計(jì)算素?cái)?shù),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
數(shù)學(xué)中，兩個(gè)素?cái)?shù)的乘積所得的自然數(shù)我們稱之為半素?cái)?shù)(也叫雙素?cái)?shù)，二次殆素?cái)?shù)）
http://en.wikipedia.org/wiki/Goldbach's_conjecture
http://baike.baidu.com/view/1808.htm
【陳景潤與哥德巴赫猜想】Goldbach Conjecture
一
陳景潤在福州英華中學(xué)讀書時(shí)，有幸聆聽了清華大學(xué)調(diào)來的一名很有學(xué)問的數(shù)學(xué)教師講
課。他給同學(xué)們講了一道世界數(shù)學(xué)難題：“大約在200年前，一位名叫哥德巴赫的德國數(shù)學(xué)
家提出了‘任何一個(gè)偶數(shù)均可表示兩個(gè)素?cái)?shù)之和’，簡稱1＋1。他一生也沒證明出來，便給
俄國圣彼得堡的數(shù)學(xué)家歐拉寫信，請他幫助證明這道難題。歐拉接到信后，就著手計(jì)算。他
費(fèi)盡了腦筋，直到離開人世，也沒有證明出來。之后，哥德巴赫帶著一生的遺憾也離開了人
世，卻留下了這道數(shù)學(xué)難題。200多年來，這個(gè)哥德巴赫猜想之謎吸引了眾多的數(shù)學(xué)家，從
而使它成為世界數(shù)學(xué)界一大懸案”。老師講到這里還打了一個(gè)有趣的比喻，數(shù)學(xué)是自然科學(xué)
皇后，“哥德巴赫猜想”則是皇后王冠上的明珠！這引人入勝的故事給陳景潤留下了深刻的
印象，“哥德巴赫猜想”像磁石一般吸引著陳景潤。從此，陳景潤開始了摘取數(shù)學(xué)皇冠上的
明珠的艱辛歷程......
PRIME NUMBERS NOT SO RANDOM?
來自美國數(shù)學(xué)學(xué)會(huì)的網(wǎng)頁：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,...
稍微具體的介紹在http://aimath.org/goldston_tech/
其中有一段提到了已故的偉大數(shù)學(xué)家陳景潤：
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.
隨后是相鄰素?cái)?shù)的距離估計(jì)的進(jìn)展，盡管歷史上每一次壓縮的數(shù)值看起來顯得很小，可難度
是難以想象的。這次的牛人卻把結(jié)果提高了一個(gè)數(shù)量級，直接得出：
Pn+1 - Pn < (logPn)^(8/9)
Nature網(wǎng)站上有人撰文給予了高度評價(jià)：
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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