Primes and Composites (Math Chat)
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|Frank Morgan, MAA Online|
|Answering the challenge: Consider the sequence of integers 10n + 1: 11, 101, 1001, ... Are there infinitely many primes? Infinitely many composite numbers? Whenever n is odd, 10n + 1 is divisible by 11. Modulo 11, 10n + 1 = (-1)n + 1 = 0 if n is odd, so there are infinitely many composite numbers. It seems to be an open question whether there are infinitely many primes... New challenge: What is the shortest line segment fencing off prescribed area 0 < A < 1 in a unit square? (What about the least-area piece of plane dividing off prescribed volume 0 < V < 1 in a unit cube? What about a 4D cube?)|
|Levels:||High School (9-12), College|
|Math Topics:||Number Sense/About Numbers, Prime Numbers|
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