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# Math - Prime number

87 replies to this topic

### #71 Royal

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Posted 23 October 2008 - 01:30 AM

Spoiler for Thoughts

Edited by Royal, 23 October 2008 - 01:31 AM.

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### #72 nobody

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Posted 23 October 2008 - 08:02 AM

Spoiler for Thoughts

Why 26 is a herring?
Then proof the same problem when 26 is 27.
I mean proof that a*a + 27 is not prime when a is prime.
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### #73 Prime

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Posted 23 October 2008 - 08:44 AM

...
Now, since a is prime, it can not be a mutliplier of 3. Then either (a+1) or (a-1) should be a multiplier of 3.
Then (a-1)*(a+1) is multiplier of 3
And (a-1)*(a+1) +27 is also multiplier of 3
Then it's not prime.
...

3 is a prime, yet it is a multiplier of 3.
(3-1)*(3+1) is not a multiplier of 3.
(3-1)*(3+1) + 27 is also not a multiplier of 3.
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Past prime, actually.

### #74 Prime

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Posted 23 October 2008 - 08:49 AM

Spoiler for Thoughts

Try P2 + 40. Where P is a prime and P > 5.
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Past prime, actually.

### #75 nobody

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Posted 23 October 2008 - 09:03 AM

3 is a prime, yet it is a multiplier of 3.
(3-1)*(3+1) is not a multiplier of 3.
(3-1)*(3+1) + 27 is also not a multiplier of 3.

You're right, but this doesn't make my proof invalid.
I should only make a modification:
Now, since a is prime, IF IT IS NOT 3 THEN it can not be a mutliplier of 3. Then either (a+1) or (a-1) should be a multiplier of 3.
IF IT IS 3 THEN 3*3 + 26= 35 and it is not prime. Then in all conditions, if a is prime a*a+26 is not prime.
I'll work on p^2 + 40
I've worked: 7^2 + 40 = 89
then it can be both prime and not.

Edited by nobody, 23 October 2008 - 09:05 AM.

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### #76 Prime

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Posted 23 October 2008 - 05:53 PM

You're right, but this doesn't make my proof invalid.
I should only make a modification:
Now, since a is prime, IF IT IS NOT 3 THEN it can not be a mutliplier of 3. Then either (a+1) or (a-1) should be a multiplier of 3.
IF IT IS 3 THEN 3*3 + 26= 35 and it is not prime. Then in all conditions, if a is prime a*a+26 is not prime.
I'll work on p^2 + 40
I've worked: 7^2 + 40 = 89
then it can be both prime and not.

Now your proof is complete. (I made the same omission, see my earlier posts.)
I suggested P2 + 40 to Royal to shake the apparent notion that P2 + X is likely to be non-prime.
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Past prime, actually.

### #77 danashalang2

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Posted 10 December 2008 - 05:57 AM

Hmmm... Is it this easy? The square of any two primes over 7 (if I remember correctly) can be notated as either (6n+1)^2 or (6n-1)^2
This gives 36n^2+12n+1 and 36n^2-12n+1. Both have the +1 as part of it, so if you add 26 then both will have +27.

So using the first you have 36n^2+12n+27 and in the second you have 36n^2-12n+27. Both of these factor by 3, so therefore no prime over 7 when squared and added to 26 can equal a prime.

I just realized that the 6n+1 notation is good for 7 also. As is the 6n-1 for 5.

So 3,2,&1:

(3^2)+26 = 35 Non prime
(2^2)+26 = 30 Non prime
27 = Non Prime

Therefore where A = Prime, A^2+26=Prime is false.

hmmm....excuse me, i just want to point out one thing that i think most of you are wrong about is: that "1" is not a prime number!!!!!
my way for doing this question will be the followings:
A^2+26
then we can have A^2-4+30
(A-2)(A+2)+30
(A-2)(A+2) has to be a non prime number except when A=2,3
and it came out as:
when a=2, then A^2+26=30
a=3, then A^2+26=35

if you test for A^2+26 the answer will be a non-prime number!
therefore: A^2+26 is a non Prime
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### #78 DrPie

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Posted 19 December 2008 - 04:31 PM

a=2

(2*2)+ 26=30
4+26=30
30=30
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### #79 etothepii

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Posted 13 February 2009 - 06:57 PM

If "a" is a prime number, then prove, that a*a+26 is NOT a prime number (whether it is true).

i didn't read all of the posts but i think i have the proof.
if a is prime
prove a^2+26 is not prime
a^2 + 26 = a^2 - 4 +30 = (a+2)(a-2) + 30
a is prime there for it can not be divisible by 3
thus a mod3 = 1 or 2
if a mod 3 = 1 then a +2 is divisible by 3
if a mod 3 = 2 then a - 2 is divisible by 3
thus (a+2)(a-2) is divisible by 3 as is 30
therefore a^2 +26 is divisibly by 3
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### #80 Prime

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Posted 13 February 2009 - 09:53 PM

i didn't read all of the posts but i think i have the proof.
if a is prime
prove a^2+26 is not prime
a^2 + 26 = a^2 - 4 +30 = (a+2)(a-2) + 30
a is prime there for it can not be divisible by 3
thus a mod3 = 1 or 2
if a mod 3 = 1 then a +2 is divisible by 3
if a mod 3 = 2 then a - 2 is divisible by 3
thus (a+2)(a-2) is divisible by 3 as is 30
therefore a^2 +26 is divisibly by 3

Good proof, but it lacks the final touch. (Same as several other proofs here.)
a=3 Then a is a prime and it is divisible by 3. This case must be tested separately.
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Past prime, actually.

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