Answer:
no
Step-by-step explanation:
Suppose the numbers of interest are x, x+2, x+4. If we divide x by 3, its remainder will be one of 0, 1, or 2.
If x mod 3 = 0, then x will be a multiple of 3, so won't be prime (unless x=3).
If x mod 3 = 1, then x+2 will be a multiple of 3, so won't be prime.
if x mod 3 = 2, then x+4 will be a multiple of 3, so won't be prime.
Hence the only three sequential odd numbers that are prime are 3, 5, and 7. There are no more such "triplet primes."
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Consequently, the name "prime triplet" is given to sequences of primes that have the largest and smallest differ by 6. The middle one differs from one of the other two by 2. It is conjectured there are an infinite number of that sort of prime triplet.
