Question

What will be the remainder when sum of squares of all prime numbers greater than 3 but less than 100 is divided than 6

Answer 1

@sidsiddhartha @tkhunny @mathslover @ganeshie8
I got the answer as 23

Answer 2

@experimentX

Answer 3

Remainder? How could it be greater than 6?

Answer 4

There are 23 Prime Numbers between 3 and 100 (noninclusive)

Find them. Add them up. Divide by 6. THEN you will have a Remainder.

Answer 5

wolf calculated it as 5
http://www.wolframalpha.com/input/?i=Mod%5BSum%5BPrime%5Bi%5D%2C+%7Bi%2C+3%2C+25%7D%5D%2C+6%5D
but i don't know how to prove it.

Answer 6

I did it using a algebraic method

Answer 7

how did you represent the prime number?

Answer 8

@tkhunny its sum of the squares

Answer 9

woops!! sorry ...

Answer 10

We can represent prime numbers greater than 3 using the most unknown rule called
"greater than three prime number rule" in mathematics

Answer 11

interesting ... could you give me links??

Answer 12

That's true. Square them before you add them up.

Answer 13

Actually it is very simple, but can be a usefull tool for such questions actually

Answer 14

The rule says that it is possible to represent prime numbers greater than 3 in the form
(6n+1) and (6n-1)

But its converse is not true

Answer 15

interesting to see that
http://www.wolframalpha.com/input/?i=Mod%5BTable%5BPrime%5Bi%5D%2C+%7Bi%2C+3%2C+25%7D%5D%2C+6%5D

Answer 16

Yup, I heard the rule today

Answer 17

So 23 is the answer right?

Answer 18

23 mod 6 lol

Answer 19

No, no, no and no. We are dividing by 6. The REMAINDER must be 0, 1, 2, 3, 4, or 5

Answer 20

the remainder is 1 or 5 ... according to wolf. check the link i posted above.

Answer 21

or no remainder at all...

Answer 22

Options are
(a) 23
(b)23/6
(c)30
(d)40

Answer 23

how are those remainders if you are dividing by 6?

Answer 24

looks like you added it all up ...