What are the Numbers?
Number Theory
Level
2
12345 can be expressed as the summation of two prime numbers in only one way. What is the value of the larger prime number?
The answer is 12343.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Notice that 1 2 3 4 5 is odd. Two primes which are odd always add up to an even number. Since 1 2 3 4 5 is odd, both primes cannot be odd, which implies that one of the primes is even. But the only even prime is 2. Thus one of the primes is 2 and the other one is 1 2 3 4 3 .