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Landon Curt Noll
2024-07-11 22:03:52 -07:00
parent fe9cefe6ef
commit db77e29a23
631 changed files with 90607 additions and 90600 deletions
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34
help/ptest
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@@ -5,11 +5,11 @@ SYNOPSIS
ptest(n [,count [,skip]])
TYPES
n integer
count integer with absolute value less than 2^24, defaults to 1
skip integer, defaults to 1
n integer
count integer with absolute value less than 2^24, defaults to 1
skip integer, defaults to 1
return 0 or 1
return 0 or 1
DESCRIPTION
In ptest(n, ...) the sign of n is ignored; here we assume n >= 0.
@@ -49,11 +49,11 @@ DESCRIPTION
The bases for ptest(n, count, skip) are selected as follows:
skip = 0: random in [2, n-2]
skip = 1: successive primes 2, 3, 5, ...
not exceeding min(n, 65536)
otherwise: successive integers skip, skip + 1, ...,
skip+abs(count)-1
skip = 0: random in [2, n-2]
skip = 1: successive primes 2, 3, 5, ...
not exceeding min(n, 65536)
otherwise: successive integers skip, skip + 1, ...,
skip+abs(count)-1
In particular, if m > 0, ptest(n, -m, 2) == 1 shows that n is either
prime or a strong pseudoprime for all positive integer bases <= m + 1.
@@ -63,7 +63,7 @@ DESCRIPTION
For the random case (skip = 0), the probability that any one test
with random base b will return 1 if n is composite is always
less than 1/4, so with count = k, the probability is less
than 1/4^k. For most values of n the probability is much
than 1/4^k. For most values of n the probability is much
smaller (possibly zero).
RUNTIME
@@ -85,7 +85,7 @@ RUNTIME
If the word-count for n is less than conf("redc2"), REDC algorithms
are used in evaluating ptest(n, count, skip) when small-factor
cases have been eliminated. For small word-counts (say < 10)
cases have been eliminated. For small word-counts (say < 10)
this may more than double the speed of evaluation compared with
the standard algorithms.
@@ -122,7 +122,7 @@ EXAMPLE
These results show that a is a strong pseudoprime for all 11 prime
bases less than or equal to 31, and for all positive integer bases
less than or equal to 21, but not for the bases 37 and 22. The
less than or equal to 21, but not for the bases 37 and 22. The
probability that ptest(a,-1,0) (or ptest(a,1,0)) will return 1 is
about 0.19.
@@ -145,7 +145,7 @@ SEE ALSO
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -153,8 +153,8 @@ SEE ALSO
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## Under source code control: 1996/02/25 00:27:43
## File existed as early as: 1996
## Under source code control: 1996/02/25 00:27:43
## File existed as early as: 1996
##
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/