# The only 3 consecutive odd numbers that are primes are 3,5,7

by CmbkG
Tags: consecutive, numbers, primes
 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??
 P: 1,284 One way of proving that a number (or at least one of 3 numbers) isn't prime, is proving that it is divisible by another prime. We know the numbers are odd, so 3 is the next candidate. One way of proving a result concerning divisibility by a particular number, is to consider all cases modulo that number, in this case p=0,1,2 (mod 3).

 Related Discussions General Math 6 General Math 7 Calculus & Beyond Homework 3 Linear & Abstract Algebra 5 General Math 1