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Old 2007-06-23, 22:11   #1
gd_barnes's Avatar
May 2007
Kansas; USA

3·11·307 Posts
Default List of most small twins of form k*2^n+/-1

To whom may be interested,

I went through an excercise to find an easy way to get most of the primes of the form k * 2 ^ n +/- 1 with small values of k. What I did was I extracted all of the k's and n's from the RPS site, the Primesearch site, and the Proth search site into Excel spreadsheets. I then used Excel formulas to match up primes for the -1 sites (RPS and Primesearch) to the +1 site (Proth). The largest value of k that I could use was 599 because that is the highest that the Proth search site goes to.

Attached is a Notepad file that shows what I came up with. The first part is sorted by n. The second part by k.

Although the largest twins that I found don't come close to the top 10 or 20 twins, I think it's good to have comprehensive lists like this as 'building blocks' for future searches.

The largest twins that I found from the effort are:
1. 459 * 2 ^ 8529 +/- 1
2. 291 * 2 ^ 1553 +/- 1
3. 177 * 2 ^ 1032 +/- 1

Not too bad considering I could only match up to k=599. Obviously this list is constrainted by the lower limits of how far each k has been searched for BOTH Riesel primes and Proth primes.

If anyone knows of a more comprehensive list of Proth primes (i.e. of the form k * 2^n + 1) where k > 600 like we have at RPS for Rielsel primes, I'll extend this effort to include more k's.

Attached Files
File Type: txt twin primes match.txt (3.7 KB, 331 views)
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