Fix docstring and comment in private _nth_prime_bounds function by rhettinger · Pull Request #1036 · more-itertools/more-itertools

rhettinger · 2025-07-26T17:42:19Z

The sieve call in nth_prime relies on the upper bound being exclusive. Adjust the comment in _nth_prime_bounds function to match. Demonstration:

for n, p in enumerate(sieve(10**8), start=1):
    l, u = _nth_prime_bounds(n)
    assert l < p < u

The spread ratio noted in the comment should be relative to the nth prime rather than n.

>>> l, u = _nth_prime_bounds(688_383)
>>> (u - l) / l
0.0029597587292980792

Note that tighter estimates may be added in the future. See https://cs.uwaterloo.ca/journals/JIS/VOL22/Axler/axler17.pdf for some of the possiblities.

more_itertools/more.py

rhettinger added 3 commits July 26, 2025 11:15

Spread is relative to nth prime not n.

42a9798

Bounds are exclusive

fb30d30

Leave room for refinement

b0adf48

bbayles reviewed Jul 28, 2025

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Remove future warning

113f3e6

bbayles merged commit e048f12 into more-itertools:master Jul 28, 2025
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rhettinger deleted the nth_prime_comment_typo branch July 28, 2025 15:18

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