primelimit

Function: _def_primelimit
Class: default
Section: default
C-Name: sd_primelimit
Prototype:
Help:
Doc: \kbd{gp} precomputes a list of
 all primes less than \kbd{primelimit} at initialization time, and can build
 fast sieves on demand to quickly iterate over primes up to the \emph{square}
 of \kbd{primelimit}. These are used by many arithmetic functions, usually for
 trial division purposes. The maximal value is $2^{32} - 2049$ (resp $2^{64} -
 2049$) on a 32-bit (resp.~64-bit) machine, but values beyond $10^8$,
 allowing to iterate over primes up to $10^{16}$, do not seem useful.

 Since almost all arithmetic functions eventually require some table of prime
 numbers, PARI guarantees that the first 6547 primes, up to and
 including 65557, are precomputed, even if \kbd{primelimit} is $1$.

 This default is only used on startup: changing it will not recompute a new
 table.

 \misctitle{Deprecated feature} \kbd{primelimit} was used in some
 situations by algebraic number theory functions using the
 \tet{nf_PARTIALFACT} flag (\tet{nfbasis}, \tet{nfdisc}, \tet{nfinit}, \dots):
 this assumes that all primes $p > \kbd{primelimit}$ have a certain
 property (the equation order is $p$-maximal). This is never done by default,
 and must be explicitly set by the user of such functions. Nevertheless,
 these functions now provide a more flexible interface, and their use
 of the global default \kbd{primelimit} is deprecated.

 \misctitle{Deprecated feature} \kbd{factor(N, 0)} was used to partially
 factor integers by removing all prime factors $\leq$ \kbd{primelimit}.
 Don't use this, supply an explicit bound: \kbd{factor(N, bound)},
 which avoids relying on an unpredictable global variable.

 The default value is \kbd{500k}.