（加分題：如果n + 1和n + 3為孿生質數，你可以就數字n 寫出一個排列方法嗎？）

#### 註︰

1. 猜想：還沒有得到證明的數學論述；如果猜想得到證明就會變成定理。
2. 題外話：相減之差為六的質數對在英文被稱為「sexy primes（性感質數）」，就像孿生質數被稱為「twin primes」一樣，名字由來是因為「sex」在拉丁文中是代表「六」的前綴。在中文，「sexy primes」只是平平無其地被叫作「六質數」，並沒有任何幽默感可言。

#### 參考資料︰

1. Caldwell, C. K. (2021). The Largest Known Primes -- A Summary. Retrieved from https://primes.utm.edu/largest.html
2. Wilkinson, A. (2015, February 2). The Pursuit of Beauty. The New Yorker. Retrieved from https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty
3. Gowers, W. T. (2009, March 24). Can Polymath be scaled up [Web log post]? Retrieved from https://gowers.wordpress.com/2009/03/24/can-polymath-be-scaled-up/
4. Kalai, G. (2021, January 12). Proposals for polymath projects. Retrieved from https://mathoverflow.net/questions/219638/proposals-for-polymath-projects
5. Tao, T. (2014). Polymath8 | What’s New [Web log post]. Retrieved from https://terrytao.wordpress.com/tag/polymath8/
6. Polymath, D. H. J. (2014). New equidistribution estimates of Zhang type. Algebra & Number Theory, 8(9), 2067-2199. doi:10.2140/ant.2014.8.2067
7. Maynard, J. (2019). Gaps between primes. ArXiv. arXiv:1910.13450 [math.NT]
8. Polymath, D. H. J. (2014). Variants of the Selberg sieve, and bounded intervals containing many primes. Research in the Mathematical Sciences, 1. doi:10.1186/s40687-014-0012-7
9. Polymath Project. (2014). Bounded gaps between primes - Polymath Wiki. Retrieved from https://asone.ai/polymath/index.php?title=Bounded_gaps_between_primes
10. Polymath, D. H. J. (2014). The "bounded gaps between primes" Polymath project - a retrospective. ArXiv. arXiv:1409.8361 [math.HO]
11. Massachusetts Institute of Technology. (2020). PRIMES Math Problem Set: Solutions. Retrieved from https://math.mit.edu/research/highschool/primes/materials/2020/entpro20sol.pdf

《科言》學生編輯

《科言》學生設計師

2022年1月