Question

The sum of two prime numbers is 39. Find the product of the prime numbers.

Answer 1

Step-by-step explanation:

37+2=39(both 37 and 2 are prime number))

37×2=74( product)

Answer 2

The product of the two prime numbers 2 and 37 is given as 74.

Prime numbers are numbers which do not have any divisors expect the number 1 and the number itself.

This means that prime numbers are not divisible by any other number other than one and itself.

When divided the prime numbers should not give the remainder as 0 making it a prime number as it is not divisible or does not follow the divisibility rules for any number.

The sum of two prime numbers are said to be 39 and hence the numbers that add up to 39 are to be found out.

The prime numbers which when added should give the result as 39 so all the prime numbers below 39 must be considered.

We know that the smallest prime number is said to be the number 2 and thus the prime numbers which sums up to 39 would be between this interval.

The list of prime numbers below 39 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

Let the two prime numbers be x and y.

$\implies x+y=39$

If we consider $x=2$ then

$y=39-x$

$\implies y=39-2\\\implies y=37$

Since, 2 and 37 are both prime numbers which sum up to 39 these are the x and y values.

Their product thus becomes 74.

If we consider checking another pair and take $x=3$ then

$y=39-3=36$

36 is not a prime number so this pair is not considered.

Similarly if we take $x=5$ then $y=39-5=34$ which is also not a prime number.

If we try this with all the other numbers it would still result in one of the numbers to be a non prime one.

Thus, the pair of numbers that sum up to 39 are 2 and 37 and their corresponding product is 74.

A point to be noted here is that all the numbers in the above given list of possible prime numbers are odd numbers and 39 is and odd number as well.

The difference between two odd numbers will always be an even number which is always divisible by 2 as we know and hence none of the pairs would satisfy the condition except 2 which is an even number.

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