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

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# Math - Prime number

### #71

Posted 23 October 2008 - 01:30 AM

### #72

Posted 23 October 2008 - 08:02 AM

Why 26 is a herring?Spoiler for Thoughts

Then proof the same problem when 26 is 27.

I mean proof that a*a + 27 is not prime when a is prime.

### #73

Posted 23 October 2008 - 08:44 AM

3 is a prime, yet it is a multiplier of 3....

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.

...

(3-1)*(3+1) is not a multiplier of 3.

(3-1)*(3+1) + 27 is also not a multiplier of 3.

Past prime, actually.

### #74

Posted 23 October 2008 - 08:49 AM

Try PSpoiler for Thoughts

^{2}+ 40. Where P is a prime and P > 5.

Past prime, actually.

### #75

Posted 23 October 2008 - 09:03 AM

You're right, but this doesn't make my proof invalid.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.

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.**

### #76

Posted 23 October 2008 - 05:53 PM

Now your proof is complete. (I made the same omission, see my earlier posts.)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.

I suggested P

^{2}+ 40 to Royal to shake the apparent notion that P

^{2}+ X is likely to be non-prime.

Past prime, actually.

### #77

Posted 10 December 2008 - 05:57 AM

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!!!!!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.

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

### #78

Posted 19 December 2008 - 04:31 PM

(2*2)+ 26=30

4+26=30

30=30

### #79

Posted 13 February 2009 - 06:57 PM

i didn't read all of the posts but i think i have the proof.If "a" is a prime number, then prove, that a*a+26 is NOT a prime number (whether it is true).

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

### #80

Posted 13 February 2009 - 09:53 PM

Good proof, but it lacks the final touch. (Same as several other proofs here.)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) + 30a 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

**a=3**Then

**a**is a prime and it is divisible by 3. This case must be tested separately.

Past prime, actually.

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