Prime numbers

13
Found 2nd Apr
A>3

A, A+2, A+4

Can all the above 3 numbers be prime?

Yes/No and a reason why
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12 Comments
If A=1,then yes. 1,3 and 5 are prime numbers. Same if A=3.
Does A>3 indicate A is greater than 3 ?
A=5 7 11
kester763 m ago

A=5 7 11


That would be 5+4 =9
u6645412 m ago

That would be 5+4 =9


My bad, added 4 to 7.
kester7614 m ago

Does A>3 indicate A is greater than 3 ?


Yep.

To Ollie's original question - no, they can't all be prime, as exactly one of {a,a+2,a+4} must be divisible by 3.
To see this, do you understand modular arithmetic?

If a ≡ 0 (mod 3), then it's divisible by 3 and hence not prime.
If a ≡ 1 (mod 3), then (a + 2) ≡ 0 (mod 3) and hence is not prime
If a ≡ 2 (mod 3), then (a + 1) ≡ 0 (mod 3) and hence is not prime


If the above doesn't make sense, let me know.


I'm hopng that we're not just doing your homework for you?
Edited by: "Illusionary" 2nd Apr
A=17

i will leave it there for my stupidity

in my head it went 17 19 23 haha
Edited by: "pinkleponkle" 2nd Apr
pinkleponkle1 m ago

A=17


Then a + 4 = 21 = 3 × 7
Edited by: "Illusionary" 2nd Apr
I’m going to say no. Without any real proof but logical enough. All prime numbers over 3 must be odd.
If you add 2 it will probably make it divisible by 3 and if not the it will be divisible by 5.
A=7 9 11 9/3
A=11 13 15 15/5
A=9 11 13 9/3
A= 13 15 17 15/3 or 5

All primes can’t be even after 2 and cannot end with 5 or 0.
Oneday775 m ago

I’m going to say no. Without any real proof but logical enough. All prime n …I’m going to say no. Without any real proof but logical enough. All prime numbers over 3 must be odd. If you add 2 it will probably make it divisible by 3 and if not the it will be divisible by 5.A=7 9 11 9/3 A=11 13 15 15/5A=9 11 13 9/3A= 13 15 17 15/3 or 5All primes can’t be even after 2 and cannot end with 5 or 0.


Divisibility by 5 is a red herring, but considering divisibility by 3 is indeed the way to go. See my post above for a full explanation.
Original Poster
A+2 cannot be even otherwise it would be divisible by 2.

Therefore if A+2 is odd, A, A+2 and A+4 are 3 consecutive odd numbers. Out of 3 consecutive odd numbers one will always be divisible by 3.

Where A>3 it eliminates 1,3,5 and 3,5,7 which are the only 2 exceptions.
OllieSt12 m ago

A+2 cannot be even otherwise it would be divisible by 2.Therefore if A+2 …A+2 cannot be even otherwise it would be divisible by 2.Therefore if A+2 is odd, A, A+2 and A+4 are 3 consecutive odd numbers. Out of 3 consecutive odd numbers one will always be divisible by 3. Where A>3 it eliminates 1,3,5 and 3,5,7 which are the only 2 exceptions.


Yep - just make sure that you understand how to prove your assertion about three consutive odd numbers.
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