Prime Number
Find All Numbers P such that all six numbers P , P+2 , P+6 , P+8 , P+12 ,and P+14 are Primes
The answer is 5.
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1 solution
there is only one such number, namely p=5 , We easily find that the required property does not hold for p smaller than 5 . For p=5 we obtain primes 5,7,11,13,17,19 - If p is bigger than 5 and p=5k with some positive integer k , then p is composite. - if p=5k+1 then p+14 is divisible by 5 - if p=5k+2 then p+8 is divisible by 5 - if p=5k+3 then p+12 is divisible by 5 - Finally , if p=5k+4 then p+6 is divisible by 5