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Because of the reason above, it is possible to represent values like 1 + 2 −1074, which is the smallest representable number greater than 1. In addition to the double-double arithmetic, it is also possible to generate triple-double or quad-double arithmetic if higher precision is required without any higher precision floating-point library.
largest subnormal number 0 00001 0000000000: 0400: 2 −14 × (1 + 0 / 1024 ) ≈ 0.00006103515625: smallest positive normal number 0 01101 0101010101: 3555: 2 −2 × (1 + 341 / 1024 ) ≈ 0.33325195: nearest value to 1/3 0 01110 1111111111: 3bff: 2 −1 × (1 + 1023 / 1024 ) ≈ 0.99951172: largest number less than one 0 ...
0 00000001 00000000000000000000000 2 = 0080 0000 16 = 2 −126 ≈ 1.1754943508 × 10 −38 (smallest positive normal number) 0 11111110 11111111111111111111111 2 = 7f7f ffff 16 = 2 127 × (2 − 2 −23 ) ≈ 3.4028234664 × 10 38 (largest normal number)
Given this formula, Rayo's number is defined as: [5] The smallest number bigger than every finite number with the following property: there is a formula () in the language of first-order set-theory (as presented in the definition of ) with less than a googol symbols and as its only free variable such that: (a) there is a variable assignment ...
The number of normal floating-point numbers in a system (B, P, L, U) where B is the base of the system, P is the precision of the significand (in base B), L is the smallest exponent of the system, U is the largest exponent of the system, is () (+).
A highly composite number is a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive integer n, then a positive integer N is highly composite if d(N) > d(n) for all n < N. For example, 6 is highly composite because d(6)=4 and d(n)=1,2,2,3,2 for n=1,2,3,4,5 respectively.
In computer science, quickselect is a selection algorithm to find the kth smallest element in an unordered list, also known as the kth order statistic.Like the related quicksort sorting algorithm, it was developed by Tony Hoare, and thus is also known as Hoare's selection algorithm. [1]
The following table lists the progression of the largest known prime number in ascending order. [4] Here M p = 2 p − 1 is the Mersenne number with exponent p, where p is a prime number. The longest record-holder known was M 19 = 524,287, which was the largest known prime for 144 years. No records are known prior to 1456.