Prove or disprove that there is a prime p>3 such that p, p+2, and p+4 are prime.
This is for an online discrete math class and I know it should be easy but I just can't figure out where to start!
2007-07-14 05:24:28 · 2 answers · asked by maria c 1 in Science & Mathematics ➔ Mathematics
One of p, p+2, p+4 has to be divisible by 3. If p = 3n+1, then p+2 = 3n+3. If p = 3n+2, then p+4 = 3n+6. QED
2007-07-14 05:29:48 · answer #1 · answered by Scythian1950 7 · 4⤊ 0⤋
There is no such prime.
Of p, p+2 and p+4, one of these is a multiple of 3.
Let's show this.
If p is a multiple of 3, then p, being prime, is equal to 3.
Suppose p = 3n+1,
Then p+2 = 3n +1+2 = 3n+3, a multiple of 3.
Finally, suppose p = 3n+2
Then p + 4 = 3n+2+4 = 3n+6, also a multiple of 3.
So the only possibility is p=3.
2007-07-14 11:45:47 · answer #2 · answered by steiner1745 7 · 0⤊ 0⤋