Discussion
What is the sum of the next two numbers in the following pattern ?
13, 17, 19, 23, 29, ____, ____
Answer: A
The sum is 68.
The pattern is the sequence of consecutive prime numbers: 13, 17, 19, 23, 29. The next two primes are 31 and 37, since 30, 32, 33, 34, 35 and 36 all have factors other than 1 and themselves.
\[ 31 + 37 = 68 \]
A common slip is to look for a constant difference. The gaps here are 4, 2, 4, 6, which follow no fixed rule, a clue that the numbers are primes. Taking 31 and then 41, or 37 and 41, gives sums such as 72 or 78, none of which are among the options.
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