What is a One-In-A-Million Number™?

This is in the spirit of the What is a Word™/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.

If a number conforms to a special rule, I call it a One-In-A-Million Number™.
Use the following examples below to find the rule.

$$\begin{array}{|c|c|}\hline \bbox[yellow]{\textbf{One-In-A-Million Number }^™}& \bbox[yellow]{\textbf{Not One-In-A-Million Number }^™}\\ \hline \text{ 15320 }&\text{ 13520 }\\ \hline \text{ 22326 }&\text{ 23226 }\\ \hline \text{ 35052 }&\text{ 30552 }\\ \hline \text{ 57521 }&\text{ 57251 }\\ \hline \text{ 69768 }&\text{ 69678 }\\ \hline \text{ 85476 }&\text{ 58476 }\\ \hline \text{ 88297 }&\text{ 88279 }\\ \hline \text{ 92758 }&\text{ 29758 }\\ \hline \text{ 357513 }&\text{ 537513 }\\ \hline \text{ 368427 }&\text{ 386427 }\\ \hline \text{ 549580 }&\text{ 594580 }\\ \hline \text{ 580953 }&\text{ 589053 }\\ \hline \text{ 653768 }&\text{ 653678 }\\ \hline \text{ 719100 }&\text{ 791100 }\\ \hline \text{ 932341 }&\text{ 933241 }\\ \hline \text{ 1142337 }&\text{ 1143237 }\\ \hline \text{ 5568067 }&\text{ 5560867 }\\ \hline \text{ 5975388 }&\text{ 5957388 }\\ \hline \text{ 6198604 }&\text{ 1698604 }\\ \hline \text{ 6559965 }&\text{ 6595965 }\\ \hline \end{array}$$

And, if you want to analyze, here is a CSV version:

One-In-A-Million Number™,Not One-In-A-Million Number™
15320,13520
22326,23226
35052,30552
57521,57251
69768,69678
85476,58476
88297,88279
92758,29758
357513,537513
368427,386427
549580,594580
580953,589053
653768,653678
719100,791100
932341,933241
1142337,1143237
5568067,5560867
5975388,5957388
6198604,1698604
6559965,6595965


The puzzle relies on the series' inbuilt assumption, that each number can be tested for whether it is a One-In-A-Million Number™ without relying on the other numbers.

These are not the only examples of One-In-A-Million Number™, many more exist.

Hints

Check the tags.

George W. Bush or Donald Trump could conceivably solve this.
While they were alive, none of the Founding Fathers, nor Abraham Lincoln, nor Roosevelt (either one), nor JFK nor LBJ could have.

The previous hint is entirely true. It's also a red herring.
The special rule is completely unrelated to presidents, election results, or anything even close.
Nevertheless, that hint did give you some potentially useful information....

• Hm, One-In-A-Million Numbers seem to happen significantly more often than once every million numbers.
– Deusovi
Nov 10 '16 at 1:02
• @Deusovi So they do. :)
– Rubio
Nov 10 '16 at 1:03
• Is it something to do with this, by any chance? Nov 13 '16 at 0:25
• @randal'thor No. :)
– Rubio
Nov 13 '16 at 1:23

A One-In-A-Million number is one

that is found exactly once in the first one million digits of pi.

Solution:

I started off with some simple guesses related to permutations given the computer-puzzle tag and the fact that each yes-case was a permutation of the corresponding no-case. This lead me nowhere so I looked at the title for hints. I searched the OEIS for "million" and had my eureka moment when I saw a million digits of pi as reference to A000796. I tried my guess out in a program, and it worked!

Hint level 0:

number-sequence refers to the digits of pi. computer-puzzle to not try to attempt doing this hand (checking the first million digits of pi to find a substring would be a little tedious by hand).

Hint level 1 and 2:

George W. Bush or Donald Trump would be able to solve this since the first million digits of pi are well known. The others would not have been able to during their time alive since (according to Wikipedia) the first one million digits of pi were not computed until 1973.

Program:

    yes_cases = [
'15320',
'22326',
'35052',
'57521',
'69768',
'85476',
'88297',
'92758',
'357513',
'368427',
'549580',
'580953',
'653768',
'719100',
'932341',
'1142337',
'5568067',
'5975388',
'6198604',
'6559965',
]

no_cases = [
'13520',
'23226',
'30552',
'57251',
'69678',
'58476',
'88279',
'29758',
'537513',
'386427',
'594580',
'589053',
'653678',
'791100',
'933241',
'1143237',
'5560867',
'5957388',
'1698604',
'6595965',
]

with open('pi.txt', 'r') as fr: # pi.txt comes from http://www.exploratorium.edu/pi/pi_archive/Pi10-6.html
pi = ''.join([c for c in fr.read() if c != ' ' and c != '\n'])

print '--- YES CASES ---'
for case in yes_cases:
print '{} -> {}'.format(case, pi.count(case))

print '--- NO CASES ---'
for case in no_cases:
print '{} -> {}'.format(case, pi.count(case))

'''Outputs the following:
--- YES CASES ---
15320 -> 1
22326 -> 1
35052 -> 1
57521 -> 1
69768 -> 1
85476 -> 1
88297 -> 1
92758 -> 1
357513 -> 1
368427 -> 1
549580 -> 1
580953 -> 1
653768 -> 1
719100 -> 1
932341 -> 1
1142337 -> 1
5568067 -> 1
5975388 -> 1
6198604 -> 1
6559965 -> 1
--- NO CASES ---
13520 -> 16
23226 -> 13
30552 -> 5
57251 -> 17
69678 -> 10
58476 -> 13
88279 -> 7
29758 -> 9
537513 -> 0
386427 -> 2
594580 -> 2
589053 -> 0
653678 -> 0
791100 -> 0
933241 -> 2
1143237 -> 0
5560867 -> 0
5957388 -> 0
1698604 -> 0
6595965 -> 0
'''

• Nicely done! I had some more fun hints to give, one of which was an image of slices of apple pie if it had gotten that far. Amusingly enough, the next hint would have been "You won't find any of us in OEIS", and was coming in another hour.
– Rubio
Nov 13 '16 at 1:14