# An MMG Special

What are the next three numbers in the following sequence?

4, 6, 12, 18, 30, 42, 60, 72, 102, 108, ?, ?, ?

(Sent to us by MMG)

### 4 guesses to An MMG Special

• Martin

114, 144, 156

• Dude

Nope, that’s not it. Keep trying.

(and show your reasoning if you can)

• Nanao Ise

…138, 150, 180?

I think it’s a sequence of numbers that have a prime number both before and after them.

For example, the number four has the primes three and five, and the number six has the primes five and seven.

• Dude

Correct Nanao Ise.

The series lists numbers that are flanked by two prime numbers so the answer is 138, 150, and 180.

4 (3 and 5 are prime)
6 (5 and 7 are prime)
12 (11 and 13 are prime)
18 (17 and 19 are prime)
30 (29 and 31 are prime)
42 (41 and 43 are prime)
60 (59 and 61 are prime)
72 (71 and 73 are prime)
102 (101 and 103 are prime)
108 (107 and 109 are prime)
So therefore:
138 (137 and 139 are prime).
150 (149 and 151 are prime).
180 (179 and 181 are prime).

You are today’s winner.