k=2003663613 and k=65516468355 primes

[kar_bon]

NewPGen can create fixed-k searches as well: click on the "Type" dropdown box and scroll down and you'll find: "k*b^n+1 (or -1) with fixed k"!

But sr(x)sieve is way better: faster and NewPGen will delete small primes (because if a primefactor is that small prime, it will be deleted from the remaining list in NewPGen!).

[mdettweiler]

Originally Posted by Puzzle-Peter

Something related: I tried using LLR on candidates of the form k*b^n-1 with b =/= 2 and the output was giving me "not prime" or "PRP". Can I use PFGW for the final primality test on these PRPs?

This would be an older version of LLR (3.7.1c or older). The current version (available from http://jpenne.free.fr/index2.html) is 3.8.1, which does full primality tests on all k*b^n+-1 numbers, regardless of base. (For base != 2, it actually does an N-1/N+1 test like PFGW does with -t/-tp, but it implements the algorithm differently so it takes no longer than a regular PRP test for nonprimes.)

But yes, for PRPs as found either by PFGW or pre-3.8 LLR, PFGW can be used for the final primality test. To do that, run it with -t or -tp as described earlier.

[Puzzle-Peter]

Great, thanks folks! You just never stop learning...

[Puzzle-Peter]

I'm going to suspend this for the duration of the Prime Grid challenge. Taking a break at n=91K for -1 and n=126K for +1

I'll be back...

[Puzzle-Peter]

OK, so here's what I got for the +1 side (-1 will take another day or so):

2003663613*2^69317+1
2003663613*2^87910+1
2003663613*2^97740+1
2003663613*2^129397+1
2003663613*2^132632+1
2003663613*2^145134+1
2003663613*2^154988+1
2003663613*2^183092+1
2003663613*2^195000+1

Looking at the 0-50K list, I had expected a bit more. But since the verification number 195000 was detected correctly, I suppose it's alright.

[mdettweiler]

Originally Posted by Puzzle-Peter

OK, so here's what I got for the +1 side (-1 will take another day or so):

2003663613*2^69317+1
2003663613*2^87910+1
2003663613*2^97740+1
2003663613*2^129397+1
2003663613*2^132632+1
2003663613*2^145134+1
2003663613*2^154988+1
2003663613*2^183092+1
2003663613*2^195000+1

Looking at the 0-50K list, I had expected a bit more. But since the verification number 195000 was detected correctly, I suppose it's alright.

From my experience with searches like this, I would concur that that amount of primes looks about right for that range on a high-weight k. The frequency of primes drops quite rapidly as n increases (so not only are the primes harder to test, they're also farther apart--hence why big primes are considered rare).

[Puzzle-Peter]

And here's the -1 side:

2003663613*2^57003-1
2003663613*2^61287-1
2003663613*2^64884-1
2003663613*2^66664-1
2003663613*2^77126-1
2003663613*2^94787-1
2003663613*2^96979-1
2003663613*2^109828-1
2003663613*2^152383-1
2003663613*2^187323-1
2003663613*2^193956-1
2003663613*2^195000-1

[Merfighters]

-1 side:

65516468355*2^15-1
65516468355*2^181-1
65516468355*2^213-1
65516468355*2^315-1
65516468355*2^373-1
65516468355*2^675-1
65516468355*2^1275-1
65516468355*2^2023-1
65516468355*2^4770-1
65516468355*2^7738-1
65516468355*2^13122-1
65516468355*2^17641-1
65516468355*2^24373-1
65516468355*2^58711-1
65516468355*2^206050-1

15 primes, completed to 221911

+1 side:

65516468355*2^23+1
65516468355*2^59+1
65516468355*2^81+1
65516468355*2^91+1
65516468355*2^94+1
65516468355*2^113+1
65516468355*2^144+1
65516468355*2^155+1
65516468355*2^173+1
65516468355*2^176+1
65516468355*2^188+1
65516468355*2^219+1
65516468355*2^253+1
65516468355*2^275+1
65516468355*2^289+1
65516468355*2^296+1
65516468355*2^365+1
65516468355*2^443+1
65516468355*2^505+1
65516468355*2^523+1
65516468355*2^600+1
65516468355*2^745+1
65516468355*2^759+1
65516468355*2^949+1
65516468355*2^1000+1
65516468355*2^1033+1
65516468355*2^1268+1
65516468355*2^1435+1
65516468355*2^3216+1
65516468355*2^3721+1
65516468355*2^3728+1
65516468355*2^5089+1
65516468355*2^5583+1
65516468355*2^5588+1
65516468355*2^6115+1
65516468355*2^6480+1
65516468355*2^6505+1
65516468355*2^8436+1
65516468355*2^10896+1
65516468355*2^13907+1
65516468355*2^16635+1
65516468355*2^20264+1
65516468355*2^20709+1
65516468355*2^21105+1
65516468355*2^21263+1
65516468355*2^28323+1
65516468355*2^30845+1
65516468355*2^45420+1
65516468355*2^67296+1
65516468355*2^70983+1
65516468355*2^79625+1
65516468355*2^80756+1
65516468355*2^97171+1
65516468355*2^103856+1

54 primes, completed to 150319

I will test both of them to 333333.

[Merfighters]

-1 side: Completed to 333333.
No additional primes (except 65516468355*2^333333-1)

+1 side: Completed to 204688. Still testing.
Additional primes: 65516468355*2^159247+1

[Merfighters]

It's been a while since the last update.
+1 side of k=65516468355 is now completed to n=295700.
Still testing.

More primes:
65516468355*2^236464+1
65516468355*2^276270+1

Oddball: Can you move the information of k=65516468355 primes to the first post?

[Oddball]

Originally Posted by Merfighters

Oddball: Can you move the information of k=65516468355 primes to the first post?

Done.