Is random.randint() in Python truly random?

Question

So I was using the random module in Python with some loops and was printing out a batch of numbers to check what they looked like. I noticed that when I input:

random.randint(0,100000)

most of the numbers would be six figure numbers with a few at five figures and fewer at 4. There were barely any single figures at all. It makes me question how random rand.int really is.

Have you tried counting how many of each length there actually *are*? — Ignacio Vazquez-Abrams, Jan 26 '14 at 20:34
Barely any of the numbers between 0 and 10000 are between 0 and 10. — rlms, Jan 26 '14 at 20:34
Oh, and the answer is no, but not for the reason you're asking about. — Ignacio Vazquez-Abrams, Jan 26 '14 at 20:34
Math hasn't figured out how to put 90,000 integers between 0 and 10 yet. — roippi, Jan 26 '14 at 20:36
You might want to look at http://stackoverflow.com/questions/14556451/is-there-a-random-number-distribution-that-obeys-benfords-law — Mark Ransom, Dec 02 '14 at 21:47

score 5 · Answer 1 · answered Jan 26 '14 at 20:34

Between 0 and 100000, 90% of the numbers have 5 figures! Only 0.01% have 1 figure. So the behavior is what I'd expect. EDIT: And note what ignacio says. The numbers are definitely not "truly" random as that would require some sort of quantum event. They are "pseudo" random numbers.

Milo P · Answer 2 · 2014-12-02T21:20:01.133

To expand on ooga's answer, between 0 and 100,000, there are:

10 single-digit numbers (0-9)
90 two-digit numbers (10-99)
900 three-digit numbers (100-999)
9000 four-digit numbers (1,000-9,999)
90000 five-digit numbers (10,000-99,999)

This is why you'd expect a 90% chance of a random number having five digits, a 9% chance of four digits, a .9% chance of three digits, and so on. Another way to look at it is to think of any positive number with fewer than five digits as having a 0 in the ten thousands place (e.g. 07,734), so there are nine times as many five-digit numbers, since there are nine non-zero possibilities for the ten thousands place.

(Also, I'm assuming you meant you're getting mostly five-figure numbers or the range went up to 1,000,000, since there shouldn't be any six-figure integers between 0 and 100,000.)

Is random.randint() in Python truly random?

2 Answers2