Constant difference between primes?

Number Theory Level 2

$79, \; 109, \; 139, \; 1\text{\_}9, \; 199, \; 229$

The above are 6 distinct prime numbers arranged in increasing order. One of the numbers is missing its tens digit.

Which of the following can be the missing digit?

5 6 7 8

2 solutions

Munem Shahriar
Nov 27, 2017

By observation, we see that

$79 + 30= 109$

$109+ 30= 139$

$139+ 30= 169$

$169+ 30 = 199$

$199+30 = 229$

But 169 is not a prime number because $169 \div 13 = 13$ .

Among the given options, $179$ is the only prime number. Hence the missing digit is $\boxed{7}$

A Former Brilliant Member
Nov 29, 2017

It's obvious that 159 & 189 are divisible by 3, and that 169 is the square of 13. Answer can be obtained through deduction.