Bases 33-100 reservations/statuses/primes

[Dougal]

Originally Posted by Dougal

ive ran the script up to n=1028 and k=1000000 there are 12156 k's remaining,i also have k=1-100000 sieved to 10000 and currently testing.tested to 2500 and a further 170 k's eliminated from 1030 in that range.just checked it again and it's actually at n=4000 and 220 k's have been eliminated.

sorry,ive highlighted my mistake.that should be 50000.

[KEP]

I'm reserving S58, sieving is already begun on the dual core. If my Quad has in fact lost all it's work, due to the break down of the main harddisk, then this conjecture will at least somehow be ready to be attacked and worked further on, when my Quad returns from the workshop in less than 2 weeks

KEP

[gd_barnes]

Originally Posted by Siemelink

For Riesel base 40 I filtered the k's with b*k = square:
k = 110250, k*b = 2100^2, even n have factor 41 => k can be eliminated.
k = 1232010, k*b = 7020^2, even n have factor 41 => k can be eliminated.
k = 1497690, k*b = 7740^2, even n have factor 41 => k can be eliminated.
k = 2162250, k*b = 9300^2, even n have differents factors => nothing.

Did I get it right? Willem.

I inspected this base and now have a pretty clear picture on generalizing these across entire bases. This list looks right to me.

For Riesel base 40, the only k's that have this "new" condition of algebraic factors are k's where k=10*m^2 and m==(18 or 23 mod 41). Since k=2162250=10*465^2 and 465==(14 mod 41), k=2162250 does not have the sufficient condition that would give it a common factor on even-n, hence why you showed "nothing".

In the next few hours, I will have the pages entirely updated for all of these known new algebraic factors.

Eliminating the above 3 k's on Riesel base 40 leaves 2489 k's remaining at n=15K.

For bases where even-n have the common factor of 5, m must be m==(1 or 4 mod 5). What varies greatly by base, and it is based on the non-squared prime factored part of the base, is the f-value. I define the f-value as the value in the requirement equation k=f*m^2. For base 40, f=10. For bases 24 and 54, f=6, for bases 444 and 999, f=111. If you divide the base by the f value, you get a perfect square. The f-value could be said to be the largest divisor of the base that leaves a quotient that is a perfect square > 1.

Generalizing these situations across ALL bases is much more difficult then generalizing them where the common factor is on odd n and the algebraic factor are on even n, like I've already done, but they can be fairly easily generalized across individual bases.


Gary

[KEP]

Originally Posted by KEP

I'm reserving S58, sieving is already begun on the dual core. If my Quad has in fact lost all it's work, due to the break down of the main harddisk, then this conjecture will at least somehow be ready to be attacked and worked further on, when my Quad returns from the workshop in less than 2 weeks

KEP

Is also reserving Sierpinski base 60 all k's. Both this reservation aswell the reservation for Sierpinski base 58, is going for a maximum n of 125K for now It appears that optimal sievedepth is somewhere around p=1T for both bases.

Regards

KEP

[gd_barnes]

Originally Posted by Dougal

im doing some work on R79,im hoping to test it up to n=10000,at least

Since this base is b==(4 mod 5), it will have a slew of k's that can be eliminated as a result of partial algebraic factors that make a full covering set. I'll show the "old" kind on the pages but am not sure if there is the "new" kind. I don't think it will since the base is prime.

Good luck with it.

[MyDogBuster]

Sierp Base 95
Conjectured k = 41354
Covering Set = 3, 7, 13, 229
Trivial Factors k == 1 mod 2(2) and k == 46 mod 47(47)

Found Primes: 19546k's - File attached

Remaining k's: 531k's - File attached - Tested to n=25K

Trivial Factor Eliminations: 440k's

MOB Eliminations: 159k's - File attached

Base Released

[gd_barnes]

Originally Posted by MyDogBuster

Sierp Base 95
Conjectured k = 41354
Covering Set = 3, 7, 13, 229
Trivial Factors k == 1 mod 2(2) and k == 46 mod 47(47)

Found Primes: 19546k's - File attached

Remaining k's: 531k's - File attached - Tested to n=25K

Trivial Factor Eliminations: 440k's

MOB Eliminations: 159k's - File attached

Base Released

Now, THAT is an ugly base! Thanks for taking it on.

Nice new avitar. Is it a pic of your former dog?

[MyDogBuster]

Nice new avitar. Is it a pic of your former dog?

Yup, that was Buster.

S95 was getting worse and worse as time went by. Glad it's over.

[kar_bon]

currently at n=15k: since last report 190 new PRPs found. all proven prime with -tp option.

i've inlcuded the updated page for Gary, too.

[gd_barnes]

Originally Posted by kar_bon

currently at n=15k: since last report 190 new PRPs found. all proven prime with -tp option.

i've inlcuded the updated page for Gary, too.

Great. It's nice to see that one pushed a littler higher. Thanks for the page update. That helped a lot.

[gd_barnes]

R78 is complete to n=25K; 49 primes found for n=10K-25K; 98 k's remaining; base released