𝑳′ 生成卢卡斯质数Generate Lucas Primes
列出既是卢卡斯数又是质数的项。可设要找多少个，本地用 Baillie–PSW 判断（大整数）。可设置「个数」。List Lucas numbers that are prime. Set how many to find; primality uses the Baillie–PSW test locally. Settings: How many.
使用说明与常见问题How-to & FAQ
「生成卢卡斯质数」是什么？What is the Generate Lucas Primes tool?
列出既是卢卡斯数又是质数的项。可设要找多少个，本地用 Baillie–PSW 判断（大整数）。可设置「个数」。List Lucas numbers that are prime. Set how many to find; primality uses the Baillie–PSW test locally. Settings: How many.
如何使用「生成卢卡斯质数」？How do I use the Generate Lucas Primes tool?
在「生成卢卡斯质数」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 Lucas Primes: Adjust "How many"; the result appears below instantly — click "Copy result" to copy it.
L0=2 算质数吗？Is L0=2 prime?
是。卢卡斯数从 L0=2、L1=1 开始，2 是最小的卢卡斯质数，接下来是 L2=3、L4=7、L5=11、L7=29…，与 OEIS A005479 一致。Yes. Lucas numbers start L0=2, L1=1, and 2 is the smallest Lucas prime, followed by L2=3, L4=7, L5=11, L7=29…, matching OEIS A005479.
最多能列多少个？How many can it list?
1–25 个，第 25 个是 L(617)，有 129 位。L(n) 是质数时 n 只能是 0、质数或 2、4、8、16，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）：对 3.3×10^24 以下是确定性的，更大的项是概率质数，但这个检验目前没有已知反例。1 to 25; the 25th is L(617), with 129 digits. L(n) can only be prime when n is 0, a prime, or 2, 4, 8 or 16, 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): exact below 3.3×10^24; larger terms are probable primes, though no counterexample to this test is known.
输入和输出是什么样的？What does the input and output look like?
例如在「生成卢卡斯质数」中把「个数」设为 4，输出为：2 ⏎ 3 ⏎ 7 ⏎ 11（⏎ 表示换行）。For example, in the Generate Lucas Primes with "How many" set to 4, the output is: 2 ⏎ 3 ⏎ 7 ⏎ 11 (⏎ marks a line break).
有哪些选项可以调整？What options can I adjust?
「生成卢卡斯质数」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 Lucas Primes — "How many" default 8. The result always uses the current settings.
计算精度如何？How precise are the results?
「生成卢卡斯质数」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 Lucas 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.
「生成卢卡斯质数」免费吗？需要注册吗？Is the Generate Lucas Primes free? Do I need an account?
「生成卢卡斯质数」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 Lucas 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.