你知道下面的梅森數, M1567271, M1567259, M1567103, M1567031, and M1566923,有下列的3134543, 3134519, 3134207, 31340633133847對應因子嗎?上例中的數字都是素數. 使得找的該數們的因子有其困難的程度. 尤其是當素數的值大到一定程度以上如前面所提的例子. 找他們的因子就很難了,甚至於用電腦來找. 相較下,2ab – 1, ab是素數, 證明它是素數且有 (2a– 1) (2b– 1) 的因子就比較容易了. Do you know the following Mersenne Numbers, M1567271, M1567259, M1567103, M1567031, and M1566923, have factors as 3134543, 3134519, 3134207, 3134063 and 3133847, respectively?  The above numbers are all primes that contribute the difficulty nature for people to find their cofactors.  When the values of the prime numbers become large to some extend as the aforementioned examples, it is hard to obtain their cofactors, even with the aid of a computer. On the other hand, it is relatively easier to prove and find the cofactor of Mcomposite that has the form of 2ab – 1. Note that ab is not a prime.  The following is one of the proofs of 2ab – 1 that shows 2ab – 1 has (2a– 1) and (2b– 1) as its factors.

 

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