Register to reply 
The only 3 consecutive odd numbers that are primes are 3,5,7 
Share this thread: 
#1
Oct2809, 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?? 


#2
Oct2809, 12:45 PM

P: 1,398

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  
NonConsecutive 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 