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.
The name "primorial", coined by Harvey Dubner, draws an analogy to primes similar to the way the name "factorial" relates to factors.
free dictionary. In mathematics, and more particularly in number theory, primorial, denoted by "#", is a function from natural numbers to natural numbers...
In mathematics, a primorial prime is a prime number of the form pn# ± 1, where pn# is the primorial of pn (i.e. the product of the first n primes). Primality...
numbers are integers of the form En = pn # + 1, where pn # is the nth primorial, i.e. the product of the first n prime numbers. They are named after the...
primorial must be at least 1·2·3·5·7·11·13, and 7×11×13 = 1001. Fuller also refers to powers of 1001 as Scheherazade numbers. The smallest primorial containing...
the localization of prime numbers (the smallest better base being the primorial base six, senary). Quaternary shares with all fixed-radix numeral systems...
{(p_{r-1}\#)^{k}}{J_{k}(p_{r}\#)}}\qquad k=2,3,\ldots .} Here pn# is the primorial sequence and Jk is Jordan's totient function. The function ζ can be represented...
12, ...} Odd double factorial number system {1, 3, 5, 7, 9, 11, ...} Primorial number system {2, 3, 5, 7, 11, 13, ...} Fibonorial number system {1, 2...
\log x\right).} The first Chebyshev function is the logarithm of the primorial of x, denoted x #: ϑ ( x ) = ∑ p ≤ x log p = log ∏ p ≤ x p = log ...
the input to the algorithm has already passed a probabilistic test. The primorial function of n {\displaystyle n} , denoted by n # {\displaystyle n\#} ...
967, 971, 983, 991 (OEIS: A006567) Of the form pn# + 1 (a subset of primorial primes). 3, 7, 31, 211, 2311, 200560490131 (OEIS: A018239) A prime p {\displaystyle...
and B, or of knots A and B in knot theory. In number theory, n# is the primorial of n. In constructive mathematics, # denotes an apartness relation. In...
including the binomial coefficients, double factorials, falling factorials, primorials, and subfactorials. Implementations of the factorial function are commonly...
prime factor in the primorial is less than one of the divisors of the previous primorial. By induction, it follows that every primorial satisfies the characterization...
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. For example, to find...
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