如何在 Sage 中获得给定长度的素数？

Question

如何在 Sage 中获得给定位长的随机素数？

例如，为了得到一个 512 位的素数，我尝试了

p = random_prime(2^512)

但根据文档：

The command random_prime(a, True) will return a random prime between 2 and a

所以我不能使用它，因为我需要一个精确长度的素数。

Answer 1

sage: random_prime?
Signature:      random_prime(n, proof=None, lbound=2)
Docstring:
   Returns a random prime p between lbound and n (i.e. lbound <= p <=
   n). The returned prime is chosen uniformly at random from the set
   of prime numbers less than or equal to n.

   INPUT:

   * "n" - an integer >= 2.

   * "proof" - bool or None (default: None) If False, the function
     uses a pseudo-primality test, which is much faster for really big
     numbers but does not provide a proof of primality. If None, uses
     the global default (see "sage.structure.proof.proof")

   * "lbound" - an integer >= 2 lower bound for the chosen primes

这就够了吗？

sage: random_prime(2^512-1,False,2^511)
7484165189517896027318192121767201416039872004910529422703501933303497309177247161202453673508851750059292999942026203470027056226694857512284815420448467
sage: is_prime(7484165189517896027318192121767201416039872004910529422703501933303497309177247161202453673508851750059292999942026203470027056226694857512284815420448467)
True

如何在 Sage 中获得给定长度的素数？

How to get a prime of a given length in Sage?

primes

sage