Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**mjdm****Guest**

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

like this: 7= prime - prime

**mjdm****Guest**

Anyone plz help me!!!!

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

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..."

Offline

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

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

**igloo** **myrtilles** **fourmis**

Offline

**mjdm****Guest**

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

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

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

Offline

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

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..."

Offline