Largest Known Prime Number


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The largest known prime was discovered on September 4, 2006. It is a Mersenne prime, which means that it is of the form

The largest prime number has 9 808 358 digits (the previous largest prime known was 7 816 230 digits long) and is also a Mersenne prime:

You can download it here.

Mersenne's prime are usually the largest primes, because they are relatively easy to find. Merin Mersenne(1588-1648) stated in the preface to his Cogitata Physica-Mathematica (1644) that the numbers as described above are primes when p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257 
and were composite for all other positive integers n < 257.

Mersenne's conjecture was incorrect, but there are prime numbers which fit his formula, and they are said to be Mersenne primes.

Mersenne's primes have a curious connection with some perfect numbers. Check here to see which and why...


Main number page

Prime numbers

Largest Prime Number known

See Eratosthenes' Prime Number sieve and download some worksheets: 100, 200 or 500 number sieve.

What people thought of primes through the history

Prime number (as the one defined by Aristotle, Euclid and Theon of Smyrna) is a number "measured by no number but by an unit alone" Iambilicus said that a prime number is also called "odd times odd".

Prime number was apparently first described by Pythagoras.

Iamblichus writes that Thymaridas called a prime number rectilinear since it can only be represented one-dimensionally.

In English prime number is found in Sir Henry Billingsley's 1570 translation of Euclid's Elements (OED2).

Some older textbooks include 1 as a prime number.

In his Algebra (1770), Euler did not consider 1 a prime [William C. Waterhouse].


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