[justplay]

does the current largest prime number have any practical implications as for today ?

[sklivvz1971]

Yes: https://math.stackexchange.com/questions/443706/why-it-is-im...

[TZubiri]

Most cryptography is based on factoring difficulty

[schoen]

Not using primes anywhere near the range of the largest-known ones.

The primes in your RSA keys are likely to be 1024-bit primes, or about 308 digits.

[hansvm]

Plus, the (known) large ones are all of a nice enough pattern that you could almost factor just by looking at the digit count of the product.

[schoen]

Or by finding them in one of the lists of largest known primes. :-)

[hansvm]

Yes, sorry, the implicit assumption I accidentally left in my head is that when we're talking about factoring being important, it's products of 2 biggish primes (hence an answer one step removed from the lists of largest known primes).

[graboy]

No.