Find all Belphegor primes
Wolfram Language (Mathematica), 51 bytes

outputs the n value
"...program that does not stop and will eventually output all..."

PrimeQ[10^c*666+1+100^++c]~If~Print[c-2]~Do~{c,∞}     


Try it online!   

thanks to @DanTheMan for saving 4 bytes
and also to @mypronoun -7 bytes