4, 6, 8, 9, 10, 12, 14, 15, 16, 18
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The first ten consecutive composite positive integers are: 114 115 116 117 118 119 120 121 122 123
The sum first Prime number is (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 ) = 129 The sum of the first composite numbers is (4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18) = 112 The difference is 129 - 112 = 17 !!!!!
There are infinitely many composite numbers. There are, therefore, infinitely many subsets of ten such numbers. There are, therefore, infinitely many possible sums.
There are more than ten composite numbers and what they have in common is that they all have more than two factors whereas prime numbers have only two factors which are themselves and one.
-- Write down a list of the first ten whole numbers. -- For each one, multiply it by itself, and write the product next to it.