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Word Problems

Browse Middle School Prime Numbers
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Testing for primality.

Prime or Composite? [09/30/1997]
Wouldn't every number be composite?

Primes and Repeating Unit Numbers [12/09/1998]
How do you prove this statement: For every prime number there exists a repeated unit number that is a multiple of that prime.

Products of Digits [03/02/2003]
The product of digits in the number 234 is 24: 2*3*4 = 24. Can you describe a general procedure for figuring out how many x-digit numbers have a product equal to p, where x and p are counting numbers? How many different three-digit numbers have a product equal to 12? to 18? Why?

Proving a Number is Prime [10/13/2004]
How do you really prove that 2 or some other number is a prime number?

Pythagorean Triples [04/14/1997]
Why can't all the numbers in a Pythagorean triple be prime?

Relatively Prime [10/07/1999]
What does the term relatively prime mean, and how can you determine if two numbers are relative primes?

Relative Primes [11/24/1997]
Given these numbers: 8, 9, 11, 12, 14, 15, 21, 24, 25, 28, which numbers are relatively prime to 4? to 6?

The Sieve, and Ceiling, of Eratosthenes [07/27/2012]
Before introducing children to the sieve of Eratosthenes, a parent seeks to reconcile different methods found online. Doctor Peterson sees a didactic opportunity in the discrepant steps: how many factors do you actually need to check?

Spacing between Prime Numbers [11/08/2005]
Where is the first place that the difference between two consecutive prime numbers exceeds 2000? Is there a formula or general approach to finding such differences without having to just read through lists of known primes?

Sum of Consecutive Prime Numbers [6/29/1996]
Why is the sum of two consecutive prime numbers always twice a composite number?

Sums of Sets of Prime Numbers [01/07/2003]
Given several sets of prime numbers, use each of the nine non-zero digits exactly once. What is the smallest possible sum such a set could have?

Testing Prime Numbers [05/12/2003]
Besides the Sieve of Eratosthenes, what other methods can be used to determine all prime numbers within a given range? Is there a more efficient method?

Twin Primes [5/16/1996]
Is there an infinite number of twin primes?

Two Prime Numbers with 400-Digit Product [07/29/2006]
Find two prime numbers whose product is a 400-digit number.

Was 1 Ever Considered to Be a Prime Number? [02/29/2004]
I learned that a prime number was one divisible by only itself and 1, but my 4th grader says that per her book a prime requires 2 different factors. I note your Greek reference for 1 not being prime, which would indicate that I'm wrong and there was no change in definition. However, Ray's New Higher Arithmetic (1880) states, "A prime number is one that can be exactly divided by no other whole number but itself and 1, as 1, 2, 3, 5, 7, 11, etc." Can you tell me when this change happened and why?

What is "Relatively Prime"? [8/3/1996]
What does it mean when something is relatively prime?

What Type of Number Are Zero and One? [11/08/2004]
If 1 and 0 are not considered prime or composite numbers, then what are they?

Why Aren't There Negative Prime Numbers? [12/10/1999]
Why can't negative numbers be prime numbers?

Why is 1 Not Considered Prime? [3/20/1995]
Just recently a grade six student asked me, "Why is 1 not considered prime?" I tried to answer, but as usual, could not since I do not understand this either. I thought the answer might lie in the fact that we aren't using the true definition or we are interpreting it wrong.

Why Prime Numbers? [10/21/2001]
What are prime numbers used for in math?

Why Study Prime and Composite Numbers? [01/25/2001]
My husband and I wonder why this is taught in school at all. Who uses this in the real world? Why does someone need to know whether a number is a prime number or not?

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