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Primes in a magic square needs a correct solution

Main post link -> https://brilliant.org/mathematics-problem/primes-in-a-magic-square/?group=YUgoPeVAfUIe

In this week's Combinatorics question, solutions merely showed a possible maximum, but failed to justify that it is indeed the maximum. Nicholas T., along with several other members, want to know why there isn't a magic square with more primes.

For those who solved it, can you demonstrate that you have actually solved the problem?

Hurry, the community eagerly awaits! Oodles of glory to those with the correct argument.

Please post your solution on the problem, and not here. It is still a live problem. Solutions posted here will be removed.


Update: Kudos to C L. for presenting a complete solution. The community delights in learning from you.

What is the smallest magic sum of a magic square which uses 9 (positive) prime numbers? Sounds like a coding challenge for all you eager beavers out there!

Note by Calvin Lin
4 years, 1 month ago

No vote yet
4 votes

  Easy Math Editor

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**bold** or __bold__ bold

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[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

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