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      /  美國科學家發現迄今為止的最大質數
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 美國科學家發現迄今為止的最大質數

美國科學家發現迄今為止的最大質數
中廣新聞網 2006-01-05 07:30

美國密蘇里大學的科學家發現到目前為止最大的質數。質數也稱為素數,除了本身和一以外,不能被其他任何數字整除。這個由密蘇里州大學兩位教授找出來的質數,是一個莫仙尼質數,莫仙尼是十六到十七世紀的一個法國數學家。而密蘇里大學的研究團隊用七百台電腦運算,得出的最新質數有910萬位數,它是2的3千040萬2457次方減一。

 2006-01-05 14:28
孫文先
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註冊日: 2002-07-30
發表數: 1094


 Re: 美國科學家發現迄今為止的最大質數

http://www.mersenne.org/

On December 15, 2005, Dr. Curtis Cooper and Dr. Steven Boone, professors at Central Missouri State University, discovered the 43rd Mersenne Prime,( 2^30,402,457)-1. The CMSU team is the most prolific contributor to the GIMPS project. The discovery is the largest known prime number.

The new prime is 9,152,052 digits long. This means the Electronic Frontier Foundation $100,000 award for the discovery of the first 10 million digit prime is still up for grabs! The new prime was independently verified in 5 days by Tony Reix of Bull S.A. in Grenoble, France using 16 Itanium2 1.5 GHz CPUs of a Bull NovaScale 6160 HPC at Bull Grenoble Research Center, running the Glucas program by Guillermo Ballester Valor of Granada, Spain.

Dr. Cooper joined GIMPS over 7 years ago with colleague Dr. Vince Edmondson. Edmondson was instrumental in the campus-wide effort until he passed away in 2003. Cooper, Boone, and CMSU truly earned this discovery, diligently coordinating over 700 PCs!

However, Dr. Cooper and Dr. Boone could not have made this discovery alone. In recognition of contributions made by tens of thousands GIMPS volunteers, credit for this new discovery goes to "Cooper, Boone, Woltman, Kurowski, et al". The discovery is the ninth record prime for the GIMPS project. Join now and you could find the next record-breaking prime! You could even win some cash.


_________________
孫文先 敬上

 2006-01-05 14:37個人資料傳送 Email 給 孫文先
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 Re: 美國科學家發現迄今為止的最大質數

發現梅森質數 美國研究生發現最大的質數

據《新科學家》雜誌 2003年12月2日報導,美國密西根州立大學化工系研究生麥克.薛佛,發現到目前為止最大的一個梅森質數,它可用220,996,011-1表示,共有6,320,430位數。

麥克•薛佛是「網際網路梅森質數搜尋計畫」( GIMPS)的志願參與者,他是在2003年11月17日發現這個質數,但同年12月2日才得到驗證。之前,人類發現的最大梅森質數,有4百多萬位數。

西元前 350年,希臘數學家歐基里德證明質數是無限的。此後,釵h數學家曾對這種質數進行研究。而後在17世紀,法國神父馬丁•梅森提出一個可能構成一部分質數的公式:Mp =2p-1,這堛歉也是個質數,因此後人將2p-1形式的質數稱為梅森質數。

牛津大學數學家馬庫斯.桑托伊說,梅森質數的發現對我們理解質數的分布,沒有多大的助益,但可以幫助人類測試電腦運算能力。目前全世界有 6萬多名參賽者響應GIMPS。也部A很多人無法理解這樣的行徑,但就如GIMPS發起人之一的喬治.沃特曼(George F. Woltman),1996年接受加拿大全國廣播電台訪問時所說的,尋找梅森質數這件事情本身並無任何價值可言,但是當你找到一個新的梅森質數時,心情就像登上聖母峰頂,有種征服的快感。

        

A 26-year-old graduate student in the US has made mathematical history by discovering the largest known prime number.

The new number is 6,320,430 digits long. It took just over two years to find using a distributed network(分散式運算) of more than 200,000 computers.

Michael Shafer a chemical engineering student at Michigan State University used his office computer to contribute spare processing power to the Great Internet Mersenne Prime Search (GIMPS). The project has more than 60,000 volunteers from all over the world taking part.

"I had just finished a meeting with my advisor when I saw the computer had found the new prime," Shafer says. "After a short victory dance, I called up my wife and friends involved with GIMPS to share the great news."

Prime numbers are positive integers that can only be divided by themselves and one. Mersenne primes are an especially rare type of prime that take the form 2 p-1, where p is also a prime number. The new number can be represented as 220,996,011-1. It is only the 40th Mersenne prime to have ever been found.

Mersenne primes were first discussed by Euclid in 350 BC and have been central to the branch of mathematics known as number theory ever since. They are named after a 17th century French monk who first came up with an important conjecture about which values of p would yield a prime.

Primes are the building blocks of all positive numbers. They have practical uses too, for example by providing a way of exchanging the cryptographic keys that keep internet communications secure from eavesdropping. However, despite their significance, mathematicians do not understand the way prime numbers are distributed making it very difficult to identify new primes.

Marcus du Sautoy, a mathematician at Oxford University and author of The Music of the Primes, says the discovery is unlikely to add much to our understanding of the way primes are distributed but is still significant.

"It's a really good measure of what our computational capabilities are," he told New Scientist. "It's a really fun project. Everyone gets a different bit of the number universe to look at. It's a bit like the lottery."

The GIMPS project uses a central computer server and free software to coordinate the activity of all its contributors. Contributing machines are each allocated different prime number candidates to test.

Some people contribute to GIMPS out of mathematical curiosity or to test their computer hardware, while others just hope to go down in history as the discoverer of a massive prime. There is also a financial incentive with the Electronic Frontier Foundation, a non-profit US group, offering a $100,000 prize for the discovery of the first prime with 10 million digits.

Shafer's discovery was made on 17 November but it was not independently verified until now. "It's humbling to see so many people of varied lands, ages and vocations volunteering for this fun and amazing project," says Scott Kurowski, whose company Entropia manages the GIMPS server.

"There are more primes out there," adds George Woltman, who started the GIMPS project in 1996. "And anyone with an internet-connected computer can participate."

這兩則新聞希望提供給熱愛數學的學生一個訊息,有機會得到獎金喔!

「電子前鋒基金會」( Electronic Frontier Foundation)也對這項計畫發出了懸賞,第一個找出超過千萬位質數的參賽者或機構,將頒給10萬美金;超過1億位數,將頒給15萬美元;找到10億位的,則可獲頒25萬美元。 當然,這筆獎金得來並不容易,專家預估,第 41個梅森質數所需要的運算量,將是第40個的125倍。當然,誰也說不準,在成札鰷v為25萬分之一的情況下,也釦A就是下一個獲得獎金的幸運兒。

想知道近年質數的研究,請看這個網址資料(轉貼立報)
http://iwebs.url.com.tw/main/html/lipo1/1041.shtml

熱心媽媽


 2006-01-05 14:38


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