[**Ed.** Prof. Zeilberger has [explained](http://mathoverflow.tqft.net/discussion/1091/3/how-many-integer-partitions-of-a-googol-10100-into-at-most-60-parts/#Item_27) 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))



How many integer partitions of a googol (10^100) into at most 60 parts
Can you do p\_60(10^1000)? p\_60(10^10000)? – Doron Zeilberger


8.6656581294960581213175060679076908106704497466613.. \* 10^5737 Dollar 100
8.6656581294960581213175060679076908106704497466613.. \* 10^58837 Dollar 1000
8.6656581294960581213175060679076908106704497466613.. \* 10^589837 Dollar 10000


