#If p < q are two consecutive odd prime numbers, show that p + q has atleast 3 prime factors

59 messages · Page 1 of 1 (latest)

ripe aurora
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The factors not necessary district

So

Cause they are consecutive we get

Q=p+2
So that means

P+q=2p+2

2(p+1)

P is odd so we get

2×2×(x)

Now how can we proof that x is prime or we can just ignore some cases

pearl perchBOT
#
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ripe aurora
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If p < q are two consecutive odd prime numbers, show that p + q has atleast 3 prime factors

vernal hedge
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q = p+2 ??? Explain?

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@ripe aurora

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It's not necessarily true

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For example 7 and 11

ripe aurora
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Yeah I'm tryna use 2k instead this is my friend version

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So it was wrong?

vernal hedge
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No 2k seems fine

ripe aurora
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Okay then its going to be

2(p+k)

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Well do you know what step should I do next

vernal hedge
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OK so are you aware that any composite number greater than 1 has atleast 2 prime factors

ripe aurora
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No im not aware abt that

But that's true

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So based of this

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We get at least 2 prime factor

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But we still need one more

vernal hedge
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No so p + q is divisible by 2 right?

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so p+q/2 is composite

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3 factors

ripe aurora
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Make sense

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Thank you

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Uhhh wait actually no

vernal hedge
# ripe aurora Make sense

Are you sure? You should look up the proof of why composite numbers greate than 1 have atleast 2 factors

ripe aurora
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What if (p+q)/2 is R and R is prim

vernal hedge
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Sum of 2 consecutive primes / 2 , prime?

ripe aurora
vernal hedge
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No if primes are greater than 2 then no

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I can prove it if you want

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@ripe aurora

ripe aurora
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Yeah thank you I like to see it

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It will grant me more idea

vernal hedge
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So let's start with little basic stuff

a+b/2 lies between ?

ripe aurora
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A and b

vernal hedge
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OK so in our case

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It will be between p and q

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Right?

ripe aurora
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Yup

vernal hedge
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p and q are consecutive primes

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There are no primes in between them

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So It's can't be prime

ripe aurora
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Oh yeah

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That explains

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Dang I found this idea earlier but somehow I forgot it

vernal hedge
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This is only true for consecutive *

ripe aurora
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So we finally proof it now?

vernal hedge
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Yeah we have 2 as one of the factor and 2 others

ripe aurora
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Maybe not all quora answer is right

vernal hedge
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Don't forget to look up the proof of why composite number have 2 prime factors

ripe aurora
vernal hedge
ripe aurora
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Goodbye anywah hope we meet again

vernal hedge
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If it doesn't have 2 prime factors then it will be prime itself

ripe aurora
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+close

fierce jettyBOT
# ripe aurora +close
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# fierce jetty

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