Curious mathematics

Posted by MacDood
Jen has posted an excerpt of a book she's reading, but unfortunately the author's math knowledge is poor. I feel obligated to correct some of the misstatements.

1. This is how you work out what prime numbers are. First you write down...

I have an easier way to show what a prime number is. A prime number is a natural number greater than 1 whose only positive divisors are 1 and itself. The author's method of determining prime numbers is a clumsy version of the Sieve of Eratosthenes, and it doesn't really define the notion of primality.

2. The rule for working out prime numbers is really simple, but no one has ever worked out a simple formula for telling you whether a very big number is a prime number or what the next one will be. If a number is really, really big it can take a computer years to work out whether it is a prime number.

This is completely incorrect, though it was partially correct before 2002. Today we have the AKS primality test and its variants, which can determine whether a number is prime or composite in a reasonable amount of time. However, the problem of factorizing a number into its prime factors is still unsolved and very difficult, and can take many computer years using existing methods.

3. Prime numbers are useful in writing codes and in America they are classed as Military Material and if you find one over 100 digits long you have to tell the CIA and they will buy it off you for $10,000. But it would not be a very good way of making a living.

I have never heard of this before. I suspect it is complete bullshit, but if you have a source to back it up, I'd love to see it. [Geekable.com]