Every positive integer is expressible as a product of prime numbers in a unique way.
Although it is easily proven, that such a factorization exists, it is believed to be very hard to actually find it for a given large integer. For knowledge about group structures it can be however quite important to know all the prime factors of a number. The work that we are doing in K ln, and now also in Helsinki, and which has caused some inconvenience to users at the department, is trying to break up large integers, with up to now unknown factorization and at the same time speeding up this process by all means of theory and hardware. The time needed for factorization is most interesting for another reason. Since multiplication and division by a known integer are simple tasks for a computer, even when the numbers involved are of considerable size, the hardness of factorization can be exploited for coding data.