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 2012-09-11, 21:32 #45 kar_bon     Mar 2006 Germany 24×3×61 Posts On occasion of the recent finds I've updated my pages for Home Prime Base 10 (49) and the Euclid-Mullin-Sequence.
 2012-11-23, 17:49 #46 kar_bon     Mar 2006 Germany 24·3·61 Posts I've extended the page with First odd k with Sophie Germain from n=4000 to n=10000.
 2012-11-24, 06:44 #47 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 24×613 Posts I don't really understand what the yellow values in that table are. The comment say "jumping champion - the highest k so far", but this can't be. For some of them there are very easy to find higher k's. For example for n=10, the table say k=141, in yellow. A one-liner in pari stops indeed at 141: Code:  gp > k=1; until(isprime(a)&&isprime(b), k++; print(k", "a=1024*k-1", "factorint(a)",\t"b=2048*k-1", "factorint(b))) 2, 2047, [23, 1; 89, 1], 4095, [3, 2; 5, 1; 7, 1; 13, 1] 3, 3071, [37, 1; 83, 1], 6143, Mat([6143, 1]) 4, 4095, [3, 2; 5, 1; 7, 1; 13, 1], 8191, Mat([8191, 1]) 5, 5119, Mat([5119, 1]), 10239, [3, 1; 3413, 1] 6, 6143, Mat([6143, 1]), 12287, [11, 1; 1117, 1] .... snip many lines .... 139, 142335, [3, 2; 5, 1; 3163, 1], 284671, [23, 1; 12377, 1] 140, 143359, [23, 2; 271, 1], 286719, [3, 1; 31, 1; 3083, 1] 141, 144383, Mat([144383, 1]), 288767, Mat([288767, 1]) gp> But then we can continue higher, removing the "k=1" in front, and it still stops at 153, then a couple of uninteresting (even) values, then 735, etc. These are not primes, but they are odd. From the other columns I see the numbers in the table are odd, not necessary primes (and there is no mention of primarity, indeed). I could easily "extend" some of the yellow cells higher. So, what exactly is the meaning of the yellow cells?
2012-11-24, 10:29   #48
kar_bon

Mar 2006
Germany

292810 Posts

Quote:
 Originally Posted by LaurV So, what exactly is the meaning of the yellow cells?
The table shows the first odd k-value of Riesel-type numbers a=k*2^n-1 and b=k*2^(n+1)-1 for which a and b both primes (Sophie Germains).

The yellow values are the highest in this table, so for n=10 k=141 is highest of all lower n and every time a k-value is higher than the last yellow, it is marked yellow as new highest.

 2012-11-24, 10:59 #49 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 24·613 Posts Ah, got it now. Not very useful, however...

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