To determine Recall that a prime number is a natural number whose only factors are itself and 1 (for example, 2, 3, 5, 7, 11 ...). The Goldbach conjecture, posed in 1742, claims that every even number greater than 2 can expressed as the sum of two primes. For examples, 4 =2+2, 6=3+3, 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? Explanation Prime Numbers: A number whose only factors are itself and one. For examples 1,3,5,7,11,13,17,19,23,.... Now consider the following argument: 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. Thus, all 11 test cases are each different, yet the rule works for all 11. This outcome offers a strong inductive argument in favour of the conclusion or rule specified...

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ISBN: 9780135237236

Author: Bennett

Publisher: PEARSON

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Chapter 1.D, Problem 67E

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Recall that a prime number is a natural number whose only factors are itself and 1 (for example, 2, 3, 5, 7, 11 ...). The Goldbach conjecture, posed in 1742, claims that every even number greater than 2 can expressed as the sum of two primes. For examples,

4 =2+2, 6=3+3, 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?

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Chapter 1.D, Problem 66E

Chapter 1.D, Problem 68E

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USING+UNDERSTANDING MATH.(LL)-W/MYMATH.

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