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.