Question

In 1742, Christian Goldbach conjectured that every even number greater than 2 can be written as the sum of two prime numbers. Many mathematicians have tried to prove or disprove this conjecture without succeeding. Show that Goldbach's conjecture is true for each of the following even numbers. (There may be more than one correct answer.)

Answer 1

The Goldbach's conjecture is true for each of the following even numbers.

(a) 19+5

(b) 43+7

(c) 83+3

(d) 139+5

(e) 199+11

(f) 257+7

What is Goldbach's conjecture?

One of the most well-known and enduring open questions in number theory and all of mathematics is Goldbach's conjecture. It says that the sum of two prime numbers is the even natural number higher than two.

According to the given information:

A. 24 can be expressed as:

   24 = 19 + 5

B. 50 can be expressed as:

    50 = 43 + 7

C. 86 can be expressed as:

    86  = 83 + 3

D. 144 can be expressed as:

    144 = 139 + 5

E. 210 can be expresses as:

    210 = 199 + 11

F. 264 can be expresses as:

  264 = 257 + 7

The Goldbach's conjecture is true for each of the following even numbers.

(a) 19+5

(b) 43+7

(c) 83+3

(d) 139+5

(e) 199+11

(f) 257+7

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I understand that the question you are looking for is:

In 1742, Christian Goldbach conjectured that every even number greater than 2 can be written as the sum of two prime numbers. Many mathematicians have tried to prove or disprove this conjecture without succeeding. Show that Goldbach’s conjecture is true for each of the following even numbers.

a. 24,

b. 50,

c. 86,

d. 144,

e. 210,

f. 264