secret key. If there are only a few possible keys, the eavesdropper can use "brute force" applying each possible key until he finds one that works.

Since there are very few Mersenne Primes, I don't see any way that they could be effectively used for encryption.

It was a nice thought, but you will need to find some other use.

Good luck on your story.

Richard

[dsouza123]

A side use of the Prime95 program is to test the stability/fitness of the PC.
There is a test mode (number of torture tests) that will test the PC
with known correct results of certain Mersenne numbers, with error
messages that declare a PC has hardware errors.

This is valuable for finding/testing RAM (many times the RAM is very
marginal, this can detect it). Also good for testing if a CPU has an issue
such as insufficient cooling (fan/heatsink coated in dust, not enough airflow),
voltage too low,thermal paste too much/little.

Valuable for finding if the PC is prone to overheating.
If bought in winter you might not find out until the heat of summer
that the PC needs to remove more heat to run OK.

If a PC can run a few days in the torture test without errors, it is very
likely stable with correctly working main components.

Running the actual Mersenne primality tests take more time and also
record errors that can help determine the PC's level of stability/ability to
correctly do very large computations.

[Prime95]

Originally Posted by Wacky

When numbers are used for encryption, they obscure the "message" only because the number actually used is one of a very large set of possible numbers.

Since there are very few Mersenne Primes, I don't see any way that they could be effectively used for encryption.

Apple Computer patented an encryption algorithm by Richard Crandall using Mersenne primes. So, yes, they could be used for encryption, but does one really need a 25 million bit key?

[Mystwalker]

In addition, it's pretty easy to guess which prime number has been taken.

[Prime95]

Originally Posted by Mystwalker

In addition, it's pretty easy to guess which prime number has been taken.

Your key is actually a number between 1 and the Mersenne number. That makes the key *very* hard to guess!

[jasonp]

Originally Posted by Unregistered

Hi there,

I'm writing a story and one of my characters is a mathematician. He is looking for the next Mersenne Prime (yes, I'll be mentioning GIMPS). Another character, who knows little about math and is a "practical person" asks him, "What's the point?"

[...]
Does anyone have any ideas as to how my character should respond?

1. The usual reasons: http://www.utm.edu/research/primes/notes/faq/why.html

Plus:

2. By the time your code is fast enough to really do the search efficiently, you've learned enough to be a world-class programmer

3. Searching for Mersenne primes requires FFTs. FFTs appear everywhere in the real world. Your FFTs are faster than just about everyone else's.

You never know what may spin off from your work. Thomas Nicely found a hardware problem in the Pentium's floating point divider in the process of (I think) calculating Brun's constant.

"What's the point?" is a more polite version of another question: "why does what you do for a living matter?". I think most people would bristle at such a question.

jasonp

Thank you everyone,

All of your responses will be very helpful, especially the list you linked to, Jason.

I hope my question doesn't come across wrong - that I didn't cause anyone to 'bristle' :) . Personally I think the whole idea is incredibly cool. It was the really tangible, less pure-knowledge applications that I was having trouble expressing, and you guys really helped.

Susan

[jasonp]

Originally Posted by Unregistered

I hope my question doesn't come across wrong - that I didn't cause anyone to 'bristle' :) . Personally I think the whole idea is incredibly cool.

Your question came across clearly. I have often had to deal with
'What good is that', and it never gets easier

jasonp