Problem 45429. Prime Sum

Asif Newaz

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What is the minimum value that can be written as sum of primes in n different ways?

For example, 10 is the minimum value that can be written as the sum of primes in exactly five different ways:

 2 + 2 + 2 + 2 + 2
 2 + 2 + 3 + 3
 2 + 3 + 5
 5 + 5
 3 +7

8 can be written in 3 different ways but 7 can also be written in 3 different ways. So 7 is the right answer.

https://projecteuler.net/problem=77

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Last Solution submitted on Jul 18, 2023

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Rafael S.T. Vieira on 1 Oct 2020

what are the three ways to obtain 7 by summing primes?! 2+5, 2+2+3, and?

Rafael S.T. Vieira on 1 Oct 2020

Found at a blog that if a number is prime, wrongly some people consider this a sum. So the third way to obtain 7 would be 7 by itself, which is wrong, because it should actually be 7+0, but 0 is not a prime (and 7 by itself is not a sum). https://medium.com/@yevgeniy.v.filatov/counting-the-ways-to-express-a-number-as-a-sum-of-primes-e5e871b48193#:~:text=For%20the%20number%207%20we,as%20a%20sum%20of%20primes.

ChrisR on 14 Jun 2022

Maybe it's more precise to say partitions instead of a sum. In any case, solving CP 1240 helps here as well.

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