the only prime that is the sum and difference of two primes?

Answer 1

5 is the sum of 2 and 3 and 5 is the difference between 2 and 7.

Stop posting questions from your homework. It's that worksheet where there are sixty-two questions, whose answers are days of the month twice.

Answer 2

5

Answer 3

Your question is what is the only prime with this property. 5 has this property. To show it is the only such prime:

If p is the sum of two primes

p = p2 + p3

Then since p must be odd, either p2 or p3 is even, so one of these is the prime 2 which is the only even prime. Assume p3 = 2 and p = p2 + 2

If p is the difference of two primes

p = p3 - p4, then both p3 and p4 cannot be odd since p is odd, so p4 = 2 and p = p3 -2.

Setting p = p2 + 2 = p3 -2, we see that the numbers

p2, p2+2, p2+4 are all prime. If p2 is not 3, then p2 = 3k+1 or p2 = 3k+2.

If p2 = 3k+1 then p2 = 3k +3 is a multiple of 3, a contradiction.

If p2 = 3k + 2 then p2 + 4 = 3k+6 is a multiple of 3, a contradiction.

Therefore p2 = 3 and the only possible value for p is 5.

Answer 4

Just to give a bit of help in solving these yourself. You should first think that nearly all primes are odd. If you add two of these together then you have an even number which will not be prime. So one of the numbers added must be even.

The only even prime is 2.

Now just try trial and error on the small primes and the answer is soon found.

Answer 5

2+3=5, 7-2=5, 2, 3, 5 and 7 are all prime numbers, so your answer is 5. Although someone suggested 1, you'll find that neither 1 nor 0 is a prime number because 0 times anything is 0 making it a composite number and 1 is neither prime nor composite.

Answer 6

2+3=5
7-2=5

Answer 7

2+3=5
7-2=5

Answer 8

the answer is 5

2 + 3 = 5

7 - 2 = 5

Answer 9

9

Answer 10

0 + 1 = 1
1- 0 = 1

Though zero isn't thought of as prime. Anyway, it doesn't match the other answers, so you have something to stir a debate with your teacher. I'd choose to be a smart &%$ whenever possible. It makes math more fun.