37 is not in the Fibonacci number series, but is the sum of two Fibonacci numbers, 34 and 3. Fibonacci numbers are with 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.
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There is no upper bound to the sum of the numbers in the Fibonacci sequence; both the last number in the series and consequently the sum of all these numbers can be made as large as desired by continuing the series to sufficiently many numbers.
1,1,2,3,5,8,13,21,34,55,89 Each number is the sum of the two preceding numbers.
Each term of the series is the sum of the two terms before it.
1,1,2,3,5 and so on, where each number (after the first two) is the sum of the previous two numbers.
The prime numbers between 34 and 44 are: 37 41 43 The sum of these numbers is 37 + 41 + 43 = 121