Standard Lemma guide

primorial

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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/pɹaɪ̯ˈmɔːɹi.əl/
rhymes with -ɔːɹiəl

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, number-theory, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: primorial number

Antonyms: none provided

noun

Meaning 2

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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, number-theory, sciences

Examples

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

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Blend of prime + factorial. Coined by American engineer and mathematician Harvey Dubner.

Across languages

Translations

4 source translations are retained for this English entry.

German: Primorial — product of primes
German: Primfakultät — product of primes
Italian: primoriale — product of primes
Turkish: primoriyel — product of primes

Word forms

Inflections and variants

primorials — plural

Word family

Derived and related words

Derived: none provided

Related: primorial prime

Semantic map

Other relationships

Sources

Where this information comes from

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Real reading context

Meaning relationships

Examples

Meaning relationships

primorial in complete knowledge articles