Problem One: draw or illustrate how you would draw a line of infinte length enclosed in finite space.

normally its the simplest problems in mathematics that provide us with the best problems. or worst, depending on what your stand point is. take for example arithmetic, and the multiplicative structure of the integers 1, 2, 3......... from this comes the idea of the prime number (a number that can not be obtained by multipling two smaller numbers, except for itself and one.) yet even with the discovery and development of mathematics like chaos theory or knot theory, there is still no known formula to determine if a number is prime.
the largest known prime is 2^13466917 - 1 (that is - two to the power of thirteen million four hundread and sixty six thousand, nine hundread and seventeen minus one) found on 14-november-2001.
Problem Two: write a program or equation to find the largest prime number...?
Problem Three: write a program or equation to find primality, for all x.
...or just go playing about with it and make your processor work for the money you paid for it.
the greeks used a method known as 'the sieve of Erathosthenese' which for all x|Z, basically boils down to multiplying all combinations of integers <x and not getting x.
heres the source for more primes. click here if you want to see a previous largest prime (2^6,972,593 - 1) written out in decimal?

as you all know, a compiler converts a program written in high level language into an equivalent program in machine language then the linker resolves symbolic refferences and generates a file that can be loaded into memory and executed. therefor the program exists in the hardware electronic signals that are interprited as one's and zero's. when a computation is performed its the threads of binary that are run through the processor.
Problem Four: write a program whose binary output is random or write down a binary string that is random and prove its random.
note: a random sequence has no pattern. hence a not random sequence has a pattern. so a sequence has a pattern if it can be computed by a shorter sequence. so by definition a random sequence can not be computed by a shorter definition because it has no pattern.


one of the above was actually done i believe.eof(max)