<jupyter_start><jupyter_text>Euler Problem 46================It was proposed by <NAME> that every odd composite number can be written as the sum of a prime and twice a square.- 9 = 7 + 2×12- 15 = 7 + 2×22- 21 = 3 + 2×32- 25 = 7 + 2×32- 27 = 19 + 2×22- 33 = 31 + 2×12It turns out that the conjecture was false.What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?<jupyter_code>N = 10000
sieve = [False, False] + [True]*N
for p in range(N):
    if sieve[p]:
        for m in range(p*p, N, p):
            sieve[m] = False
for n in range(9, N, 2):
    if sieve[n]:
        continue
    delta = 6
    m = n - 2
    while m > 2 and not sieve[m]:
        m -= delta
        delta += 4
    if m <= 2:
        print(n)
        break<jupyter_output>5777
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