Sum of Primes?
Number Theory
Level
4
Find the smallest number with 3 representations as a sum of 3 prime numbers?
Note: Prime numbers used may be same.
The answer is 15.
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1 solution
Moderator note:
Simple approach of checking all small cases.
Smallest prime numbers start from 2,3,5,7,11,13.. By initial observation 2+3 =>5, 2+5=>7;
Since minimum 3 representations are required, our number has to be > 10; 5+5+5 =>15, ...(equation 1) now shift one 2 from one of the 5's to any other 5's => (5-2)+(5+2)+5 or => 3+7+5 =>15 shifting one 3's from eq 1 , or two 2's from two 5's would not lead in prime number for the third.. Shifting two 3's lead in the same (5-3)+(5-3)+(5+6) => 15 2+2+11 =>15
Hence 15 :)