Adding primes

Number Theory Level 3

How many positive integers n n ( ≤ 2017 \leq2017 ) can be expressed as sum of distinct prime numbers?


The answer is 2014.

Áron Bán-Szabó by Áron Bán-Szabó , 17, Hungary

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1 solution

Daniel Branscombe
Aug 11, 2017

My solution was based on an as yet unproven theorem that every integer greater than 6 can be expressed as the sum of distinct primes. Exceptions under 7 being 1,4, and 6. Thus giving the solution of 2017-3=2014. Of course on could try an exhaustive search by computer and thus get around the need for an as yet unproven theorem.

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what about 5?

5=2+3

2 and 3 are distinct primes

Tri Nguyen - 3 years, 9 months ago

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I think you misunderstood me, what I meant is that the theorem states that the smallest integer for which all other integers greater than it is expressible as the sum of distinct primes is 6. This does not mean that all integers less than or equal to 6 can't be, just that every integer past 6 can be. The exceptions being 1,4, and 6.

Daniel Branscombe - 3 years, 9 months ago

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