Question

The sum of the first 1 million primes is N. Without knowing N's value, one can determine that the ones'digit of N cannot be

A) 1
B) 2
C) 3
D) 9

Answer 1

Please help!

Answer 2

Let's think about this. The set of prime numbers, beginning with 2 is: {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...} Do you notice anything strange? Only one of those numbers is even, and that's because if any number in that list other than 2 were even, it'd be divisible by 2, and not be a prime number. So, that means that every prime number except for the first one is an odd number. When you add 2 odd numbers, you get an even number. If you add an even number and an odd number, you get an odd number. So, in the first 1000000 primes, you're adding 1 even number and 999999 odd numbers. So, based on that, can you get your answer?

Answer 3

B?

Answer 4

Yeah, it'd be B or rather, it cannot be any even number in the units digit. THis is because adding 999999 odd numbers will still yield an odd number since you're adding an odd number of odd numbers. So, finally, you're adding 2 with that odd number, making the units digit of N an odd number.

Answer 5

Understood, thanks! :)

Answer 6

Ohh i see now
thanks!