Problem 46 - Find the first four consecutive integers to have four distinct primes factors.

링크

It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.

9 = 7 + 21²
15 = 7 + 22²
21 = 3 + 23²
25 = 7 + 23²
27 = 19 + 22²
33 = 31 + 21²

It 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?

python

limit = 10000 isPrime = [True] * limit isPrime[0] = isPrime[1] = False for i in range(2, int(round(limit**0.5))+1): if isPrime[i]: isPrime[2*i:limit:i] = [False] * ((limit-1)/i-1) primes = [x for x in range(2, limit) if isPrime[x]] dsq = set([2*x*x for x in range(1, limit)]) x = 35 while True: ok = False if isPrime[x] == False: for p in primes: if p >= x: break if x - p in dsq: ok = True break else: ok = True if ok == False: break x += 2 print x