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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