Prime Numbers - Magic Trick!! - Part 2 | Fun Math | Don't Memorise

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[InfinityLearn_NEET]

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[amoldalmia]

Every prime number > 3 can be expressed as 6n + 1 or 6n - 1. That is because:

6n + 2 = 3 (n+1) which has 3 as a factor, hence it is composite.
6n + 3 = 2 (n+1) which has 2 as a factor, hence it is composite.
6n + 4 = 2 (3n + 2) which has 2 as a factor, hence it is composite.
6n + 5 = 6 (n+1) - 1. In this case, (n + 1) is the new n, so it can be expressed as 6n - 1.
6n + 6 = 6 (n+1) which has 6 as a factor, hence it is composite.

However, not every number in the series 6n + 1 and 6n - 1 is prime. For example, for n = 20, 6n + 1 = 121 (divisible by 11) and 6n - 1 = 119 (divisible by 7 and 17) are not primes.

[InfinityLearn_NEET]

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Not always!
For eg:
If n = 4, (6n + 1) = [6(4) + 1] = 25 —> Not Prime
If n = 6, (6n - 1) = [6(6) - 1] = 35 —> Not Prime
Do let us know more such numbers…

[wiiziples]

1:01 something that needs to be cleared is he said if the number is a prime these functions are applicable but that doesn't mean here n can be any number...

[Daudkhan]

Amazing work you guys are doing
Thank you so much
Huge respect to you guys
It helped me a lot

[satishkumarsingh]

Nice explanation with proof one thing if you add in it. It will be applicable for only prime numbers only. Ie greater then 3 and less then 25.

[adithyar]

(6n+1) >3 is not always prime number because
6n+1
Were we can substitute 8 in the term n
So we get 6*8+1
That is
48+1
So it is 49
It in not prime number
Similarly for 6n-1 also

[shubhnandu]

why did you square and subtract 1? what does it prove?

[SuperMtheory]

What is the proof that a prime grater than 3 can be written as either 6n+1 or 6n-1?

[utkarshgaurav]

No in the case of 4 as n because when we take n=4, 6n+1= (6*4)+1= 25 which is not a prime number.

[sonytv]

Neet playlist and new neet videos can you make sir

[PRIYAK-cu]

what about 91??
91 is not a prime number. But 91^2-1=8280 is divisible by 24.

[castle]

527 = 6*88 - 1, but it is not prime number..it is divisible but 17 and 31
Similarly 391 is not prime number

[nikhilsevakula]

It is failed for number 527.
527 is not prime number.
But it follows (a^2-1)/24

[sujatasharma]

For a laymen, Euclid's lemma proof of the same is more understandable.

[prasoon]

No, if we take n=4 then 6(4)+1=25 which is not a prime number

[sorokaibamprempremchandra]

who can answer this ..five triplet of prime numbers such that the sum of the first two is the third

[quark]

No it's not 🚫.if n=4, (6n+1)= 25, which is not a prime no.

[gorikasinghal]

But, why isnt converse true? Is there any proof of it?

[SunilSingh-rsdq]

No
6* 4 = 24 + 1 =25
Which is not primw