View Single Post
CmbkG
#1
Oct28-09, 10:05 AM
P: 10
1. The problem statement, all variables and given/known data
Show that the only three consecutive numbers that are primes are 3,5,7.


2. Relevant equations



3. The attempt at a solution
let p, p+2, p+4 be three consecutive odd numbers
If p=0(mod3), p is divisible by 3
If p=1(mod 3), p+2 is divisible by 3
If p=2(mod3), p+4 is divisible by 3

This means at least one of p, p+2, p+4 is divisible by 3

Since we are looking for prime numbers 3 can be the only number that is divisible by 3. Therefore we only have 3 possible solutions:

-1,1,3
1,3,5
3,5,7

Since -1 and 1 are not primes the only possible solution is 3,5,7


-I no i have the solution here, its just i was helped with this and i dont quite understand why we bring in (mod3) is that just the way it is done or why do you include it??
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100