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For example a Prime triplet where each prime number is separated by a single even number is: $$3, 5, 7$$ it contains 3 prime numbers each separated by 2

What is the longest such sequence known to exist where each consecutive prime number is separated by a single even number?

And is there a name for such sequences?

So say if the longest such sequence was n long with the first primer being p, then the sequence would be:

$$ p, p+2, p+4, \ldots, 2(n-1)+p $$

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The longest consequtive twin primes sequence is $3,5,7$.

There thre numbers are actually the only three numbers of the forms $n, n+2, n+4$ in which all three numbers are prime. Any other such sequence (if $n\geq 2$) has at least one of the numbers divisible by $3$.

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