Even for someone very interested in science, technology and its applications to our lives, I can't quite understand why people would spend enormous amounts of time and money in pursuing something like this. I mean, what's the point? And whom are you proving it to? This is not even in the category of those findings that one would associate with "pure science", since it's all about some exotic category of numbers (I found about what Mersenne primes are, btw, but I'm sure I'll forget all about them in a week or two). What exactly does this huge monster of a number mean to scientists anyway?
For all of science's claim to rationality, such news argues against it. And I, for one, am not impressed; not one bit!
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That you are not impressed one bit shows something about how little you know than about how meaningless it is.
ReplyDeleteWhat is a prime number? A number that is divisible only by 1 and itself. I.e. they cannot be factored by any other number.
Take two prime numbers and multiply them - what do you get? You get something that looks ordinary, but is very special.
For example, 7 times 11 is 77. 77 looks ordinary. But it is special because it can be factored only by prime numbers and no other numbers. On the other hand, look at 64. It is not a product of primes and hence can be factored as 2 times 32 or 4 times 16 or 8 times 8 - clearly it has multiple factors.
Why is this important? Cryptography. If I wanted to share a secret with you, I would encrypt it with a key and publish it on my blog and ask you to look at it. But you need the key to decrypt it and I can't safely transmit the key to you over my blog or send it to you by IM or email or say it to you over the phone as any of those could be intercepted fairly easily. So, I have to share a part of the key with you and you have to use that part to arrive at the actual key. This is where multiples of prime number come in helpful. I will give you a number that is a product of two prime numbers. You take the number and you factor it and one of the factors is a key. So in this case I will give you 77 and you know that the key has to be either 7 or 11 and nothing else. If I had used a square of a prime number, say 11 times 11, the result is a special number 121 that can be factored only as 11 times 11 - so you would take the number I give you and take the square root of it and get the key.
Clearly, in this case, 121 was trivial to factor - you could do it mentally or use the most basic calculator to do it for you.
What if I have to make the factoring difficult? Well, I have to use a really big prime number and use it to encrypt the message and then square it and give you the result. We are talking real big prime numbers. Imagine how long it will take to factor a number that is the result of squaring a 13 million sequence number? The resulting number will be a monstrosity - but it will be special because it can be factored ONLY by ONE prime number and NOTHING else. But since you and I are associates, we both have a list of big prime numbers that we can use and it is relatively easy for you to figure out the factors whereas a bad guy snooping around will be faced with a computationally humungous task of factoring the prime product (we are talking years and years).
This is why primes are a hot topic in the cryptographic community - the bigger the prime, even bigger the prime product and even longer the time to factor them and the secret information remains secret longer.
Yours is just a blog and hence just an opinion, but before you trivialize/ridicule the uselessness of something that escapes your imagination, I would suggest you think about it a little more. Next time you use SSL to transfer money from your bank account to your child's campus account, a "meaningless" prime number is at work making sure your child gets the money and not some crook in between.
Dear er, Anonymous,
ReplyDeleteIt was not my intention to trivialize the usefulness of prime numbers (in my school days, I was a numbers nut), nor am I anti-science in general. However, the applicability of an accomplishment such as finding the biggest prime number is narrow (cryptography, as you pointed out, to secure communications channels) that I feel it's simply not worth the time, money or effort spent on it.
Ridicule science I don't; on the contrary, I usually defend it (see http://blog.maheshj.info/2008/03/dont-ridicule-science.html). However, I just couldn't accept the money spent on something like finding even bigger primes. Agreed that research must go on, but shouldn't we at least pause to consider whether research expenses are justified?
Incidentally, I'm not new to the applications of cryptography either, having implemented a script version of RSA encryption in the course of my job; it certainly didn't escape my imagination earlier, and I don't think my imagination has developed a new habit either.