Primorial

Quick meaning: Primorial is a noun meaning (number theory) Any number belonging to the integer sequence whose nth element is the product of the first n primes.

Meaning

(number theory) Any number belonging to the integer sequence whose nth element is the product of the first n primes.

More Meanings

1. (number theory) A unary operation, denoted by the postfix symbol # and defined on the nonnegative integers, which maps 0 to 1, 1 to 1, and each subsequent number to the product of all primes less than or equal to it; the value mapped to by said operation for a given input.

Example Sentences

The primorial of 6 is #92;textstyle 6#92;#35;#61;2#92;times 3#92;times 5#61;30.

For example, up to 10⁹, every positive integer which is a multiple of a primorial and is less than the following primorial satisfies the given inequality. There has also been little discussion on which primorials qualify in the different situations when RH fails.

2020, Rong Pan, Qinheping Hu, Rishabh Singh, Loris D'Antoni, Solving Problem Sketches with Large Integer Values, Peter Müller (editor), Programming Languages and Systems: 29th European Symposium, Proceedings, Springer, LNCS 12075, page 587, The following number theory result relates the primorial to the Chebyshev function. θ(n)= log (n#)= log 2⁽¹⁺ᵒ⁽ⁿ⁾⁾ⁿ=(1+o(n))n

Word Forms

• primorials

Related Words

Related dictionary entries include superprime, prime, semiprime, totient, antiprime, radical.

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