[Ed. Prof. Zeilberger has explained why he was asking this question. In joint work with Sills he had developed one approach to this problem, and he asked this question to see how this method compared to the current state of the art. Thus in order to be most useful, answers should explain a technique for computing the number of partitions of a given number and explain how quickly that technique works on large numbers.]
I am offering $100 (one hundred US dollars) for the EXACT number of integer-partitions of 10^100 (googol) into at most 60 parts. The answer has to come by 23:59:59 Sat. July 30, 2011, by Email to zeilberg at math dot rutgers dot edu . The first correct answer would get the prize. Please have
Subject: MathIsFun; Computational Challenge for p_60(10^100) ;
Of course, the answer should also be posted on mathoverflow, this way people would know that it has been answered.
P.S. A quick reminder, the number in question is the coefficient of q^(10^100) in the Maclaurin expansion of 1/((1-q)(1-q^2)(1-q^3) .....(1-q^60))