（加分题：如果n + 1和n + 3为孪生质数，你可以就数字n 写出一个排列方法吗？）

注︰

1. 猜想：还没有得到证明的数学论述；如果猜想得到证明就会变成定理。
2. 题外话：相减之差为六的质数对在英文被称为「sexy primes（性感质数）」，就像孪生质数被称为「twin primes」一样，名字由来是因为「sex」在拉丁文中是代表「六」的前缀。在中文，「sexy primes」只是平平无其地被叫作「六质数」，并没有任何幽默感可言。

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

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2022年1月