Question:

A mathematician proposed that "Every even number greater than 2 can be expressed as a sum of two prime numbers." Do you agree? Why?

I agree with the mathematician as:

4 is equal to 2+2

6 is equal to 3+3

8 is equal to 5+3

10 is equal to 5+5

6 is equal to 3+3

8 is equal to 5+3

10 is equal to 5+5

12 is equal to 7+5

14 is equal to 7+7

16 is equal to 13+3

18 is equal to 13+5

20 is equal to 17+3

22 is equal to 17+5

24 is equal to 19+5

26 is equal to 19+7

28 is equal to 23+5

30 is equal to 23+7

32 is equal to 29+3

34 is equal to 29+5

36 is equal to 31+5

38 is equal to 31+7

40 is equal to 37+3

42 is equal to 37+5

44 is equal to 41+3

46 is equal to 41+5

48 is equal to 43+5

50 is equal to 43+7

52 is equal to 47+5

54 is equal to 47+7

56 is equal to 53+3

58 is equal to 53+5

60 is equal to 53+7

62 is equal to 59+3

64 is equal to 59+5

66 is equal to 61+5

68 is equal to 61+7

70 is equal to 67+3

72 is equal to 67+5

74 is equal to 71+3

76 is equal to 71+5

78 is equal to 73+5

80 is equal to 73+7

82 is equal to 79+3

84 is equal to 79+5

86 is equal to 83+3

88 is equal to 83+5

90 is equal to 83+7

92 is equal to 89+3

94 is equal to 89+5

96 is equal to 89+7

98 is equal to 19+79

100 is equal to 97+3

102 is equal to 97+5

These are the first 50 even numbers after 2 and they all are sums of 2 prime numbers. One reason that this statement made by the mathematician is possible is that when 2 primes

(odd numbers except the first prime number(2)) are added together, they form an even number that is always greater than 2.

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