The number 2,147,483,647 is the eighth Mersenne prime, equal to 2 − 1. It is one of only four known double Mersenne primes.
The primality of this number was proved by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772. Euler used trial division, improving on Cataldi's method, so that at most 372 divisions were needed. The number 2,147,483,647 may have remained the largest known prime until 1867. In 1814, Peter ...
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The number 2,147,483,647 is the eighth Mersenne prime, equal to 2 − 1. It is one of only four known double Mersenne primes.
The primality of this number was proved by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772. Euler used trial division, improving on Cataldi's method, so that at most 372 divisions were needed. The number 2,147,483,647 may have remained the largest known prime until 1867. In 1814, Peter Barlow, not anticipating future interest in prime numbers, wrote (in A New Mathematical and Philosophical Dictionary):
Euler ascertained that 2 − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and consequently the last of the above perfect numbers [i.e., 2(2 − 1)], which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for as they are merely curious, without being useful, it is not likely that any person will attempt to find one...
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