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

• 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.

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

• This function will cache some intermediate results to speed up the computation.

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

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2 Systems

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

• cl-prime-maker

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3 Modules

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

• cl-prime-maker/package-init
• cl-prime-maker/sources

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4 Files

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

• Lisp

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5 Packages

Packages are listed by definition order.

• cl-prime-maker

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6 Definitions

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

• Public Interface
• Internals

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