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): $33$