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Big primes make passwords more secure

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The reason lies in the fact that given two big primes [math]p_{1}[/math] and [math]p_{2}[/math] it would be difficult to factorize [math]p_{1}p_{2}[/math].
The bigger [math]p_{1},p_{2}[/math], the better.

Can on the other hand exclusive knowledge of big primes be used to crack them?
I don't know how this would work so I'm just asking.
>>
>>9169241
Nah, you can download a list of big primes on the internet, it's still np-hard to factor though
>>
>>9169257
Sorry, It's not NP-hard. No polynomial algorithm exists for factoring on current architectures.
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