In Issue 2, of Infinity, we generated primes by simply testing random numbers for divisors. However for large primes such a process is inefficient. A better strategy would be to identify a pattern which generates primes. For instance each of the numbers
2² - 1 = 3

2³ - 1 = 7

2⁵ - 1 = 31

2⁷ -1 = 127

is prime. So in general one can ask,

`If p is a prime number is 2^p - 1 also prime?'

While this rule is not true in general it has been used to generate some very large primes. See if you can write a QBASIC program (or modify the one from Issue 2 of Infinity) to find all primes, p, less than 30 for which 2^p - 1 is not prime.

What is the largest prime number you can generate using this rule?