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发表于 2018-4-8 11:14:56
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2018-04-05: PrimeGrid, ESP Mega Prime!
On 3 April 2018, 15:55:55 UTC, PrimeGrid?s Extended Sierpinski Problem Prime Search project found the Mega Prime:
193997*2^11452891+1
The prime is 3,447,670 digits long and will enter Chris Caldwell's The Largest Known Primes Database ranked 23th overall. This find eliminates k=193997; 10 k's remain in the Extended Sierpinski Problem.
The discovery was made by Tom Greer (tng*) of the United States using an Intel(R) Xeon(R) E5-2620 v3 CPU @ 2.40GHz with 16GB RAM, running Microsoft Windows 10. This computer took about 3 hours 45 minutes to complete the primality test using multithreaded LLR. Tom is a member of the Sicituradastra. team.
The prime was verified on 4 April 2018, 00:17:20 UTC by Gary Bauer (GDB) of the United States using an Intel(R) Core(TM) i7-8700K CPU @ 3.70GHz with 16GB RAM, running Microsoft Windows 10. This computer took about 2 hours 25 minutes to complete the primality test using multithreaded LLR.
For more details, please see the official announcement.
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2018-04-05: PrimeGrid, ESP(Extended Sierpinski Problem )子项目发现了一个超大质数
2018年4月3日,PrimeGird 的Extended Sierpinski Problem 子项目发现了一个超大质数:
193997*2^11452891+1
该数长度为三百四十四万七千六百七十位,在目前已知质数中排名第二十三。This find eliminates k=193997; 10 k's remain in the Extended Sierpinski Problem.
该数的发现者为来自美国的老铁Tom Greer (tng*),使用的计算机为Intel(R) Xeon(R) E5-2620 v3 CPU @ 2.40GHz with 16GB RAM, running Microsoft Windows 10 。这台计算机用了月3小时45分钟完成了验证。这位发现者是Sicituradastra. team 团队的成员。
*验证信息略
*这个质数是Sierpinski问题的一个解还是什么,我不懂,所以文中关于这个的内容我直接放了原文。
这是@fwjmath 关于Sierpinski Problem 的解释:
一个数k如果满足以下性质的话,被称为Sierpinski数:k*2^n+1对于所有n都是合数。
那么,最小的Sierpinski数是多少呢?这是当年的Seventeen Or Bust的项目要做的。
而关于Extended Sierpinski Problem ,项目官网是这样描述的。太专业了不敢贸然翻译,所以贴个原文。
In 1962, John Selfridge discovered the Sierpinski number k = 78557, which is believed to be the smallest such number. The Sierpinski problem attempts to prove that it is, in fact, the smallest Sierpinski number. In 1976, Nathan Mendelsohn determined that the second provable Sierpinski number is the prime k = 271129. The prime Sierpinski problem attempts to prove that this is the smallest prime Sierpinski number.
Should both of these problems be solved, k = 78557 will be established as the smallest Sierpinski number, and k = 271129 will be established as the smallest prime Sierpinski number. However, this would not prove that k = 271129 is the second provable Sierpinski number. Since the prime Sierpinski problem is testing all prime k's for 78557 < k < 271129, all that's needed is to test the composite k's for 78557 < k < 271129. Thus, the extended Sierpinski problem is established.
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