Project Euler Problem 97： Large non-Mersenne prime【快速冪】

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Large non-Mersenne prime

Problem 97

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The first known prime found to exceed one million digits was discovered in 1999, and is a Mersenne prime of the form $2^{6972593}−1$; it contains exactly 2,098,960 digits. Subsequently other Mersenne primes, of the form 2p−1, have been found which contain more digits.

However, in 2004 there was found a massive non-Mersenne prime which contains 2,357,207 digits: $28433×2^{7830457}+1.$

Find the last ten digits of this prime number.

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題意：

讓你求$28433×2^{7830457}+1.$的最後十位

分析：

快速冪直接搞定

參考代碼

mod = int(1e10)
def quick_pow(a, b):
    res = 1
    while (b):
        if (b & 1): res = res * a % mod
        a *= a
        b >>= 1
    return res
print((28433 * quick_pow(2, 7830457) + 1)%mod)

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