计算素数,prime numbers
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ppm> search prime
Searching in Active Repositories
1. Bio-MCPrimers [1.04] Bio-MCPrimers
2. Math-Prime-Simple [0.12] Math-Prime-Simple
3. Math-Prime-TiedArray [0.02] Math-Prime-TiedArray
ppm> install 2
Package 2:
====================
Install 'Math-Prime-Simple' version 0.12 in ActivePerl 5.8.8.817.
====================
Downloaded 1782 bytes.
Extracting 5/5: blib/arch/auto/Math/Prime/Simple/.exists
Installing C:\Perl\html\site\lib\Math\Prime\Simple.html
Installing C:\Perl\site\lib\Math\Prime\Simple.pm
Successfully installed Math-Prime-Simple version 0.12 in ActivePerl 5.8.8.817.
NAME
Math::Prime::Simple - Calculate prime numbers
SYNOPSIS
use Math::Prime::Simple qw(prime each_prime);
@ranges = ( [ 1000, 1100 ],
[ 10000, 11000 ],
);
# primes calculation
$primes = prime( @ranges );
# primes iteration
while ($prime = each_prime( 0, $primes )) {
print "$prime\n";
}
DESCRIPTION
Math::Prime::Simple calculates prime numbers by applying the Sieve of
Eratosthenes.
FUNCTIONS
prime
Calculates prime numbers.
@ranges = ( [ 1000, 1100 ],
[ 10000, 11000 ],
);
$primes = prime( @ranges );
Each range within @ranges will be evaluated and its prime numbers will
be saved within the arrayref $primes, accessible by the array index; the
prime numbers of the first range may be accessed by @{$primes->[0]}.
each_prime
Returns each prime number as string.
while ($prime = each_prime( $index, $primes )) {
print "$prime\n";
}
$index equals the array index of @ranges.
If not all prime numbers are being evaluated by each_prime(), it is
recommended to undef @{"Math::Prime::Simple::each_prime_$index"} after
usage of each_prime().
EXPORT
"prime(), each_prime()" are exportable.
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Semiprime
数学中，两个素数的乘积所得的自然数我们称之为半素数(也叫双素数，二次殆素数）
http://en.wikipedia.org/wiki/Goldbach's_conjecture
http://baike.baidu.com/view/1808.htm
【陈景润与哥德巴赫猜想】Goldbach Conjecture
一
陈景润在福州英华中学读书时，有幸聆听了清华大学调来的一名很有学问的数学教师讲
课。他给同学们讲了一道世界数学难题：“大约在200年前，一位名叫哥德巴赫的德国数学
家提出了‘任何一个偶数均可表示两个素数之和’，简称1＋1。他一生也没证明出来，便给
俄国圣彼得堡的数学家欧拉写信，请他帮助证明这道难题。欧拉接到信后，就着手计算。他
费尽了脑筋，直到离开人世，也没有证明出来。之后，哥德巴赫带着一生的遗憾也离开了人
世，却留下了这道数学难题。200多年来，这个哥德巴赫猜想之谜吸引了众多的数学家，从
而使它成为世界数学界一大悬案”。老师讲到这里还打了一个有趣的比喻，数学是自然科学
皇后，“哥德巴赫猜想”则是皇后王冠上的明珠！这引人入胜的故事给陈景润留下了深刻的
印象，“哥德巴赫猜想”像磁石一般吸引着陈景润。从此，陈景润开始了摘取数学皇冠上的
明珠的艰辛历程......
PRIME NUMBERS NOT SO RANDOM?
来自美国数学学会的网页：http://aimath.org/
Dan Goldston and his Turkish colleague Yalcin Cem Yildirim have smashed all
previous records on the size of small gaps between prime numbers. This work is
a major step toward the centuries-old problem of showing that there are
infinitely many 'twin primes': prime numbers which differ by 2, such as 11 and
13, 17 and 19, 29 and 31,...
稍微具体的介绍在http://aimath.org/goldston_tech/
其中有一段提到了已故的伟大数学家陈景润：
In the 1960's and 1970's sieve methods developed to the point where the great
Chinese mathematician Chen was able to prove that for infinitely many primes p
the number p+2 is either prime or a product of two primes. However the
well-known ``parity problem'' in sieve theory prevents further progress.
随后是相邻素数的距离估计的进展，尽管历史上每一次压缩的数值看起来显得很小，可难度
是难以想象的。这次的牛人却把结果提高了一个数量级，直接得出：
Pn+1 - Pn < (logPn)^(8/9)
Nature网站上有人撰文给予了高度评价：
A team of physicists may have stumbled upon a surprising discovery about one of
the deepest and best-studied questions in pure mathematics: whether or not
prime numbers appear randomly in the sequence of whole numbers.
(http://www.nature.com/nsu/030317/030317-13.html)
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