A belated reply here, but check my webpage www.glasgowg43.freeserve.co.uk/nashprim.htm

for straightforwardly-generated numbers with very high Proth weight - in the equivalent context of Nash weight.

In terms of searching through those in the webage, some of the k-values are already taken, including:

986963835

302627325

302442855

806586495

(the last by me). There will be plenty of others available which should provide large numbers of small primes of the form k*2^n+1.

If you want to know more about the divisibility properties of these numbers, then go to

www.glasgowg43.freeserve.co.uk/pfaq6.htm

Joe.

-----Original Message-----

From: robert44444uk <

100620.2351@...>

To:

primenumbers@yahoogroups.com <

primenumbers@yahoogroups.com>

Date: 08 April 2002 02:33

Subject: [PrimeNumbers] Re: k.2^n+/-1 series

On the question of proth weights for k, the highest I found to date

is for 39.37#+2.31#+20.29# (289939302102450) which has a weight of

4.216. I'm sure there are higher values than this.

I am not 100% convinced by the proth weight concept. I ran this

number up to n= circa 3,200 both plus and minus one, and got 43 and

31 primes, which seems pretty average to me. As a comparison,

67#.2^n+1 plus yielded 70 primes up to n=3,300, (and 88 up to

n=18,000) with a proth weight of (only) 4.191

That said, Jack's applet is an interesting tool and I use it!

Carlos Rivera has rejected 23#.2^n-1 as the most populous -1 series,

(95 primes) because it has an index p/ln(n) of 8.00, compared to

Jack's record of 9.083. It seems you must beat not only the absolute

number of primes, but also the index to get a listing for puzzle 6

(see

http://www.primepuzzles.net/puzzles/puzz_006.htm)
On processing speed - on my machine, PRP and pfgw are about the same.

Regards

Robert Smith

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