Testwiki:Reference desk/Archives/Mathematics/2024 December 20

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December 20

Give a base b and two base b digits x and z, must there be a base b digits y such that the 3-digit number xyz in base b is prime?

Give a base b and two base b digits x and z (x is not 0, z is coprime to b), must there be a base b digits y such that the 3-digit number xyz in base b is prime? 1.165.207.39 (talk) 02:10, 20 December 2024 (UTC)

In base 5, $3Y{1}_5=76+5Y$ is composite for all base-5 Y. GalacticShoe (talk) 03:39, 20 December 2024 (UTC)

$3Y{1}_7$ also offers a counterexample. While there are many counterexamples for most odd bases, I did not find any for even bases.  --Lambiam 09:58, 20 December 2024 (UTC)