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Euler ascertained that 2 31 − 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 30 (2 31 − 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 ...
The naming procedure for large numbers is based on taking the number n occurring in 10 3n+3 (short scale) or 10 6n (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix -illion. In this way, numbers up to 10 3·999+3 = 10 3000 (short scale) or 10 6·999 = 10 5994 (long scale
The Rayo function of a natural number , notated as (), is 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 symbols and as its only free variable such that: (a) there is a variable assignment assigning to such that ([()],), and (b) for any variable ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
The Avogadro constant is the number of "elementary entities" (usually atoms or molecules) in one mole; the number of atoms in 12 grams of carbon-12 – approximately 6.022 × 10 23, or 602.2 sextillion. The total number of DNA base pairs within the entire biomass on Earth, as a possible approximation of global biodiversity, is estimated at (5.3 ...
The following table lists the first 1000 primes, with 20 columns of consecutive primes in each of the 50 rows. ... Primes in the Lucas number sequence L 0 = 2, L 1 ...
The aleph numbers differ from the infinity (∞) commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the ...
In mathematics, the extended real number system [a] is obtained from the real number system by adding two elements denoted + and [b] that are respectively greater and lower than every real number. This allows for treating the potential infinities of infinitely increasing sequences and infinitely decreasing series as actual infinities .