# Fungrim entry: 9f703a

Symbol: PrimeSum $\sum_{p} f(p)$ Sum over primes
PrimeSum(f(p), For(p)), rendered as $\sum_{p} f(p)$, represents the sum of $f(p)$ taken over all prime numbers $p$.
PrimeSum(f(p), For(p), P(p)), rendered as $\sum_{P(p)} f(p)$, represents the sum of $f(p)$ taken over all prime numbers $p$ satisfying the predicate $P(p)$.
The special expression For(p) defines p as a locally bound variable.
The empty sum is equal to zero. Sums taken over an infinite number of terms are required to be absolutely convergent.
Definitions:
Fungrim symbol Notation Short description
PrimeSum$\sum_{p} f(p)$ Sum over primes
Source code for this entry:
Entry(ID("9f703a"),
SymbolDefinition(PrimeSum, PrimeSum(f(p), For(p)), "Sum over primes"),
Description(SourceForm(PrimeSum(f(p), For(p))), ", rendered as ", PrimeSum(f(p), For(p)), ", represents the sum of", f(p), "taken over all prime numbers", p, "."),
Description(SourceForm(PrimeSum(f(p), For(p), P(p))), ", rendered as ", PrimeSum(f(p), For(p), P(p)), ", represents the sum of", f(p), "taken over all prime numbers", p, "satisfying the predicate", P(p), "."),
Description("The special expression", SourceForm(For(p)), "defines", SourceForm(p), "as a locally bound variable."),
Description("The empty sum is equal to zero. Sums taken over an infinite number of terms are required to be absolutely convergent."))

## Topics using this entry

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2021-03-15 19:12:00.328586 UTC