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A sixth grade math student made this conjecture: every prime number can be expressed as the product of two prime numbers. Do you agree with the conjecture? Why or why not?

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Answer:

No, I do not agree with the conjecture because 1 is not a prime number.

Explanation:

A prime number is one that can be divided by 1 and itself only. Thus it can be expressed in 2 factors only, 1 and the number itself.

Examples are; 2, 3, 5, 13, 19 , 23 etc.

So, 2 = 1 x 2

3 = 1 x 3

23 = 1 x 23

Prime numbers must be expressed as the product of 1 and the number.

The conjecture that every prime number can be expressed as the product of two prime numbers is false. Because 1 is not a prime number, since it has no 2 factors.

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