2. What is the smallest prime which is the sum of five different primes?
A 39
B 41
C 43
D 47
E 53
Solution
C
If five different primes include 2 , they consist of 2 and four odd primes. Hence their sum is even and hence is not prime.
Therefore five different primes whose sum is also prime cannot include 2. Hence they are five odd primes.
The sum of the first five odd primes is $3+5+7+11+13=39$, which not prime.
The smallest prime greater than 13 is 17 . If we replace 13 by 17 we obtain the sum $3+5+7+$ $11+17=43$, which is prime.

It follows that the smallest prime that is the sum of five different primes is 43 .
For INVESTIGATION
2.1 Which is the smallest prime which is the sum of six different primes?
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