Express following prime number as the sum of three primes - :
$41 = . . . . . . . . . . + . . . . . . . . . . + . . . . . . . . . . . .$

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Solution

Since, we can express prime number as the sum of three prime numbers.
So, $41 = 3 + 7 + 31 = 3 + 19 + 19 = 5 + 5 + 31 = 5 + 7 + 29 = 5 + 13 + 23 = 5 + 17 + 19 = 7 + 11 + 23 = 7 + 17 + 17 = 11 + 11 + 19 = 11 + 13 + 17$
In this expression prime number expressed as the sum of the three prime numbers $3, 7, 31$ and many more combinations.

Hence , we can write $41 = 3 + 7 + 31 = 3 + 19 + 19 = 5 + 5 + 31 = 5 + 7 + 29 = 5 + 13 + 23 = 5 + 17 + 19 = 7 + 11 + 23 = 7 + 17 + 17 = 11 + 11 + 19 = 11 + 13 + 17$

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