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发表于 2018-3-18 12:32:23
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2018-03-17: PrimeGrid, Another World Record Generalized Cullen Prime!
On 11 March 2018, 23:54:40 UTC, PrimeGrid?s Generalized Cullen/Woodall Prime Search found the largest known Generalized Cullen prime:
1806676*41^1806676+1
Generalized Cullen numbers are of the form: n*b^n+1. Generalized Cullen numbers that are prime are called Generalized Cullen primes. For more information, please see ?Cullen prime? in The Prime Glossary.
The prime is 2,913,785 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Generalized Cullen primes and 27th overall.
Base 41 was one of 12 prime-less Generalized Cullen bases below b=121 that PrimeGrid is searching. The remaining bases are 13, 25, 29, 47, 49, 55, 69, 73, 101, 109 & 121.
The discovery was made by Hiroyuki Okazaki (zunewantan) of Japan using an Intel(R) Xeon(R) E5-2670 CPU @ 2.60GHz with 4GB RAM, running Linux. This computer took about 7 hours and 13 minutes to complete the primality test using multithreaded LLR. Hiroyuki is a member of the Aggie The Pew team.
The prime was verified on 12 March 2018 09:07:23 UTC by Scott Brown (Scott Brown) of the United States using an Intel(R) CPU @ 2.30GHz with 16GB RAM, running Windows 10 Professional Edition. This computer took about 15 hours 22 minutes to complete the primality test using LLR. Scott is also a member of the Aggie The Pew team.
For more details, please see the official announcement.
http://www.primegrid.com/forum_thread.php?id=7922
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2018-03-17: PrimeGrid,又一个创纪录的广义卡伦质数（Generalized Cullen Prime）
2018年3月11日，PrimeGrid 的子项目“卡伦/胡道尔质数搜索”找到了目前已知最大的广义卡伦质数：
1806676*41^1806676+1
广义卡伦数(Generalized Cullen numbers)是指形如n*b^n+1的数。其中的质数就称为广义卡伦质数。
该质数长为二百九十一万三千七百八十五位，为目前已知最大的卡伦质数，在已知质数排行榜中位列第27名。
该数的发现者是来自日本的老铁Hiroyuki Okazaki (zunewantan)，使用硬件为 Intel(R) Xeon(R) E5-2670 CPU @ 2.60GHz with 4GB RAM, running Linux 。这台计算机用了大约七小时十三分钟完成了对该质数的检验。Hiroyuki 是the Aggie The Pew 团队的成员。
验证信息略
附科普信息：
卡伦数：（百度百科）
卡伦数是形式如n×2^n+1（写作Cn）的自然数。若质数p = 8k − 3 = 2n − 1，Cn能被p整除。根据费马小定理，若p是奇质数，p能整除Cm(k)对于m(k) = (2k − k)(p − 1) − k (对于k > 0)。
广义卡伦数：（fwjmath）
Cullen prime是形如n*2^n+1的素数，而广义Cullen prime是形如n*b^n+1的素数，将原来的2推广成了任意的b。 |
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