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kar_bon 2012-09-11 21:32

On occasion of the recent finds I've updated my pages for [url=http://www.rieselprime.de/Others/HomePrime10.htm]Home Prime Base 10 (49)[/url] and the [url=http://www.rieselprime.de/Others/EuclidMullin.htm]Euclid-Mullin-Sequence[/url].

kar_bon 2012-11-23 17:49

I've extended the page with [url=http://www.rieselprime.de/Related/FirstSG.htm]First odd k with Sophie Germain[/url] from n=4000 to n=10000.

LaurV 2012-11-24 06:44

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>
[/CODE]

But then we can continue higher, removing the "k=1" in front, and it still stops at [B]153[/B], then a couple of uninteresting (even) values, then [B]735[/B], 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 2012-11-24 10:29

[QUOTE=LaurV;319476]So, what exactly is the meaning of the yellow cells?[/QUOTE]

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 [b]in this table[/b], 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 2012-11-24 10:59

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


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