### Brain Teasers

# Guess the Pattern 3

What are the next three numbers in this series?

3, 5, 11, 17, 31, 41, 59, ?, ?, ?

3, 5, 11, 17, 31, 41, 59, ?, ?, ?

### Answer

67, 83, 109Each number is a prime number whose position in a list of prime numbers is also a prime number.

There are ten numbers in this series (seven given and three unknown).

The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Since the 10th prime number is 29, you need a list of the first 29 prime numbers.

The first 29 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109.

1) 2 is prime, the 2nd prime number is 3

2) 3 is prime, the 3rd prime number is 5

3) 5 is prime, the 5th prime number is 11

4) 7 is prime, the 7th prime number is 17

5) 11 is prime, the 11th prime number is 31

6) 13 is prime, the 13th prime number is 41

7) 17 is prime, the 17th prime number is 59

8) 19 is prime, the 19th prime number is 67

9) 23 is prime, the 23rd prime number is 83

10) 29 is prime, the 29th prime number is 109

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