Thus consideration of the partition function has not brought a proof of GC any closer. However it does allow us to give an interesting twist to the argument of the previous section. The graph suggests that the hardest test cases for GC are likely to occur among the smallest numbers; hence the inductive sample for GC is biased, but it is biased against the chances of GC. Mathematicians’ confidence in the truth of GC is not based purely on enumerative induction. The values taken by the partition f