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29 May 2017, 12:52
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So, Is 12472315 Prime? We know that any prime number other than 2 and 3 is of the form 6n+1 or 6n+5, which basically means that number leaves a reminder of 1 or 5 when divided by 6. Correct? So, this checks out for most of the cases but does not for this number... 12472315. This number leaves a remainder of 1 when divided by 6. So, naturally, I thought this number was prime. Guess what....No. It has 5 as its factor. Any idea where I'm going wrong?
29 May 2017, 12:58
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So, Is 12472315 Prime? We know that any prime number other than 2 and 3 is of the form 6n+1 or 6n+5, which basically means that number leaves a reminder of 1 or 5 when divided by 6. Correct? So, this checks out for most of the cases but does not for this number... 12472315. This number leaves a remainder of 1 when divided by 6. So, naturally, I thought this number was prime. Guess what....No. It has 5 as its factor. Any idea where I'm going wrong?
First of all there is no known formula of prime numbers.
Next:
Any prime number p, which is greater than 3, when divided by 6 can only give the remainder of 1 or 5 (remainder cannot be 2 or 4 as in this case p would be even and the remainder cannot be 3 as in this case p would be divisible by 3).
So, any prime number p, which is greater than 3, could be expressed as \(p=6n+1\) or \(p=6n+5\) or \(p=6n-1\), where n is an integer greater than 1.
But:
Not all number which yield a remainder of 1 or 5 upon division by 6 are primes, so vise-versa of the above property is not true. For example 25 yields the remainder of 1 upon division be 6 and it's not a prime number.
Hope it's clear.
29 May 2017, 16:07
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Yes, it is! Thank you, kind sir.
