Because, at the bit-length of typical keys, very few numbers are primes, public-key systems must use very large keys to prevent exhaustive searches that try to guess the prime numbers used or to factor the keys.

• 就典型钥匙的位长而言，因为素数的数目是非常少的，故公开密钥系统必须使用非常大的密钥，以防止穷尽研究把使用的素数猜出来或把密钥的因子算出来。