https://github.com/nakrakiiya/cl-prime-maker.git

```
git clone 'https://github.com/nakrakiiya/cl-prime-maker.git'
```

(ql:quickload :cl-prime-maker)

★3

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

“The probability of mis-classifying a number is approximately 2^-100. So we can be fairly sure that the classification is correct.”

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

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
```

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
```

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