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 Writing integers as sums of primes

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Bruno
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Bruno

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Join date : 2009-09-15
Age : 32
Location : the infinite, frictionless plane of uniform density

Writing integers as sums of primes Empty
PostSubject: Writing integers as sums of primes   Writing integers as sums of primes EmptySun Dec 20, 2009 4:20 pm

Include 1 as a prime for this problem (blasphemy! Evil or Very Mad). Show that every integer is the sum of distinct primes.
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Mitch
Pythagoras
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Join date : 2009-09-16

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PostSubject: Goldbach   Writing integers as sums of primes EmptyThu Jan 14, 2010 11:50 pm

This reminds me of another problem. Show that every even integer greater than two can be written as the sum of two primes.

Note that they don't have to be distinct and 1 does not count as a prime in this case.

Kudos to any of you that solve this problem...Let's say it's a bit of a tough one...
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Bruno
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Bruno

Posts : 184
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Age : 32
Location : the infinite, frictionless plane of uniform density

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PostSubject: Re: Writing integers as sums of primes   Writing integers as sums of primes EmptyFri Jan 15, 2010 2:17 pm

Mitch wrote:
This reminds me of another problem. Show that every even integer greater than two can be written as the sum of two primes.

Note that they don't have to be distinct and 1 does not count as a prime in this case.

Kudos to any of you that solve this problem...Let's say it's a bit of a tough one...

What's up Mitch! I haven't seen you in a while! Very Happy

The problem you are giving is quite hard indeed! Here's a plot of the number of representations of each even integer as a sum of two primes. It looks very nice!

Writing integers as sums of primes Goldbach-1000000

My problem above is easier, rest assured.
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PostSubject: Re: Writing integers as sums of primes   Writing integers as sums of primes Empty

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