Sequence of 9 Primes of form 4n+1

Theorem
The following sequence of $9$ consecutive prime numbers are all of the form $4 n + 1$:
 * $11 \, 593, 11 \, 597, 11 \, 617, 11 \, 621, 11 \, 633, 11 \, 657, 11 \, 677, 11 \, 681, 11 \, 689$

Proof
It remains to be noted that:
 * the prime number before $11 \, 593$ is $11 \, 587$ which is $4 \times 2897 - 1$
 * the prime number after $11 \, 689$ is $11 \, 699$ which is $4 \times 2925 - 1$

confirming that they are not of the form $4 n + 1$.