Find all Belphegor primes A Belphegor number is a number of the form \$(10^{n+3}+666)*10^{n+1}+1\$ (1{n zeroes}666{n zeroes}1) where \$n\$ is an non-negative integer. A Belphegor prime is a Belphegor number that is also prime.

The \$n\$ values of the first few Belphegor primes are 0, 13, 42, 506 (A232448)

Task

Write a program that either:


takes no input and outputs all Belphegor primes.
takes a input \$k\$ and outputs the first \$k\$ Belphegor primes.


A reference python implementation can be found here.

Rules


You may output the \$n\$ value for the Belphegor prime instead of the prime itself
You may use probabilistic primality tests as long as there is no known counter case.


Scoring

This is code-golf so shortest bytes wins.



Inspired by The Most Evil Number - Numberphile
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