Unique Sequence of Consecutive Odd Numbers which are Prime/Mistake

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Source Work

1979: G.H. Hardy and E.M. Wright: An Introduction to the Theory of Numbers (5th ed.):

$\text I$: The Series of Primes:
$1.4$ The sequence of primes


The numbers $p$, $p + 2$, $p + 4$ cannot all be prime, since one of them must be divisible by $3$; ...


Note should be made of the triple $3$, $5$, $7$, all of which are prime.