1 Introduction

primecount

Prime counting of sublinear complexity in Common Lisp.

Using sbcl, it can count primes under 10^12 under 8s, which outperforms sympy and pari-gp.
Also it can sum primes, count primes of the forms 4m+1 and 4m+3.

Benchmarks

The benchmarks were made on my 1.9 GHz old laptop.
It can be seen that the gaps between different lisp systems
are quite large.

Usage Examples

;; count primes <= 10^11
(primecount:prime-count (expt 10 11))

;; sum primes <= 10^11
(primecount:prime-sum (expt 10 11))

;; count primes of the forms 4m+1 and 4m+3 <= 10^11
;; (values 4m+1 4m+3)
(primecount:prime-count-mod4 (expt 10 11))

;; test if the results of prime-count match those of 
;; prime-count-mod4
(defun test (range times)
  (loop repeat times
     for i = (+ 2 (random range)) 
     do (multiple-value-bind (n1 n3) 
            (primecount:prime-count-mod4 i)
          (assert (= (primecount:prime-count i)
                     (+ n1 n3 1))))))
(test 1000000000 10)

Installation

cd ~/my/quicklisp/local-projects/
git clone https://github.com/AaronChen0/primecount.git

(ql:quickload "primecount")

Algorithm

The origin idea came from Lucy_Hedgehog from projecteuler.
It uses an optimized sieving method as shown in sympy.

Todo

Implement more efficient algorithms in pure Common Lisp.
A good reference is https://github.com/kimwalisch/primecount.

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2 Systems

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

• primecount

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3 Files

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

• Lisp

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4 Packages

Packages are listed by definition order.

• primecount

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5 Definitions

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

• Public Interface
• Internals

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