Prime Or Composite - Proof required?

In summary, a prime number is a positive integer with only two factors, while a composite number has more than two factors. To determine if a number is prime or composite, you can check for divisibility or use the Sieve of Eratosthenes method. A number cannot be both prime and composite, and proof is necessary to determine the nature of a number due to the vast number of integers.
  • #1
johnny009
7
0
n^2 - 14n + 40, is this quadratic composite or prime - when n ≤ 0.

Determine, all integer values of 'n' - for which n^2 - 14n + 40 is prime?

Proof Required.

ps. I can do the workings, but the 'proof' is the problem.

Many Thanks

John.
 
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  • #2
Please continue the thread found http://mathhelpboards.com/discrete-mathematics-set-theory-logic-15/proof-amp-structures-22713.html.

Thread closed.
 

What is a prime number?

A prime number is a positive integer that is divisible only by 1 and itself. In other words, it has exactly two factors.

What is a composite number?

A composite number is a positive integer that has more than two factors. In other words, it is divisible by at least one number other than 1 and itself.

How do you determine if a number is prime or composite?

To determine if a number is prime or composite, you can use the following methods:

  • Check if the number is divisible by any number between 2 and its square root. If it is not divisible by any number, then it is prime.
  • Use the Sieve of Eratosthenes method, which involves creating a list of numbers and crossing out all the multiples of each number until you are left with a list of prime numbers.

Can a number be both prime and composite?

No, a number cannot be both prime and composite. A number is either divisible by only 1 and itself (prime) or by at least one other number (composite).

Why is proof required to determine if a number is prime or composite?

Proof is required to determine if a number is prime or composite because there are infinitely many numbers and it is not feasible to check each and every one manually. Proof provides a systematic and reliable method to determine the nature of a number.

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