Difference between revisions of "2024 AMC 10A Problems/Problem 3"
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== Solution == | == Solution == | ||
− | Recall that <math>2</math> is the only even prime. | + | Let the requested sum be <math>S.</math> Recall that <math>2</math> is the only even (and the smallest) prime, so <math>S</math> is odd. It follows that the five distinct primes are all odd. |
− | + | The first few odd primes are <math>3,5,7,11,13,17,19,\ldots,</math> so <math>S>3+5+7+11+13=39,</math> as <math>39</math> is a composite. | |
==See also== | ==See also== | ||
{{AMC10 box|year=2024|ab=A|before=2|num-a=4}} | {{AMC10 box|year=2024|ab=A|before=2|num-a=4}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 16:31, 8 November 2024
Problem
What is the sum of the digits of the smallest prime that can be written as a sum of distinct primes?
Solution
Let the requested sum be Recall that
is the only even (and the smallest) prime, so
is odd. It follows that the five distinct primes are all odd.
The first few odd primes are so
as
is a composite.
See also
2024 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.