Prime numbers

Dividability.
A number is dividable by another number only if the division does not leave a remainder. For example, dividing 100 by 23 gives a quotient of 4 and a reaminder of 8. 23*4+8=100. 100 is not dividable by 23. However, since 25*4+0=100, 100 is dividable by 25.
What are prime numbers?
Prime numbers are the special numbers that aren't dividable by any other number than 1 and itself. For example, 5 is a prime number, because it is only dividable by 1 and 5. Dividing it by 2,3 or 4 leaves a reaminder.
All numbers can be written as a product of prime numbers.
For example, 381843 can be written as 3*3*7*11*19*29.
Two numbers are relatively prime if they have no prime factos in common. For example 20=2*2*5 and 27=3*3*3 are relatively prime because 3 doesn't occur as a factor in 20 and neither 2 nor 5 occur in 27.
A prime-pair are two prime numbers that have only one even number between them. For example 11 and 13. Another example is 17 and 19.
The first 10 prime numbers are 2,3,5,7,11,13,17,19,23,29.
Three programs to calculate primes
- Example program I (Download C Source)
  This program uses the conventional but highly optimized method to calculate all primes between 1 and 1000000.
- Example program II (Download C Source)
  This program uses the "sieve" to do the same as program I.
- Example program III (Download C Source)
  This program finds out if a particular number is prime, and if it is not it finds the nearest larger prime.
  It works on bigger numbers (up to 1E18).

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