def primes_sieve(nmax):
    a = [0 for _ in range(nmax)]
    for i in range(2, nmax):
        if a[i] == 0:
            for j in range(i + i, nmax, i):
                a[j] = i
    return a


def is_number(n, primes):
    f = n // 2
    if primes[f] == 0:
        for d in [2, f]:
            if primes[d + n // d] != 0:
                return False
        return True

    for d in range(1, n // 2 + 1):
        if n % d == 0:
            if primes[d + n // d] != 0:
                return False
        if d * d > n:
            break
    return True


def euler_357():
    r = 1 # n = 1 is a number
    ps = primes_sieve(100_000_000)
    for p in range(3, len(ps)):
        if ps[p] == 0:
            n = p - 1
            if is_number(n, ps):
                r += n
    return r


if __name__ == "__main__":
    solution = euler_357()
    print("e357.py: " + str(solution))
    assert solution == 1739023853137