Smallest Sequence of Three Consecutive Semiprimes

Theorem

The smallest triple of consecutive semiprimes is:

$33, 34, 35$


Proof

We have:

\(\ds 33\) \(=\) \(\ds 3 \times 11\)
\(\ds 34\) \(=\) \(\ds 2 \times 17\)
\(\ds 35\) \(=\) \(\ds 5 \times 7\)

It can be seen from the sequence of semiprimes that there exist no smaller such triples.

$\blacksquare$


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $33$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $33$
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