14 ... 15 ... 16
20 ... 21 ... 22
24 ... 25 ... 26
25 ... 26 ... 27
26 ... 27 ... 28
32 ... 33 ... 34
33 ... 34 ... 35
34 ... 35 ... 36
38 ... 39 ... 40
44 ... 45 ... 46
48 ... 49 ... 50
49 ... 50 ... 51
50 ... 51 ... 52
54 ... 55 ... 56
55 ... 56 ... 57
56 ... 57 ... 58
.
.
.
etc.
Every even two-digit number is composite, so to have three consecutive two-digit composite numbers, all you need is an odd composite number and then the even number on either side of it. The odd composite two-digit numbers are 15, 21, 25, 27, 33, 35, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 91, 93, and 95.
A far more interesting question is what are the seven consecutive two-digit composite numbers. The only answer is 90, 91, 92, 93, 94, 95, and 96.
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24, 25 and 26 is one possible triplet.
8, 9, 10
Basically, composite numbers are the non-prime numbers. Take a table of prime numbers, and look for any two prime numbers, one after the other, that have a difference greater than 2. Any numbers in between are consecutive composite numbers. For example, the next prime number after 13 is 17; that makes 14, 15, and 16 three consecutive non-primes, i.e., composite numbers.
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