To express the numbers 21, 31, 53, and 61 as the sum of three odd prime numbers, we first need to remember that odd primes are the prime numbers greater than 2, meaning they start at 3 and include numbers like 3, 5, 7, 11, 13, 17, etc.
a) 21
One possible way to express 21 as the sum of three odd primes is:
7 + 7 + 7 = 21
Alternatively, we can also represent it as:
5 + 7 + 9 = 21
Thus, 21 can be expressed as the sum of three odd primes in various forms.
b) 31
For the number 31, one valid expression could be:
11 + 13 + 7 = 31
Here, we see that the sum of 11, 13, and 7 gives us 31, proving it’s indeed the sum of three odd primes.
c) 53
To express 53, we can use:
19 + 17 + 17 = 53
This shows that we can combine these odd primes to reach the total of 53.
d) 61
For 61, one possible sum is:
19 + 23 + 19 = 61
Again, combining these primes reaches the targeted number effectively.
By using combinations of odd primes, we can express each of the given numbers as the sum of three odd primes.