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

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Ricky
2005-12-14 16:12:06

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.

irspow
2005-12-14 10:42:04

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

mjdm
2005-12-14 10:19:56

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

John E. Franklin
2005-12-14 09:25:07

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

Ricky
2005-12-14 08:26:09

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.

mjdm
2005-12-14 08:08:11

Anyone plz help me!!!!

mjdm
2005-12-14 08:02:16

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

like this:               7= prime - prime