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Answer: Prime Partition, March 2017 Challenge Question

Posted March 30, 2017 5:46 PM

Question:

If p(n) is the number of partitions of n, defined as the number of ways to write the integer n as a sum of positive integers where the order of the addends is not significant, what n produces the 42nd largest prime p(n)?

Answer:

The 42nd largest prime p(n) is 3513035269942590955686749126214187667970579050845937, which is produced by n = 2508.

The number of partitions p(n), as stated in the question, is defined as the number of ways to write the integer n as a sum of positive integers where the order of the addends is not significant. So, for example, for n = 4, p(4) = 5 as illustrated below:

4

3 + 1

2 + 2

2 + 1 + 1

1 + 1 + 1 + 1

A prime number is a positive integer that has no positive divisors other than 1 and itself. p(n) is prime for certain values of n, the first few of which are 2, 3, 4, 5, 6, 13, 36, 77, 111… corresponding to p(n) equal to 2, 3, 5, 7, 11, 101, 17977, 10619863,...

You can follow the latest top 20 list of largest p(n) primes at http://primes.utm.edu/top20/page.php?id=54.

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#1

Re: Answer: Prime Partition, March 2017 Challenge Question

03/31/2017 2:34 PM

Yeah, that was gonna be my next guess...

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#2

Re: Answer: Prime Partition, March 2017 Challenge Question

03/31/2017 3:12 PM

except 36 is not a prime number last time I checked.

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Re: Answer: Prime Partition, March 2017 Challenge Question

03/31/2017 3:31 PM

Not 36, p(36) = 17977, a prime number and the 7th in the sequence of prime p(n)s.

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Re: Answer: Prime Partition, March 2017 Challenge Question

03/31/2017 3:38 PM

I thought the first list was n not p(n), I guess I need to understand what "of which" means. I hate that manner of sentence construction.

I get it now, and I am sure not going to worry about high order prime numbers. 2 is a good one.

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Re: Answer: Prime Partition, March 2017 Challenge Question

03/31/2017 3:39 PM

The first list is n, the elements of that list corresponding 1:1 to the elements p(n) in the second list.

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Re: Answer: Prime Partition, March 2017 Challenge Question

03/31/2017 4:07 PM

I still have no idea what is being communicated here. Is p(n) the number of partitions supposed to be a really big prime number, and we don't care if n is prime or not?

Dang! I used to like math. To heck with it.

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Re: Answer: Prime Partition, March 2017 Challenge Question

03/31/2017 6:01 PM

The original puzzle is basically asking what value of n produces a prime p(n) that is the 42nd prime p(n) in the sequence of prime p(n)s. Not all p(n)s are primes; in fact, most aren't. It doesn't matter whether the n is prime or not, just the p(n).

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Re: Answer: Prime Partition, March 2017 Challenge Question

04/03/2017 9:08 AM

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