𝐹 生成斐波那契质数Generate Fibonacci Primes
列出既是斐波那契数又是质数的项（按斐波那契下标）。可设要找多少个，本地用 Baillie–PSW 判断（大整数）。List Fibonacci numbers that are prime (by Fibonacci index). Set how many to find; primality uses the Baillie–PSW test locally.
使用说明与常见问题How-to & FAQ
「生成斐波那契质数」是什么？What is the Generate Fibonacci Primes tool?
列出既是斐波那契数又是质数的项（按斐波那契下标）。可设要找多少个，本地用 Baillie–PSW 判断（大整数）。List Fibonacci numbers that are prime (by Fibonacci index). Set how many to find; primality uses the Baillie–PSW test locally.
如何使用「生成斐波那契质数」？How do I use the Generate Fibonacci Primes tool?
在「生成斐波那契质数」中，按需设置「个数」，结果会实时显示在下方，点击「复制结果」即可复制。In the Generate Fibonacci Primes: Adjust "How many"; the result appears below instantly — click "Copy result" to copy it.
最多能列多少个？How many can it list?
1–20 个，即 F(3) 到 F(569)（第 20 个斐波那契质数有 119 位）。只有下标 n 为质数（或 n=4）时 F(n) 才可能是质数，所以只检验这些下标；判断用大整数 Baillie–PSW 检验（前 13 个质数为底的 Miller–Rabin 加强 Lucas 检验；3.3×10^24 以上是概率质数，目前没有已知反例），结果与 OEIS A005478 一致。1 to 20, i.e. F(3) up to F(569) (the 20th Fibonacci prime has 119 digits). F(n) can only be prime when n is prime (or n = 4), so only those indices are tested, using the big-integer Baillie–PSW test (Miller–Rabin with the first 13 prime bases plus a strong Lucas test; values above 3.3×10^24 are probable primes, with no known counterexample); the list matches OEIS A005478.
为何从 F3 起？Why start at F3?
F0=0、F1=F2=1 通常不视为质数；第一个斐波那契质数是 F3=2。F0=0 and F1=F2=1 are not treated as primes; the first Fibonacci prime is F3=2.
输入和输出是什么样的？What does the input and output look like?
例如在「生成斐波那契质数」中把「个数」设为 4，输出为：2 ⏎ 3 ⏎ 5 ⏎ 13（⏎ 表示换行）。For example, in the Generate Fibonacci Primes with "How many" set to 4, the output is: 2 ⏎ 3 ⏎ 5 ⏎ 13 (⏎ marks a line break).
有哪些选项可以调整？What options can I adjust?
「生成斐波那契质数」的设置：「个数」默认 8。每次生成结果都按当前设置处理。Settings in the Generate Fibonacci Primes — "How many" default 8. The result always uses the current settings.
计算精度如何？How precise are the results?
「生成斐波那契质数」中的整数都用大整数（BigInt）精确计算，不经过浮点，所以再长的项也不会丢失位数；输入超出页面说明的范围时会给出提示，而不是悄悄截断。Integers in the Generate Fibonacci Primes are computed exactly with big integers (BigInt), with no floating-point step, so even very long terms keep every digit; values outside the stated ranges give a message instead of being silently cut off.
「生成斐波那契质数」免费吗？需要注册吗？Is the Generate Fibonacci Primes free? Do I need an account?
「生成斐波那契质数」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Generate Fibonacci Primes is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.