Sieving freakishly big MMs (was "World record" phone number?)
Isn't the notion rendered nonsense by multiplying all the primes up to (say) a billion together and adding 1?
David 
2*3*5*7*11*13+1=59*509

[QUOTE=LaurV;312497]2*3*5*7*11*13+1=59*509[/QUOTE]
Hmm. So the largest prime is > 13. Euclid must have got it wrong! 
That is behind the proof that there are an infinite number of primes.

[QUOTE=LaurV;312497]2*3*5*7*11*13+1=59*509[/QUOTE]
Nothing beats a refutation as well as a simple counterexample. 
[QUOTE=davieddy;312491]Isn't the notion rendered nonsense by multiplying all the primes up to (say) a billion together and adding 1?[/QUOTE]Maybe it is composite with all factors less than M43112609?

There are tons of examples in math where we are looking for the interesting cases and ignoring the "trivial" cases which this is. Like the "nontrivial Riemann zeta function zeros".

[QUOTE=rogue;312508]That is behind the proof that there are an infinite number of primes.[/QUOTE]
Doh. Forgot that during a senile moment. 
I can say with 100% certainty that the smallest prime factor of M(M43112609) is a world record prime, but without an explicit demonstration of such a factor, that is meaningless.

[QUOTE=ewmayer;312561]I can say with 100% certainty that the smallest prime factor of M(M43112609) is a world record prime, but without an explicit demonstration of such a factor, that is meaningless.[/QUOTE]
Now you being Ernigmatic again. 
[QUOTE=ewmayer;312561]I can say with 100% certainty that the smallest prime factor of M(M43112609) is a world record prime, but without an explicit demonstration of such a factor, that is meaningless.[/QUOTE]
Just as well Bob is temporallily indisposed. 
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