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Mat126 Survey of Mathematics - Prime Numbers

by Angel











































Please help explain this I am very lost!! Thanks



Project # 2

Task: To produce prime numbers as solutions by substituting x in the formula
x2 – x + 41

Please note you MUST show your work (plugging the number into the formula and simplifying).

Here is an example of showing your work. Let’s say I start with 3 as one of my odd numbers of choice. I need to plug 3 into the formula like this:

32 – 3 + 41

= 9 – 3 + 41

= 6 + 41

= 47

Is 47 prime? Yes! In this case, the formula produced a prime number!

Please perform the above steps for all five of your numbers (0, two even numbers of your choice, and two odd numbers of your choice).

*** Note: this is NOT an equation. Instead, it is a FORMULA. Please do NOT set the formula equal to 0 and try to factor, because this is not correct. J

Step 1: First even number of your choice: plug in number into formula and simplify:

Step 2: Second even number of your choice: plug in number into formula and simplify:


Step 3: First odd number of your choice: plug in number into formula and simplify:


Step 4: Second odd number of your choice: plug in number into formula and simplify:


Step 5: Plug in 0 into formula and simplify:


Comments for Mat126 Survey of Mathematics - Prime Numbers

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Jan 30, 2012
Formula that Yields Prime Numbers
by: Staff

Question:

by Angel


Please help explain this I am very lost!! Thanks



Project # 2

Task: To produce prime numbers as solutions by substituting x in the formula

x² - x + 41

Please note you MUST show your work (plugging the number into the formula and simplifying).

Here is an example of showing your work. Let’s say I start with 3 as one of my odd numbers of choice. I need to plug 3 into the formula like this:

3² – 3 + 41

= 9 – 3 + 41

= 6 + 41

= 47

Is 47 prime? Yes! In this case, the formula produced a prime number!

Please perform the above steps for all five of your numbers (0, two even numbers of your choice, and two odd numbers of your choice).

*** Note: this is NOT an equation. Instead, it is a FORMULA. Please do NOT set the formula equal to 0 and try to factor, because this is not correct. J

Step 1: First even number of your choice: plug in number into formula and simplify:

Step 2: Second even number of your choice: plug in number into formula and simplify:


Step 3: First odd number of your choice: plug in number into formula and simplify:


Step 4: Second odd number of your choice: plug in number into formula and simplify:


Step 5: Plug in 0 into formula and simplify:


Answer:

Formula that yields prime numbers.

x² - x + 41

x values selected: 0, 6, 8, 11, 13


if x = 0

x² - x + 41

= 0² - 0 + 41

= 41

41 is a prime number


if x = 6

x² - x + 41

= 6² - 6 + 41

= 71

71 is a prime number


if x = 8

x² - x + 41

= 8² - 8 + 41

= 97

97 is a prime number


if x = 11

x² - x + 41

= 11² - 11 + 41

= 151

151 is a prime number


if x = 13

x² - x + 41

= 13² - 13 + 41

= 197

197 is a prime number


However the expression x² - x + 41 does yield composite numbers as well:

If x = 45

x² - x + 41

= 45² - 45 + 41

= 2021

2021 is a COMPOSITE number. Its factors are: 43 and 47

2021 can be factored into at least two smaller positive integers which not equal to 1.




Thanks for writing.
Staff

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