Message boards : The Riesel Problem : It is conjectured that k=509203 is the smallest Riesel number. Or what?

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Michael Millerick
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Message 53555 - Posted: 30 Apr 2012 | 0:52:09 UTC - in response to Message 53553.

The conjecture is:
k=509203 is the smallest number such that k*2^n-1 is composite for all natural n.

191249*2^3417696-1 being prime proves that k=191249 does not meet the criterion for the conjecture (since that means there exists an n such that 191249*2^n-1 is prime).
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DaveB

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Message 53559 - Posted: 30 Apr 2012 | 9:19:00 UTC

Unfortunatly this means that if 509203 is not the smallest Riesel number then we cannot ever prove a smaller one, as the test of any riesel number by PG will go on to infinity!
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TroubledBunny
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Message 53563 - Posted: 30 Apr 2012 | 10:20:14 UTC - in response to Message 53559.

Unfortunatly this means that if 509203 is not the smallest Riesel number then we cannot ever prove a smaller one, as the test of any riesel number by PG will go on to infinity!

So, just to reiterate..

It is exactly the opposite of DaveB's comment that we are hoping for:
509203 is the smallest Riesel number and we will prove it (by finding primes for the remaining Ks) within a finite time.

Message boards : The Riesel Problem : It is conjectured that k=509203 is the smallest Riesel number. Or what?