Find all positive integers n such that n, n + 2, n + 4 are all prime.
2006-09-12 10:02:49 · 8 answers · asked by jjodom1010 3 in Science & Mathematics ➔ Mathematics
n == n + 0 mod 3
n+2 == n - 1 mod 3
n+4 == n + 1 mod 3
so precisely one of these numbers must be a multiple of 3
the only multiple of 3 that is prime is 3 itself. Therefore, we have the options
n = 1: (1, 3, 5) but 1 is not prime
n = 3: (3, 5, 7) which qualifies
Therefore the only solution is n = 3.
2006-09-12 10:26:34 · answer #1 · answered by dutch_prof 4 · 0⤊ 0⤋
N=3
2006-09-12 10:31:41 · answer #2 · answered by red1967 4 · 0⤊ 0⤋
1 and 3
2006-09-12 11:01:30 · answer #3 · answered by Anonymous · 0⤊ 1⤋
3
2006-09-12 10:03:56 · answer #4 · answered by pittisit43 4 · 1⤊ 1⤋
It is easy to show that one of (n, n+2, n+4) must be divisible by 3. Now 3 is the only prime multiple of 3, therefore 3 must be one of these numbers. But (1, 3, 5) is not an answer, so it is fortunate that n=3 gives (3, 5, 7), which is an answer. There cannot be any more, because one of them would always be a composite multiple of 3.
2006-09-12 10:07:55 · answer #5 · answered by Anonymous · 0⤊ 2⤋
Your question involves two separate things! INTEGERS and PRIME NUMBERS.
Integers are just all whole numbers.
While Prime numbers are any and all Numbers that are not divisible by any integers , or whole numbers.
Like-------- 1, 3, 5,,7, 11, 13, 17, 19, 23, 29, 31, 37, 39 41, 43, 47, 49, and so on. I hope this helps you out.
2006-09-12 10:18:17 · answer #6 · answered by joey 2 · 0⤊ 2⤋
Using substitution, I find that n = the whole prime numbers less than five.( 1, 3)
2006-09-12 10:11:49 · answer #7 · answered by golden_retriever4u 2 · 0⤊ 1⤋
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2016-09-30 21:26:26 · answer #8 · answered by ? 4 · 0⤊ 0⤋