smallest n = 2
n = 2 ---> 2,4,6 nope
n = 3 ---> 3,5,7 YES
n = 5 ---> 5,7,9 nope
n = 7 ---> 7,9,11 nope
n = 11 ---> 11,13,15 nope
..
n = 23 --> 23, 25, 27, nope
Other than 2, all primes are odd
so we need 3 sequential odd numbers to have the above property
BUT, since one of every three sequential odd numbers is a multiple of three, at least one of them can't be prime
so 3,5,7 is the only one
there is 1 of them
For how many different positive integers n will n, n+2, and n+4 represent three different prime numbers?
A. none
B. 1
C. 2
D. 3
1 answer