August 2025
Problem of the Month

Prime Numbers
Submitted by Davit Banana
From the Turkish University Entry Exam

There are 5 prime numbers.

Sum of them is 100.

Product of them is a number in form of ABCABC

Find A+B+C.

Solution to the Problem:

Here is Davit Banana's solution:

If we divide ABCABC by ABC, the result is (always) 1001.

If we factorize 1001 to prime numbers, we find 7, 11 and 13.

So, 3 of the numbers are 7, 11 and 13

The other 2 numbers’ sum is
  100-7-11-13 = 69

Since 69 is odd, one of the remaining numbers has to be even (and the other, odd).

The only even prime number is 2, so the fourth number is 2.

The fifth number is 69-2 = 67.

So, ABC is 2x67 = 134

ABCABC = 134134 = 2*7*11*13*67

A+B+C = 1+3+4 = 8

Correctly solved by:

1. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
2. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
3. Seth Cohen	Concord, New Hampshire, USA
4. Kamal Lohia	Hisar, Haryana, India
5. Riley Sack	Central High School, Grand Junction, Colorado, USA
6. Kelly Stubblefield	Mobile, Alabama, USA

Send any comments or questions to: David Pleacher