Sequence of 11 Primes by Trebling and Adding 16

Theorem
The process of multiplication by $3$ and then adding $16$ produces a sequence of $11$ primes when starting from $587$:


 * $587, 1777, 5347, 16 \, 057, 48 \, 187, 144 \, 577, 433 \, 747, 1 \, 301 \, 257, 3 \, 903 \, 787, 11 \, 711 \, 377, 35 \, 134 \, 147$