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A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair. In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair.
A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller positive integer. The name can be somewhat misleading, as two highly composite numbers are not actually composite numbers.
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system. The word is a portmanteau of repeated and digit. Examples are 11, 666, 4444, and 999999. All repdigits are palindromic numbers and are multiples of repunits. Other well-known repdigits include the repunit primes and in particular the Mersenne primes.
The tables contain the prime factorization of the natural numbers from 1 to 1000.
A Wilson prime, named after English mathematician John Wilson, is a prime number p such that p2 divides (p − 1)! + 1, where "!" denotes the factorial function; compare this with Wilson's theorem, which states that every prime p divides (p − 1)! + 1.
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes.
In mathematics, a P-multimagic square is a magic square that remains magic even if all its numbers are replaced by their kth powers for 1 ≤ k ≤ P. 2-multimagic squares are called bimagic, 3-multimagic squares are called trimagic, 4-multimagic squares tetramagic, and 5-multimagic squares pentamagic.
105 is the natural number following 104 and preceding 106.
In mathematics, a primorial prime is a prime number of the form pn# ± 1, where pn# is the primorial of pn.
In mathematics, and more particularly in number theory, primorial, denoted by "#", is a function from natural numbers to natural numbers similar to the factorial function, but rather than successively multiplying positive integers, the function only multiplies prime numbers.
In mathematics, a Smarandache–Wellin number is an integer that in a given base is the concatenation of the first n prime numbers written in that base. Smarandache–Wellin numbers are named after Florentin Smarandache and Paul R. Wellin.
In mathematics, and more specifically number theory, the hyperfactorial of a positive integer is the product of the numbers of the form from to .
In mathematics, and more specifically number theory, the superfactorial of a positive integer is the product of the first factorials. They are a special case of the Jordan–Pólya numbers, which are products of arbitrary collections of factorials.
In mathematics, a superior highly composite number is a natural number which has the highest ratio of its number of divisors to some positive power of itself than any other number. It is a stronger restriction than that of a highly composite number, which is defined as having more divisors than any smaller positive integer.
In mathematics, an alternating factorial is the absolute value of the alternating sum of the first n factorials of positive integers.
In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself. Two numbers with the same "abundancy" form a friendly pair; n numbers with the same "abundancy" form a friendly n-tuple.
In mathematics, the cake number, denoted by Cn, is the maximum number of regions into which a 3-dimensional cube can be partitioned by exactly n planes. The cake number is so-called because one may imagine each partition of the cube by a plane as a slice made by a knife through a cube-shaped cake.
In recreational mathematics, a ban number is a number that does not contain a particular letter when spelled out in English; in other words, the letter is "banned." Ban numbers are not precisely defined, since some large numbers do not follow the standards of number names.
A Fortunate number, named after Reo Fortune, is the smallest integer m > 1 such that, for a given positive integer n, pn# + m is a prime number, where the primorial pn# is the product of the first n prime numbers.
In mathematics, an integer sequence prime is a prime number found as a member of an integer sequence. For example, the 8th Delannoy number, 265729, is prime. A challenge in empirical mathematics is to identify large prime values in rapidly growing sequences.