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...

of the form 2(5 − 1)(25 − 1) by the Euclid-Euler theorem. 31 is also a primorial prime like its twin prime (29), as well as both a lucky prime and a happy...

adding some subsets of its divisors (e.g., 5, 10 and 15) equals 30. A primorial. A Harshad number in decimal. Divisible by the number of prime numbers...

5, and 7), and thus a primorial, where it is the least common multiple of these four prime numbers. 210 is the first primorial number greater than 2 which...

before 30,001. 30029 = primorial prime 30030 = primorial 30031 = smallest composite number which is one more than a primorial 30203 = safe prime 30240...

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...

arithmetic progression of n primes (in this case, n = 7) that is not a primorial (a product of the first m primes). The sum of Euler's totient function...

theory, Bonse's inequality, named after H. Bonse, relates the size of a primorial to the smallest prime that does not appear in its prime factorization...

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...

510 = the product of the first seven prime numbers, thus the seventh primorial. It is also the product of four consecutive Fibonacci numbers—13, 21,...

\cdots \times 1451} ). More concisely, it is the product of seven distinct primorials: b 0 5 b 1 3 b 2 2 b 4 b 7 b 18 b 229 , {\displaystyle...

{(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...

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...

zero 2309 – primorial prime, twin prime with 2311, Mertens function zero, highly cototient number 2310 – fifth primorial 2311 – primorial prime, twin...

method first selects a primorial and then constructs an interval in which the distribution of integers coprime to the primorial is well understood. By...

the localization of prime numbers (the smallest better base being the primorial base six, senary). Quaternary shares with all fixed-radix numeral systems...

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...

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...

including the binomial coefficients, double factorials, falling factorials, primorials, and subfactorials. Implementations of the factorial function are commonly...

Highly totient Noncototient Nontotient Perfect totient Sparsely totient Aliquot sequences Amicable Perfect Sociable Untouchable Primorial Euclid Fortunate...

the input to the algorithm has already passed a probabilistic test. The primorial function of n {\displaystyle n} , denoted by n # {\displaystyle n\#} ...

February has on a leap year. 29 is the tenth prime number. 29 is the fifth primorial prime, like its twin prime 31. 29 is the smallest positive whole number...

5939, 5953, 5981, 5987} 9,694,845 = Catalan number 9,699,690 = eighth primorial 9,765,625 = 31252 = 255 = 510 9,800,817 = equal to the sum of the seventh...

Foundation. Retrieved 2023-07-31. Sloane, N. J. A. (ed.). "Sequence A002110 (Primorial numbers (first definition): product of first n primes. Sometimes written...

occurs thrice, since adding 61 to either the tenth, twelfth or seventeenth primorial gives a prime number (namely 6,469,693,291; 7,420,738,134,871; and 1,922...

\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 ⁡...

lower, rising, upper factorials) Poisson distribution Polygamma function Primorial Proof of Bertrand's postulate Sierpinski triangle Star of David theorem...

153, 369, 492, 714, 1682, 2107, 2299 (sequence A006145 in the OEIS). A primorial x# is the product of all primes from 2 to x. The first: 2, 6, 30, 210...