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

by CmbkG
Tags: consecutive, numbers, primes
CmbkG is offline
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:


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
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
willem2 is offline
Oct28-09, 12:45 PM
P: 1,351
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).

Register to reply

Related Discussions
Non-Consecutive Fibonacci Numbers... General Math 6
Product of r consecutive numbers divisible by r! General Math 7
Number Theory: Fermat Numbers coprime => infinite # primes Calculus & Beyond Homework 3
Density of primes between square numbers Linear & Abstract Algebra 5
How many primes are there in a certain range of numbers? General Math 1