## cl-prime-maker

2015-03-02

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."

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# 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`