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The semiprime $28222149$ is a semiprime $S=A*B$ (with $A=3$ and $B=9407383$) such that

-$A.B$

-$B.A$

-$S.A$

-$S.B$

-$A.S$

-$S.A.B$

-$S.B.A$

-$A.S.B$

-$A.B.S$

-$B.S.A$

-$B.A.S$

are all semiprime. (Dots here means concatenation.)

It would be a 'perfect' result if $B.S$ were also a semiprime. Unfortunately, $B.S$ is not semiprime.

I've checked semiprimes up to $10^{10}$, and I didn't find a semiprime which gives a 'perfect' result. Could you find a semiprime with 'perfect' result?

Mathphile
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  • $A=B=3$ works ($33,39,93,339,393,933$ are all semiprime), so presumably we need $A\ne B$, or possibly even that all $12$ semiprimes are distinct. – nickgard Feb 27 '19 at 16:35
  • I think they are thinking of distinct factors. squares aren't always counted then. –  Mar 01 '19 at 13:56
  • What is your definition of a semiprime? – Wlod AA Feb 04 '20 at 02:19

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