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## Dumb question

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• This is probably going to sound like a really dumb question with the answer being a resounding no, but, is there anyway, given a number which is the result of
Message 1 of 4 , Feb 1, 2002
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This is probably going to sound like a really dumb question with the answer
being a resounding no, but, is there anyway, given a number which is the
result of multiplying two primes together, to ascertain what the sum of
those two factors is? I suppose it's dumb because given the sum of the two
factors it is trivial to work out the factors and so can't be done.
TIA,
David
• If n=pq, and x=p+q, we can say x =2sqrt(n), and x
Message 2 of 4 , Feb 1, 2002
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If n=pq, and x=p+q, we can say x>=2sqrt(n), and x<(n/2)+2.

I don't think there is anything else we can infer.

>I suppose it's dumb because given the sum of the two
>factors it is trivial to work out the factors and so can't be done.

If 20=p+q, what are p and q? And from this, what is pq?

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

-----Original Message-----
From: David Litchfield [mailto:Mnemonix@...]
Sent: 01 February 2002 18:02
To: Prime Numbers List
Subject: [PrimeNumbers] Dumb question

This is probably going to sound like a really dumb question with the answer
being a resounding no, but, is there anyway, given a number which is the
result of multiplying two primes together, to ascertain what the sum of
those two factors is? I suppose it's dumb because given the sum of the two
factors it is trivial to work out the factors and so can't be done.
TIA,
David

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• Automatic typo correction program spotted a typo in Jon Perry s email: RE:[PrimeNumbers]Dumb Question Please read: x
Message 3 of 4 , Feb 1, 2002
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Automatic typo correction program spotted a typo in Jon Perry's email:

RE:[PrimeNumbers]Dumb Question

Please read:

x<=(n/2)+2

for:

x<(n/2)+2

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

-----Original Message-----
From: Jon Perry [mailto:perry@...]
Sent: 01 February 2002 18:38
To: Prime Numbers List
Subject: RE: [PrimeNumbers] Dumb question

If n=pq, and x=p+q, we can say x>=2sqrt(n), and x<(n/2)+2.

I don't think there is anything else we can infer.

>I suppose it's dumb because given the sum of the two
>factors it is trivial to work out the factors and so can't be done.

If 20=p+q, what are p and q? And from this, what is pq?

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

-----Original Message-----
From: David Litchfield [mailto:Mnemonix@...]
Sent: 01 February 2002 18:02
To: Prime Numbers List
Subject: [PrimeNumbers] Dumb question

This is probably going to sound like a really dumb question with the answer
being a resounding no, but, is there anyway, given a number which is the
result of multiplying two primes together, to ascertain what the sum of
those two factors is? I suppose it's dumb because given the sum of the two
factors it is trivial to work out the factors and so can't be done.
TIA,
David

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
The Prime Pages : http://www.primepages.org

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
The Prime Pages : http://www.primepages.org

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
• ... Hmm. Shame. ... Well, the reason I say it s trivial is for this. Assume the number you ve been given is say 51 and we want to work out p and q. If we knew
Message 4 of 4 , Feb 1, 2002
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> If n=pq, and x=p+q, we can say x>=2sqrt(n), and x<(n/2)+2.
>
> I don't think there is anything else we can infer.

Hmm. Shame.

>
> >I suppose it's dumb because given the sum of the two
> >factors it is trivial to work out the factors and so can't be done.
>
> If 20=p+q, what are p and q? And from this, what is pq?

Well, the reason I say it's trivial is for this. Assume the number you've
been given is say 51 and we want to work out p and q.

If we knew p + q = 20 we could say

20 / 2 = 100

100 - 51 = 49

sqrt(100) = 10
sqrt(49) = 7

10 - 7 = 3
10 + 7 = 17

17 * 3 = 51

All numbers whose factors add up to give n share the same perfect squares as
per fermat

e.g. p + q = 20

3 * 17 = 51, 3 + 17 = 20, 20 / 2 = 100, 100 - 51 = 49
5 * 15 = 75, 5 + 15 = 20, 20 / 2 = 100, 100 - 75 = 25
7 * 13 = 91, 7 + 13 = 20, 20 / 2 = 100, 100 - 91 = 9
9 * 11 = 99, 9 + 11 = 20, 20 / 2 = 100, 100 - 99 = 1

Cheers,
David Litchfield
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