Longest Sequence of Consecutive Primes in Arithmetic Sequence

Sequence
The longest known sequence of consecutive prime numbers in arithmetic progression starts at $121 \, 174 \, 811$, has a length of $6$ and a common difference of $30$:


 * $121 \, 174 \, 811, 121 \, 174 \, 841, 121 \, 174 \, 871, 121 \, 174 \, 901, 121 \, 174 \, 931, 121 \, 174 \, 961$