IsComposite

Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand.

IsComposite(n) returns True if n is a composite number

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageCompositeQ!↗

IsComposite(number) -> booleanas compute-engine declares it

Rustis_composite(number)

IsComposite(z)for a complex $z$, whether it is composite in $\mathbb{Z}[i]$ (neither zero, a unit nor a Gaussian prime), so $3 + i = (1 + i)(2 - i)$ is.

Rustis_composite(z)

Typed signatures

Type	Package	Applies
(number | quadratic_integer, any*) -> boolean	number-theoryreplaces compute-engine	always
(number) -> boolean	compute-engine	always

Domain: Compute engine

Examples

2 more kept as data, checked against the oracles

Basic #

The smallest composite number

live ↗

In$\mathrm{IsComposite}(4)$Out$\mathrm{True}$

A prime is not composite

live ↗

In$\mathrm{IsComposite}(13)$Out$\mathrm{False}$

Scope #

A huge number decided without factoring it

live ↗

In$\mathrm{IsComposite}(1+10^{3\,000})$Out$\mathrm{True}$

Threads over a list; 1 is neither prime nor composite

live ↗

In$\mathrm{IsComposite}(\bigl\lbrack1, 2, 3, 4, 5, 6\bigr\rbrack)$Out$\bigl\lbrack\mathrm{False}, \mathrm{False}, \mathrm{False}, \mathrm{True}, \mathrm{False}, \mathrm{True}\bigr\rbrack$

Primes are never composite

live ↗

In$\mathrm{IsComposite}(5)$Out$\mathrm{False}$

live ↗

In$\mathrm{IsComposite}(3+i)$Out$\mathrm{True}$

Properties #

A power of two beyond 2 is composite

live ↗

In$\mathrm{IsComposite}(8)$Out$\mathrm{True}$

Has the proper divisors 2, 3, 4, 6

live ↗

In$\mathrm{IsComposite}(12)$Out$\mathrm{True}$

A prime just past 64, so not composite

live ↗

In$\mathrm{IsComposite}(67)$Out$\mathrm{False}$

A perfect number, $28 = 2^2\cdot 7$, is composite

live ↗

In$\mathrm{IsComposite}(28)$Out$\mathrm{True}$

Highly divisible, with many proper divisors

live ↗

In$\mathrm{IsComposite}(60)$Out$\mathrm{True}$

A large perfect power, $5^{11}$, caught as composite

live ↗

In$\mathrm{IsComposite}(48\,828\,125)$Out$\mathrm{True}$

About

Examples	14
Checked against	Wolfram Language 12 agree2 differSymPy 13 agree1 errorJulia 11 agree2 differ1 errorRust 10 agree3 error
Crosswalk	Wolfram LanguageRust

Implementation

mappedjuliapackages/oracle/src/mappings.ts

mappedrustpackages/oracle/src/mappings.ts

Greater than 1 and not prime.

mappedsympypackages/oracle/src/mappings.ts

Greater than 1 and not prime; a negative integer is not composite here.