Finding Prime & Composite Numbers Using x Squared -x+41

[yomamacjo]

Homework Statement

Mathematicians have been searching for a formula that yields prime numbers. One such formula was:

x squared -x+41

select some numbers for x, substitute in formula- see if prime numbers occur. try to find a number for x that when substituted in the formula yields a composite number

Homework Equations

The Attempt at a Solution

 

[wildman]

x can be any number so substitute some in and see what comes out. Show us the result and we can help you further. State what your problem with this is if you still can't figure out what to do...

Do you know how to check if the number is a prime? Do you know how to substitute numbers in the formula? Try it and show us the results. If you don't know, try something and show us the results. Don't worry if it is wrong. I'm pretty dumb myself compared to Halls of Ivy and the other math experts...

 

[HallsofIvy]

Homework Statement

Mathematicians have been searching for a formula that yields prime numbers. One such formula was:

x squared -x+41

select some numbers for x, substitute in formula- see if prime numbers occur. try to find a number for x that when substituted in the formula yields a composite number

You titled this "looking for formula". Are you under the impression that you are asked to find "a formula that yields (only) prime numbers"? There is no such formula! Just DO exactly what you are told to do! Start with x= 1, 2, 3, etc., do the arithmetic and see what happens. Keep going until you find a result that is not prime. (In particular it should be obvious that x= 41 will NOT give a prime number: 41²- 41+ 41= (41)(41). That may not be the smallest.

Homework Equations

The Attempt at a Solution

 

[wildman]

I will give you an example to start you off:

Lets take 3:

3 squared is equal to 9 (3x3). minus 3 is 6. The plus 41 is 47. Now the question: Is 47 a prime?

Do you know what a prime is? It is a number greater than 2 that only itself and 1 can divide it without a remander. For instance 7 is a prime because only 1 and 7 divide it evenly -- ie no fraction (for example 7/3 = 2 1/3). Even numbers are not primes because 2 can divide any even number evenly (6/2 = 3 for example).

The best way to find if a number is prime is to divide it in 1/2 (47/2 = 23.5) get rid of the .5 (23) and then start dividing 47 by each non even number until you reach 2. (47/23 = 2.043) and then (27/21 = ...) etc. If you make it to 2 then you have a prime.

Go to it and show us the result so we can tell you if you are doing it right.