how many diffrent ways can the number 50 be written as the sum of two primes?

Question

how many different ways can the number 50 be written as the sum of two primes? (x + y and y + x are not counted as two different ways)

The answer is going to be
4 different ways: 3 + 47, 7 + 43, 13 + 37, 19 + 31

But i just cant get those answers!! i dont know how to get those answers, i would be so happy if somenone could help me :)

Answer 1

Start by LISTING THE PRIME NUMBERS UP TO 50 !!



Then check for the addend...it is a problem in BRUTE FORCE !!



2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,



check each one...what do you get ???



(3 + 47)

(7 + 43)

(13 + 37)

(19 + 31)

AND NO OTHERS !!



But i just cant get those answers!! i dont know how to get those answers...You have to look up the DEFINITION OF A PRIME NUMBER !!



MAD

Answer 2

I have 11+19, 13+37, 17+33, 19+31, 23+27, 43+7, 47+3 assuming that 11+19 and 19+11 are the same then 7 ways total?

Answer 3

3 + 47

7 + 43

13 + 37

19 + 31



There's no formula to do it. You've got to count it out manually. A prime number is any number divisible by itself and by one only, and not by any other number. So, start from one and keep the sum to less than or equal to 50... like 1 + 49, 2 + 48, 3 + 47..(there you go both primes)...

Answer 4

As the sum of two primes means you need two numbers that are both prime numbers that add up to 50 so list the prime numbers up to 50.



2,3,5,7,11,13, 17, 19,23,29,31,37,41,43,47



now out of these numbers which will add up to 50?



47+3 = 50

43+7 = 50

37+13=50

31+19=50



Notice we're picking high numbers and combining them with low numbers until we meet kind of in the middle indicating we have ran out of options.

Answer 5

I don't know of any systematic way to do this, but if you are looking to determine whether a large

number is prime, take the square root of that number. For instance the square root of 47 is (6.8)

if no prime less than 6 divides 47, you may conclude that 47 is prime. A little lesson I remember from

Number Theory. To answer your question, trial and error would be my best guess, but I could be wrong. The prime factorization of 50=2*5^2. There aren't that many primes smaller than 50 whose sum is 50. naturally, you would run into problems if the prime number was much larger, but I don't

think that's something you have to worry about.

Answer 6

start from first prime 2

2+48 rejected as 48 is not prime

3+47 yes both are prime

5+45 rejected

7+43 yes

11+39 reject

13+37 yes

17+33 reject

19+31 yes

if you proceed further you get the above accepted number to repeat

Answer 7

I'd approach it by listing the primes up (1/2)*50, and subtracting each of them from 50. If the result is a prime, then add it to your list of answers.