MHB Is 2 the Only Even Prime Number?

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2 is the only even prime number because it is greater than 1 and has no divisors other than 1 and itself. All other even numbers are divisible by 2, which disqualifies them from being prime. The confusion arises from equating prime numbers exclusively with odd numbers, which is incorrect. Prime numbers can include even numbers, with 2 being the sole even example. Understanding the definition of prime numbers clarifies why 2 holds this unique status.
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I know that 2 is an even number. I equate prime numbers with odd numbers. Why is 2 a prime number when it is listed in a group of odd numbers? Is 2 the only, even prime number? Why?
 
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RTCNTC said:
I know that 2 is an even number. I equate prime numbers with odd numbers. Why is 2 a prime number when it is listed in a group of odd numbers? Is 2 the only, even prime number? Why?

A prime number is a natural number greater than 1 that only has 1 and itself as factors. Since 2 is greater than 1 and only has 1 and 2 as factors, it is therefore a prime number. It is the only even prime number because all other even numbers also have 2 as a factor. :)
 
RTCNTC said:
I know that 2 is an even number. I equate prime numbers with odd numbers.
Well, there's your problem! You cannot "equate prime number with odd numbers". For one thing, the odd number, 9, is NOT prime!

Why is 2 a prime number when it is listed in a group of odd numbers? Is 2 the only, even prime number? Why?
Do you know what prime numbers are? What is your definition of "prime number"?
 
MarkFL said:
A prime number is a natural number greater than 1 that only has 1 and itself as factors. Since 2 is greater than 1 and only has 1 and 2 as factors, it is therefore a prime number. It is the only even prime number because all other even numbers also have 2 as a factor. :)

Thank you for your help.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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