Prime Numbers
<div class="IPBDescription">Fascinating</div> For those not familiar with prime numbers, they are basically numbers that cannot be divided by any other whole number except for 1 and itself.
Examples:
1, 2, 3, 5, 7, 11, 13 and 17 are ALL primes.
Now, a few months ago I was daydreaming in maths, doing anything BUT revision. I stumbled across a pattern.
Take any prime number except for 2. Multiply that number by 3. Now, add or minus 2 from the resulting number, and you will come up with at least one prime and at most two.
Proof
3 * 3 = 9
9 + 2 = 11, A Prime
9 - 2 = 7, A Prime
7 * 3 = 21
21 + 2 = 23, A Prime
21 - 2 = 19, A Prime
Some numbers give only one prime where the other resulting number is not a prime. Either way it looks like a coherent pattern to me.
What says the mathematically minded in here?
Examples:
1, 2, 3, 5, 7, 11, 13 and 17 are ALL primes.
Now, a few months ago I was daydreaming in maths, doing anything BUT revision. I stumbled across a pattern.
Take any prime number except for 2. Multiply that number by 3. Now, add or minus 2 from the resulting number, and you will come up with at least one prime and at most two.
Proof
3 * 3 = 9
9 + 2 = 11, A Prime
9 - 2 = 7, A Prime
7 * 3 = 21
21 + 2 = 23, A Prime
21 - 2 = 19, A Prime
Some numbers give only one prime where the other resulting number is not a prime. Either way it looks like a coherent pattern to me.
What says the mathematically minded in here?
Comments
Alg 1 or 2?
Alg 1 or 2? <!--QuoteEnd--> </td></tr></table><span class='postcolor'> <!--QuoteEEnd-->
I'm taking the second. I've failed all math subjects I've taken in high school at least once. But I somehow managed to get through and still stay only one year behind.
lol.
Interesting thing on prime numbers.
Roffles.
Nice find though.
11*3=33
33+2=35
35 is divisible by 5 and 7.
Your formula is proven wrong.
Edit: Nevermind, you've already addressed this issue.
For example. I could come up with a system such as..... "for any prime number greater than 2, multiply that number by 1.5 and round to the odd integer to get another prime number." Which works on 3,5,7,11, and 13, but when you take 17 and try to generate a new number, it doesn't work :/
Still a pretty neat find tho.
Seconded
Seconded <!--QuoteEnd--> </td></tr></table><span class='postcolor'> <!--QuoteEEnd-->
Thirded.
Seconded <!--QuoteEnd--></td></tr></table><span class='postcolor'><!--QuoteEEnd-->
Thirded. <!--QuoteEnd--> </td></tr></table><span class='postcolor'> <!--QuoteEEnd-->
refuted
Seconded <!--QuoteEnd--></td></tr></table><span class='postcolor'><!--QuoteEEnd-->
Thirded. <!--QuoteEnd--></td></tr></table><span class='postcolor'><!--QuoteEEnd-->
refuted <!--QuoteEnd--> </td></tr></table><span class='postcolor'> <!--QuoteEEnd-->
Owned <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html/emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif'><!--endemo-->
Seconded <!--QuoteEnd--></td></tr></table><span class='postcolor'><!--QuoteEEnd-->
Thirded. <!--QuoteEnd--></td></tr></table><span class='postcolor'><!--QuoteEEnd-->
refuted <!--QuoteEnd--></td></tr></table><span class='postcolor'><!--QuoteEEnd-->
Owned <!--emo&:D--><img src='http://www.unknownworlds.com/forums/html/emoticons/biggrin.gif' border='0' style='vertical-align:middle' alt='biggrin.gif'><!--endemo--> <!--QuoteEnd--> </td></tr></table><span class='postcolor'> <!--QuoteEEnd-->
multiplied by 7!
Haha yes! I think I killed it!
I'd do it myself but I'm really damn lazy <!--emo&:p--><img src='http://www.unknownworlds.com/forums/html/emoticons/tounge.gif' border='0' style='vertical-align:middle' alt='tounge.gif'><!--endemo-->
Or better yet, come up with a formal proof - I'm curious about this.
for starters you'll need the definition of a prime number in math-speak, which would probably look something like this...
an integer Q is prime if: floor(Q/k) != Q/k for all k, 1 < k < Q
but you got me as to where you'd go from there....
Proving several cases does not prove a theory. Proving 999999 cases with a computer program does not prove a theory. What <i>does</i> prove theories is the principle of Mathematical Induction, which I will briefly explain.
The basic idea is to prove that it works for one base case, then prove that it works for case n+1. The idea is that if it worked once, and it always works for "the next number" then it must always work.
Anyway, I can't help any further because while I understand the principle I'm terrible at applying it <!--emo&:)--><img src='http://www.unknownworlds.com/forums/html/emoticons/smile.gif' border='0' style='vertical-align:middle' alt='smile.gif'><!--endemo-->. Might want to do a Google, though.
I got 41 from 13, and decided to try it with 41...
(41 x 3) - 2 = 121 (121/11 = 11)
(41 x 3) + 2 = 125 (125/5 = 25)
Nice try though, maybe it works only up to numbers whose quotients are less than 100.
To lazy to try though, here are the numbers:
3 5 7 11 13 17 19 23 29
31 37
Proving several cases does not prove a theory. Proving 999999 cases with a computer program does not prove a theory. What <i>does</i> prove theories is the principle of Mathematical Induction, which I will briefly explain.
The basic idea is to prove that it works for one base case, then prove that it works for case n+1. The idea is that if it worked once, and it always works for "the next number" then it must always work.
Anyway, I can't help any further because while I understand the principle I'm terrible at applying it <!--emo&:)--><img src='http://www.unknownworlds.com/forums/html/emoticons/smile.gif' border='0' style='vertical-align:middle' alt='smile.gif'><!--endemo-->. Might want to do a Google, though. <!--QuoteEnd--> </td></tr></table><span class='postcolor'> <!--QuoteEEnd-->
to my understanding. It is not applicable to something such as prime numbers where there is no surefire method for generating the next prime number in the series.
It however applies very well to things like the fibbonacci sequence :/