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There are many such triplets.

Consider any number ending in 4. The next two numbers will end in 5 and 6. The first and last will be divisible by two and the middle one by 5.

To compile a complete list of all such triplets, first draw up a list of all odd numbers that are not prime eg 9, 15, 21 etc. A triplet with that number in the middle will meet your requirements.

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