Largest Known Lead by 4n+1 in Prime Number Race

Theorem
In the prime number race between prime numbers of the form $4 n - 1$ and $4 n + 1$, the highest known stretch of integers where $4 n + 1$ is not less than $4 n - 1$ is between $18 \, 465 \, 126 \, 293$ and $19 \, 033 \, 524 \, 538$.

Proof
First note that:

where it can be seen that prime numbers of the form $4 n + 1$ are locally increasing, and:

where it can be seen at that point prime numbers of the form $4 n - 1$ may now be in front, but this is inconclusive.