The cl-prime-maker Reference Manual

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The cl-prime-maker Reference Manual

This is the cl-prime-maker Reference Manual, version 0.2, generated automatically by Declt version 4.0 beta 2 "William Riker" on Mon Aug 15 03:55:33 2022 GMT+0.

Table of Contents


1 Introduction

cl-prime-maker

A simple library to generate big prime numbers in a fast way. But in some cases, the generated number is not a prime number (these are called pseudo-primes).

Translated from the erlang version: http://www.oschina.net/code/snippet_222150_8518

##About pseudo-primes## "The probability of mis-classifying a number is approximately 2^-100. So we can be fairly sure that the classification is correct."

##Usage##

###Load the library###

CL-USER> (ql:quickload "cl-prime-maker")
To load "cl-prime-maker":
  Load 1 ASDF system:
    cl-prime-maker

###Function: cl-prime-maker:make-prime### Generates a random prime P with at least K decimal digits. Returns nil when k <= 0. Returns NIL otherwise. K should be an INTEGER.

CL-USER> (cl-prime-maker:make-prime 10)
1028450429
CL-USER> (cl-prime-maker:make-prime 10)
247158671
CL-USER> (cl-prime-maker:make-prime 10)
9424855123
CL-USER> (cl-prime-maker:make-prime 100)
2527793987464535166219814069528290578410091106736510171938329845710426162526052832327367116801544019
CL-USER> (time (cl-prime-maker:make-prime 100))
(CL-PRIME-MAKER:MAKE-PRIME 100)
took 516 milliseconds (0.516 seconds) to run.
During that period, and with 2 available CPU cores,
     516 milliseconds (0.516 seconds) were spent in user mode
       0 milliseconds (0.000 seconds) were spent in system mode
 11,720,160 bytes of memory allocated.
5699885229276577728495724707769425629156908217502336077240701491905327286488809030648850373069454909

###Function: cl-prime-maker:primep### Tests if N is a prime number. Returns T if N is a prime number. Returns NIL otherwise.

NOTES

CL-USER> (time (cl-prime-maker:primep 5699885229276577728495724707769425629156908217502336077240701491905327286488809030648850373069454909))
(CL-PRIME-MAKER:PRIMEP 5699885229276577728495724707769425629156908217502336077240701491905327286488809030648850373069454909)
took 390 milliseconds (0.390 seconds) to run.
During that period, and with 2 available CPU cores,
     391 milliseconds (0.391 seconds) were spent in user mode
       0 milliseconds (0.000 seconds) were spent in system mode
 8,757,192 bytes of memory allocated.
T
CL-USER> (time (cl-prime-maker:primep 569988522927657772849572470776942562915690821750233607724070149190532728648880903064885037306945490))
(CL-PRIME-MAKER:PRIMEP 569988522927657772849572470776942562915690821750233607724070149190532728648880903064885037306945490)
took 0 milliseconds (0.000 seconds) to run.
During that period, and with 2 available CPU cores,
     0 milliseconds (0.000 seconds) were spent in user mode
     0 milliseconds (0.000 seconds) were spent in system mode
 89,992 bytes of memory allocated.
NIL


###Function: cl-prime-maker:get-nth-prime### Generate the Nth prime number when N >= 1. Otherwise, this function always returns 2.

NOTES

CL-USER> (loop for i from 1 to 10 do (print (cl-prime-maker:get-nth-prime i)))
2 
3 
5 
7 
11 
13 
17 
19 
23 
29 
NIL
CL-USER> (time (cl-prime-maker:get-nth-prime 4000))
(CL-PRIME-MAKER:GET-NTH-PRIME 4000)
took 9,435,975 microseconds (9.435975 seconds) to run.
       422,584 microseconds (0.422584 seconds, 4.48%) of which was spent in GC.
During that period, and with 4 available CPU cores,
     9,420,502 microseconds (9.420502 seconds) were spent in user mode
       100,228 microseconds (0.100228 seconds) were spent in system mode
 1,428,879,264 bytes of memory allocated.
 1,194 minor page faults, 0 major page faults, 0 swaps.
37813
CL-USER> (time (cl-prime-maker:get-nth-prime 4000))
(CL-PRIME-MAKER:GET-NTH-PRIME 4000)
took 16 microseconds (0.000016 seconds) to run.
During that period, and with 4 available CPU cores,
      0 microseconds (0.000000 seconds) were spent in user mode
      0 microseconds (0.000000 seconds) were spent in system mode
37813

2 Systems

The main system appears first, followed by any subsystem dependency.


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2.1 cl-prime-maker

A simple library to generate big prime numbers in a fast way. But in some cases, the generated number is not a prime number (these are called pseudo-primes). "The probability of mis-classifying a number is approximately 2^-100. So we can be fairly sure that the classification is correct."

Author

Xiaofeng Yang

License

BSD

Version

0.2

Source

cl-prime-maker.asd.

Child Components

3 Modules

Modules are listed depth-first from the system components tree.


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3.1 cl-prime-maker/package-init

Source

cl-prime-maker.asd.

Parent Component

cl-prime-maker (system).

Child Component

packages.lisp (file).


3.2 cl-prime-maker/sources

Dependency

package-init (module).

Source

cl-prime-maker.asd.

Parent Component

cl-prime-maker (system).

Child Components

4 Files

Files are sorted by type and then listed depth-first from the systems components trees.


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4.1 Lisp


4.1.1 cl-prime-maker/cl-prime-maker.asd

Source

cl-prime-maker.asd.

Parent Component

cl-prime-maker (system).

ASDF Systems

cl-prime-maker.


4.1.2 cl-prime-maker/package-init/packages.lisp

Source

cl-prime-maker.asd.

Parent Component

package-init (module).

Packages

cl-prime-maker.


4.1.3 cl-prime-maker/sources/prime-maker.lisp

Source

cl-prime-maker.asd.

Parent Component

sources (module).

Public Interface
Internals

4.1.4 cl-prime-maker/sources/sm-ruiz-2000.lisp

Dependency

prime-maker.lisp (file).

Source

cl-prime-maker.asd.

Parent Component

sources (module).

Public Interface

get-nth-prime (function).

Internals

5 Packages

Packages are listed by definition order.


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5.1 cl-prime-maker

Source

packages.lisp.

Use List

common-lisp.

Public Interface
Internals

6 Definitions

Definitions are sorted by export status, category, package, and then by lexicographic order.


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6.1 Public Interface


6.1.1 Ordinary functions

Function: get-nth-prime (n)

Generate the Nth prime number when N >= 1. Otherwise this function always returns 2.

Package

cl-prime-maker.

Source

sm-ruiz-2000.lisp.

Function: make-prime (k)

Generates a random prime P with at least K decimal digits. Returns nil when k <= 0. Returns NIL otherwise. K should be an INTEGER.

Package

cl-prime-maker.

Source

prime-maker.lisp.

Function: primep (n)

Tests if N is a prime number. Returns T if N is a prime number. Returns NIL otherwise.
NOTES:
* If n <= 65535, the detection of whether a number is prime can always get the correct answer. * If n > 65535, the detection of whether a number is prime is based on the Fermat’s little theorem.

Package

cl-prime-maker.

Source

prime-maker.lisp.


6.2 Internals


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6.2.1 Special variables

Special Variable: *ruiz-pis*
Package

cl-prime-maker.

Source

sm-ruiz-2000.lisp.

Special Variable: *ruiz-pis-part1*
Package

cl-prime-maker.

Source

sm-ruiz-2000.lisp.

Special Variable: *ruiz-results*
Package

cl-prime-maker.

Source

sm-ruiz-2000.lisp.

Special Variable: +primes-below-65535+
Package

cl-prime-maker.

Source

prime-maker.lisp.


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6.2.2 Ordinary functions

Function: compute-ruiz-pi (k)
Package

cl-prime-maker.

Source

sm-ruiz-2000.lisp.

Function: compute-ruiz-pis-part1 (j)
Package

cl-prime-maker.

Source

sm-ruiz-2000.lisp.

Function: make (n)

make(n) -> I: Generates a random integer I with N decimal digits.

Package

cl-prime-maker.

Source

prime-maker.lisp.

Function: make-prime-list-for-range (maximum)
Package

cl-prime-maker.

Source

prime-maker.lisp.

Function: make-prime/2 (k p)
Package

cl-prime-maker.

Source

prime-maker.lisp.

Function: make/2 (n d)
Package

cl-prime-maker.

Source

prime-maker.lisp.

Function: new-seed ()
Package

cl-prime-maker.

Source

prime-maker.lisp.

Function: pow (a b m)

Computes V = (A^B) mod M. It’s much faster than (mod (expt a b) m).

Package

cl-prime-maker.

Source

prime-maker.lisp.

Function: primep/2 (d ntests)
Package

cl-prime-maker.

Source

prime-maker.lisp.

Function: primep/3 (ntest n len)
Package

cl-prime-maker.

Source

prime-maker.lisp.

Function: random-uniform (n)
Package

cl-prime-maker.

Source

prime-maker.lisp.


Appendix A Indexes


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A.1 Concepts