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There are known to be infinite Carmichael numbers congruent to $a\pmod b$ for coprime integers $a$ and $b$. There are plenty of examples of small Carmichael numbers congruent to $1, 5, 7 \pmod {12}$, but what are the smallest examples $11\pmod {12}$? I couldn't find any on Richard Pinch's site, and also verified that if the smallest example is $C=p*q*r$, then $(p,q,r)>10000$. Any other further leads? Thanks.

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I pulled A205947 (Carmichael numbers not congruent to $1\bmod6$, which thus includes $11\bmod12$ numbers) and searched for those numbers congruent to $11\bmod12$. The first ten such numbers are $$10546629279551$$ $$19177682527151$$ $$22799069430611$$ $$52305745012067$$ $$118069613866751$$ $$131314855918751$$ $$225053535639791$$ $$313608281158271$$ $$591537056799431$$ $$599075226610631$$ which are also the only such numbers below $10^{15}$.

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