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‘Following this revelation, perhaps we shouldn't be too hasty to rule out the possibility that there is also a simple algorithm for factorization that has similarly been overlooked.’
‘Many computational tasks, such as decodings or the factorization of very large numbers, would become feasible that are infeasible with present machines.’
‘In fact al-Farisi's approach is based on the unique factorisation of an integer into powers of prime numbers, and, according to Rashed, he states and attempts to prove this, the so-called fundamental theorem of arithmetic, in this work.’
‘The integer 6,036, for instance, has the prime factorization 2 x 2 x 3 x 503, and 6 + 0 + 3 + 6 = 2 + 2 + 3 + 5 + 0 + 3.’
‘As a result new algorithms for solving problems can turn difficult mathematical problems, such as factorisation, into easy ones, making traditional key breaking simpler.’