The first ten consecutive composite positive integers are:
114 115 116 117 118 119 120 121 122 123
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16,17,18,19,20,21,22,23,24,25.
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 !!!!!
The ten numbers from 1 to 10.
There are infinitely many composite numbers. There are, therefore, infinitely many subsets of ten such numbers. There are, therefore, infinitely many possible sums.
4, 6, 8, 9, 10, 12, 14, 15, 16, 18