[quote=gd_barnes;224706]16*248^n+1 is only b^4+1 when n is divisible by 4 ...[/quote]
Of course, but that's exactly what's left after the sieve.
I wouldn't have mentioned them if this series were polluted by other n's.
(Same goes for S319; it has n's divisible by 4 left; half of them are divisible by 8.)

Example of a less interesting k=16 variety:
S574, k=16, and after sieve we have only n=4*m+2. So these are N^2+1 and can be sieved for p=4q+1's only.

[quote=Batalov;224707]Of course, but that's exactly what's left after the sieve.
I wouldn't have mentioned them if this series were polluted by other n's.
(Same goes for S319; it has n's divisible by 4 left; half of them are divisible by 8.)

Example of a less interesting k=16 variety:
S574, k=16, and after sieve we have only n=4*m+2. So these are N^2+1 and can be sieved for p=4q+1's only.[/quote]

I get it now. Well...one thing good about it: Since a 16*248^n+1 prime must reduce to the form b^4+1, like you said, its composites can only have factors of the form m*b^3+1. (using m instead of k since it should not be confused with the k-value, i.e. k=16, in the original form) That being the case, the n's divisible by 4 that do remain after sieving should have a better chance than usual of being prime for the same reason that "regular" GFNs have a better chance than normal of being prime if you only consider n's that are a power of 2 because they can only have factors of the form m*b^2+1.


Gary

I would like to reserve R410 to n=25K

S436 is complete to n=25K; only k=45 remains; largest prime 73*436^1553+1; base released.

I'll do these thin 1kers to 100K : R373, S401.

168*337^61657+1 (too small for Top5K, 155849 digits) proves S337.

(whoa, it appears that I'd forgotten to reserve it; I looked at R373 and mistook it for it. R373 is almost done, too; I have it under control.)

Reserve R444 and S444 to n=100K.

[quote=Batalov;225898]168*337^61657+1 (too small for Top5K, 155849 digits) proves S337.

(whoa, it appears that I'd forgotten to reserve it; I looked at R373 and mistook it for it. R373 is almost done, too; I have it under control.)[/quote]
Oh, I remember now. I've taken it because its CK is 534 :showoff:

...and I thought that I've already reserved it as I've looked at my last message with R[I]373[/I]. (which is apparently not 337 - Ian will understand me :wink-wink: )

R410 is complete to n=25K

CK=136

8 k's remain k=39,47,58,64,67,95,98,111

Results will be emailed to MyDogBuster

Also I would like to reserve R446, R488, and R497
This should complete all in the 400 range with a CK<500

Reserving S450 to n=25K.

Riesel base 493
 

Hi all,

I've taken the lone k for Riesel 493 to n = 50,000. No luck and no further plans with this k.

Willem.