2, 3, 5, and 7
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No. The sum of four consecutive integers is two odd numbers plus two even numbers which is an even number. 2001 is an odd number, therefore it cannot be the sum of four consecutive numbers.
The sum of the first four prime numbers is 17.
There is no prime number between 60 and 80 that has a consecutive sum. The prime numbers between 60 and 80 are 61, 67, and 71, but none of them have consecutive sums.
There are four consecutive 3-digit numbers with a sum of 2,494: 622, 623, 624 and 625.
19 and 23