### Brain Teasers

# 23, 31, 41, ...

Can you find the next three terms in the series shown below?

23, 31, 41, 59, 71, 83, 97, 109, ?, ?, ?, ...

23, 31, 41, 59, 71, 83, 97, 109, ?, ?, ?, ...

### Hint

This hint is a prime example that gives the sum of three useful pieces of information.### Answer

131, 173, 199Why? The series is only those prime numbers that can be expressed as the sum of three consecutive prime numbers.

23 = 5 + 7 + 11

31 = 7 + 11 + 13

41 = 11 + 13 + 17

59 = 17 + 19 + 23

71 = 19 + 23 + 29

83 = 23 + 29 + 31

97 = 29 + 31 + 37

109 = 31 + 37 + 41

131 = 41 + 43 + 47

173 = 53 + 59 + 61

199 = 61 + 67 + 71

And so on...

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