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Anonymous asked in Science & MathematicsMathematics · 12 months ago

# The sum of the first 2 million primes is even or odd?

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There will be one even number (2) in the sum, then the remaining 1,999,999 primes will be odd (because of they were even they'd have 2 as a factor and not be prime).

The sum of an odd number of odd numbers will be odd. Adding 2 to that will not change the parity, so the final sum will still be odd.

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• All primes greater than 2 are going to be odd numbers. The sum of a sequence of odd numbers can be either even or odd. The sum of the first 2 million primes will be the sum of the 1,999,999 primes greater than 2 plus two.

The sum of any sequence of odd numbers will be odd if the count of the sequence is odd and will be even if the count of the sequence is even. Adding 2 to that sum will not change the "odd/even" nature of the sum.

The sum of the first 1,999,999 primes greater than 2 will be odd. Adding 2 to the sum leaves the sum an odd number.

Ans: Odd

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• Even. Once you get to TWO (2) all the subsequent numbers that are prime are odd. So when you add two odd numbers you get an even. The last of the first two million prime numbers is 32,452,843. If you want to see how to get the EVEN answer, see the source below.

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• The sum is odd. 2 is the only even prime number, all other primes are odd. You have a total of 1,999,999 odd primes; if you have an odd number of odd primes being added, the sum is odd, and adding an even number to this sum means the grand sum is odd; odd + even = odd.

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