News

[kar_bon]

On occasion of the recent finds I've updated my pages for Home Prime Base 10 (49) and the Euclid-Mullin-Sequence.

[kar_bon]

I've extended the page with First odd k with Sophie Germain from n=4000 to n=10000.

[LaurV]

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:

 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?

[kar_bon]

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.

[LaurV]

Ah, got it now. Not very useful, however...