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That means 95,676,260,903,887,607 primes [3] (nearly 10 17), but they were not stored. ... Below are listed the first prime numbers of many named forms and types ...
If 1 were to be considered a prime, many statements involving primes would need to be awkwardly reworded. For example, the fundamental theorem of arithmetic would need to be rephrased in terms of factorizations into primes greater than 1, because every number would have multiple factorizations with any number of copies of 1. [42]
As of October 2024, the seven largest known primes are Mersenne primes. [2] The last eighteen record primes were Mersenne primes. [3] [4] The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2 k − 1 is simply k ones. [5] Finding larger prime numbers is sometimes presented as a means to stronger ...
The first row has been interpreted as the prime numbers between 10 and 20 (i.e., 19, 17, 13, and 11), while a second row appears to add and subtract 1 from 10 and 20 (i.e., 9, 19, 21, and 11); the third row contains amounts that might be halves and doubles, though these are inconsistent. [14]
The 5000 largest known primes at The PrimePages The 10,000 largest known probable primes at primenumbers.net PrimeGrid’s 321 Prime Search , about the discovery of 3×2 6090515 −1
The Lenstra–Pomerance–Wagstaff conjecture claims that there are infinitely many Mersenne primes and predicts their order of growth and frequency: For every number n, there should on average be about ≈ 5.92 primes p with n decimal digits (i.e. 10 n-1 < p < 10 n) for which is prime.
An important question is to determine the asymptotic distribution of the prime numbers; that is, a rough description of how many primes are smaller than a given number. Gauss , amongst others, after computing a large list of primes, conjectured that the number of primes less than or equal to a large number N is close to the value of the integral
c. 20,000 BC — Nile Valley, Ishango Bone: suggested, though disputed, as the earliest reference to prime numbers as also a common number. [1] c. 3400 BC — the Sumerians invent the first so-known numeral system, [dubious – discuss] and a system of weights and measures.