From a closed thread:
The Sixth came in the middle of its doorway.I've previously used a model for the original 17 values and their individual start points that gives the probability of finding "j" primes by level n. One way to define the doorway for when the jth prime "should" appear is the period when the most likely number of primes found is "j".
1st 800K-1.1M
2nd 1.1M-1.6M
3rd 1.6M-2.2M
4th 2.2M-3.1M
5th 3.1M-4.4M
6th 4.4M-6.5M
7th 6.5M-10.1M
8th 10.1M-16.8M
9th 16.8M-29.5M
10th 29.5M-57M
11th 57M-127M
12th 127M-344M
13th 344M-1.2G
14th 1.2G-7.2G
15th 7.2G-108G
16th 108G-18T
17th above 18T