The numbers are 16, 18, 20, 22 and 24.
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There are no two consecutive even numbers whose sum is 100. It is easily proved.
In 100 numbers you can select 50 all odd or 50 all even and there will be no consecutive pair. Picking another number must be of the opposite parity and so consecutive with one of your first 50.
2 and 3 are the only consecutive numbers that are prime.
104
None exist. 100 is an even number and two consecutive integers can only add up to an odd number. This is because only 2 evens can add up to an even number and no two even numbers are consecutive. (or two odds, but no two odd numbers are consecutive either)