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Consecutive numbers will always total an odd number. Consecutive odd numbers or consecutive primes would be 5 and 7.
3, 5 and 7 are consecutive odd prime numbers.
There are no two consecutive odd numbers.
None that are all odd numbers. But, there are two sets of three consecutive numbers containing a mix of even/odd that add up to 120. They are 39, 40 and 41 and also 38, 40 and 42.
The numbers are 39, 41 and 43.