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

`PrimeSum(f(p), p, P(p))`, rendered as $\sum_{P\left(p\right)} f\!\left(p\right)$, represents the sum 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 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 | $\sum_{p} f\!\left(p\right)$ | Sum over primes |

Source code for this entry:

Entry(ID("9f703a"), SymbolDefinition(PrimeSum, PrimeSum(f(p), p), "Sum over primes"), Description(SourceForm(PrimeSum(f(p), p)), ", rendered as ", PrimeSum(f(p), p), ", represents the sum of", f(p), "taken over all prime numbers", p, "."), Description(SourceForm(PrimeSum(f(p), p, P(p))), ", rendered as ", PrimeSum(f(p), p, P(p)), ", represents the sum 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 sum is equal to zero. Sums taken over an infinite number of terms are required to be absolutely convergent."))