Recall that a prime number is a natural number whose only factors are itself and 1 (for example, 2, 3, 5, . . ). the goldbach conjecture, posed in 1742, claims that every even number greater than 2 can be expressed as the sum of two primes. for example, 4 = 2 + 2, 6 = 3 + 3, and 8 = 5 + 3. a deductive proof of this conjecture has never been found. test the conjecture for at least 10 even numbers and present an inductive argument for its truth. do you think the conjecture is true? why or why not?

Prime Number is a number whose only factors are itself and one. For example 1,3,5,7,11,13,17,19,23… Now consider the following arguments : Every even number greater than 2 can be expressed as sum of two primes. Now consider the following premises:

Premise 1 : 4 = 2 + 2 

Premise 2 : 10 = 5 + 5 

Premise 3 : 12 = 5 + 7 

Premise 4 : 16 = 5 + 11 

Premise 5 : 18 = 5 + 13 

Premise 6 : 22 = 11 + 11 

Premise 7 : 30 = 7 + 23 

Premise 8 : 32 = 3 + 29 

Premise 9 : 40 = 3 + 37 

Premise 10 : 52 = 5 + 47 

Premise 11 : 100 = 3 + 97 

Conclusion : every whole number is sum of two prime numbers. 

All 11 cases are different, yet the rule applies to all. This outcome offers a strong inductive argument in favor of the conclusion or rule specified. It can be strengthened by additional cases that confirm the rule. Conjecture specified will be true because each number can be specified as sum of two primes. As each whole number will have difference os 1, 2, 3, 5, or 7 between the number and the nearest prime number. Consider the following example :

34 = 31 + 3 

36 = 33 + 3 

Hence the conjecture “Every number greater than two can ve expressed as the sum of two primes” is true.

b.an increase in a causes b to decrease