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February 6th, 2012, 06:21 AM   #11
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Re: Partition (number theory)

Oh wow! That's great, Greathouse! I guess i got a little scared looking at the summation notation and functions with seperate definitions within functions.

Do me a favor, try 10^60 and 10^600 and compare times, thanks.
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February 6th, 2012, 01:02 PM   #12
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Re: Partition (number theory)

Originally Posted by agentredlum
Do me a favor, try 10^60 and 10^600 and compare times, thanks.
Those are too big to do. 10^5 takes 10 milliseconds, 10^6 takes 200 milliseconds, 10^7 takes 7 seconds, 10^8 takes 8 minutes. 10^10 probably takes weeks and 10^15 takes longer than the age of the earth. (Of course there are faster programs and faster computers, but they won't change these results by more than a few orders of magnitude. 10^20 is going to be too large to find with all the computers on Earth, even using Ono's new algorithm, I'd wager.)

But perhaps you don't need to know these exactly -- P(10^ already has over 11,000 digits. In that case there are good estimates that will give you what you want.
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