`PrimeProduct(f(p), p)`, rendered as $\prod_{p} f\!\left(p\right)$, represents the product of $f\!\left(p\right)$ taken over all prime numbers $p$.

`PrimeProduct(f(p), p, P(p))`, rendered as $\prod_{P\left(p\right)} f\!\left(p\right)$, represents the product of $f\!\left(p\right)$ taken over all prime numbers $p$ satisfying the predicate $P\!\left(p\right)$.

The argument

`p`defines a locally bound variable.The empty product is equal to one. Products taken over an infinite number of factors are required to be absolutely convergent.

Definitions:

Fungrim symbol | Notation | Short description |
---|---|---|

PrimeProduct | $\prod_{p} f\!\left(p\right)$ | Product over primes |

Source code for this entry:

Entry(ID("2a896d"), SymbolDefinition(PrimeProduct, PrimeProduct(f(p), p), "Product over primes"), Description(SourceForm(PrimeProduct(f(p), p)), ", rendered as ", PrimeProduct(f(p), p), ", represents the product of", f(p), "taken over all prime numbers", p, "."), Description(SourceForm(PrimeProduct(f(p), p, P(p))), ", rendered as ", PrimeProduct(f(p), p, P(p)), ", represents the product of", f(p), "taken over all prime numbers", p, "satisfying the predicate", P(p), "."), Description("The argument", SourceForm(p), "defines a locally bound variable."), Description("The empty product is equal to one. Products taken over an infinite number of factors are required to be absolutely convergent."))