Since both are prime numbers ,

If divisible by 3 but not by 5, skip all those that are divisible by both among those that are divisible by 3.


First number is 201, last number is 399.

Numbers divisible by 3 :

201 204 207 210 213 216 219 222 225 228 231 234 237 240 .... 378 381 384 387 390 393 396 399

If we factorise by dividing each number by by 3, it becomes

67 68 69 70 71 72 73 74 75 76 77 78 79 80
..... 126 127 128 129 130 131 132 133


So the first number now is 67 , last number is 133.

Notice that :

67 + 133 = 200
68 + 132 = 200
69 + 131 = 200
.
.
.
97 + 103 = 200
98 + 102 = 200
99 + 101 = 200


Pairing the 1st and last, 2nd and 2nd last, 3rd and 3rd last, and so on gives 200 per pair.

The number 100 has no partner to be paired with.

From 67 to 133 , there are (133 - 67 + 1) numbers = 67 numbers

So it's an odd number. There are 66 numbers that can be grouped into 33 pairs, with a value of 200 per pair. The one remaining number is that number 100 which can't form a pair.


Now among these numbers there are those that are also. divisible by 5. Have yo exclude them.

They are 70,75,80,85,90,95,100,105,110, 115,120,125,130.


These numbers were also grouped into pairs of 200. 70 + 130, 75 + 125, etc.

To count the number of numbers here (and hence the number of pairs), we divide all by 5.

It becomes 14 15 16 17 18 19 20 21 22 23 24 25 26

Number of numbers = 26 - 14 + 1 = 13
(It is easy to manual count here but for big sequences this method is useful)

So similarly it's an odd number of numbers. 12 numbers can be grouped into 6 pairs. Number 100 has no pair.

So we remove 6 pairs from the 33.
Total number of pairs we include in our calculation = 33 - 6 = 27

27 x 200 = 5400

(So we only count 27 pairs. We do not count in that 100 as it's divisible by 5)

Now, we multiply the total by 3 as we had divided by 3 in the first place.

So 5400 x 3 = 16200