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## #1 2005-12-13 09:02:16

mjdm
Guest

### Help!!!!

Does anyone know what 2 prime numbers subtracted together that equals 7?

like this:               7= prime - prime

## #2 2005-12-13 09:08:11

mjdm
Guest

### Re: Help!!!!

Anyone plz help me!!!!

## #3 2005-12-13 09:26:09

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Help!!!!

It's not possible, and here is a simple proof to show why:

All prime numbers except 2 are odd.

Case 1: One of the prime numbers is 2:

If one of the prime numbers is 2, the other must be 9, which is not a prime number.

Case 2: Neither of the prime numbers is 2:

Then both prime numbers are odd.  Let x and y be odd numbers.  Then x = 2k + 1 for any integer k (ignoring the restriction for primeness) and y = 2l + 1 for any integer l.

Then x - y = 2k + 1 - (2l + 1) = 2k - 2l = 2(k - 1).  Since k - l is an integer, 2(k - l) is an even integer, and thus not 7.

Therefore the are no two prime numbers such that p1 - p2 = 7.  QED.

Last edited by Ricky (2005-12-13 09:26:57)

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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## #4 2005-12-13 10:25:07

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Help!!!!

What about 2 and -5?  Negatives are probably disallowed, huh?

igloo myrtilles fourmis

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## #5 2005-12-13 11:19:56

mjdm
Guest

### Re: Help!!!!

Yes i cant use negative numbers and -5-2 is -7 but if your trying to say -2+5 it would only equal3.

## #6 2005-12-13 11:42:04

irspow
Member
Registered: 2005-11-24
Posts: 457

### Re: Help!!!!

Ricky was correct in that there are no solutions to your problem.

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## #7 2005-12-13 17:12:06

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: Help!!!!

Negative numbers are not primes, although one could certainly argue that they should be.  But I'm not about to go and change the basic framework of math.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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