Database for k-b-b's:

[3.14159]

Karsten:

I finished 751 to 1000.

Here is the file:
kbb751to1000.txt

Data for 576 coming up:

197*576^576+1
351*576^576+1
438*576^576+1
1088*576^576+1
1400*576^576+1
2657*576^576+1
3658*576^576+1
3833*576^576+1
4238*576^576+1
4373*576^576+1
5196*576^576+1
5897*576^576+1
5923*576^576+1
6540*576^576+1
7101*576^576+1
7896*576^576+1
8276*576^576+1

569: No hitter

[CRGreathouse]

Originally Posted by 3.14159

For each base value, I sieved to 10⁹ and tested from there.

Originally Posted by 3.14159

I increased the trial-division bound to 131072.

Which?

[3.14159]

Originally Posted by Charles

Which?

60 to 750, sieved to 10⁹ + 1

751 to 930, trial factoring to 10000
931 to 1000, trial factoring to 131072.

[Dougal]

thats not increasing the bound,thats decreasing the bound

[CRGreathouse]

Originally Posted by 3.14159

60 to 750, sieved to 10⁹ + 1

751 to 930, trial factoring to 10000
931 to 1000, trial factoring to 131072.

Why TD and not sieving?

[kar_bon]

I'm just testing another script (slightly changed one for SG-hunting found here) which uses cnewpgen and cLLR.

Calling like "kbbp 250 500 1 10000" to search for k*b^b+1 in the range 250<=b<=500 and 1<=k<=10000.

Primes found will be written in separate file, sieved-files and LLR-results will be saved (for later checking) and a log file gives timestamps and found primes per base.

Here first timings: (cnewpgen sieves to p=1e9)

03:27 ---------- 501.RES: 5
03:29 ---------- 502.RES: 7
03:30 ---------- 503.RES: 6
03:32 ---------- 504.RES: 12
03:33 ---------- 505.RES: 5
03:34 ---------- 506.RES: 6
03:35 ---------- 507.RES: 6
03:36 ---------- 508.RES: 4

So about 1 to 2 minutes per base here!

Will run above range over night and give results later.

[3.14159]

Originally Posted by Charles

Why TD and not sieving?

Because it requires manual work, because I have no script for it.

[kar_bon]

The whole range for k*b^b+1, k=1-10000, b=500-750 took 6h 35m with my new script!

But:

I'll test with the old pfgw-script to check this:

I run pfgw with the -a1 option to reduce "round off" errors in some cases.
The comparison of the cnewpgen/cllr results with the pfgw results showed:

pfgw -q"9238*619^619+1"
9238*619^619+1 is composite: RES64: [AF5E2DAE777932BE] (0.1462s+0.0003s)

pfgw -a1 -q"9238*619^619+1"
9238*619^619+1 is 3-PRP! (0.4438s+0.0507s)

cllr says:
9238*619^619+1 is not prime. RES64: 724FCB9240CF6A8B. OLD64: 56EF62B6C26E3F9E Time : 113.720 ms.

I've posted this in the software-thread.
Also I have to complete the pfgw-script for checking against cLLR!

[3.14159]

Using -q9238*619^619+1
Special modular reduction using all-complex FFT length 768 on 9238*619^619+1
9238*619^619+1 is composite: RES64: [AF5E2DAE777932BE] (0.0741s+0.0002s)

Using -a1 flag in addition gets me the same problem. Program bug!

[3.14159]

Karsten: Apply an N-1 test to those candidates!

To settle that one: The N-1 says it's prime, too!

Primality testing 9238*619^619+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Special modular reduction using zero-padded FFT length 1024 on 9238*619^619+1
Calling Brillhart-Lehmer-Selfridge with factored part 99.77%
9238*619^619+1 is prime! (0.0949s+0.0007s)

Proth says it is prime!

9238*619^619 + 1 may be prime. (a = 2)
9238*619^619 + 1 is prime! (a = 5) [1733 digits]

Alpertron's says it is prime! (It passed 10 bases of the Miller-Rabin)

PARI's BPSW says it is prime!

(11:06) gp > 9238 * 619^619 + 1
%1 = 10521791737525042862401806764632398042923657646716674823891306969544323994101205573714689176655991243919696037400605876253090814150192720905005250600278527578603715897533064247720049370458189693194742739471331386062060226231152068132449381714203037477244507010150743857086315973307931445506463765180636402221325082260574514705043119532103371205796084602880167838795160083882742990382044393993937877942109159969176893137731505511443594195632129250974266102509197167398347241644619582544739326773184631176946557614228911246124279968467124335096832877276494708071836502597194675835760025207070058819623791589873538017514699104839516369724057476973317779549907820921238467968708101157773715775229137147445624253490812363202905314850203123750279184140101599810266564876794130176650942133667692045560517578711657310396773969859130897909422717222474450785887484430721340768732580606878583663529307704013058922465888983847570246684125064774635387489495048705818313022904661092221971580003670900196543072813582391612419312990433035693932318434028018475159448232131979475843627419327094411710193137723609876562170798883462462890788358773191400558060227927082377847828746744722363109408973769759022853500831936828573713477526188280062405873595063014082515959578625328121022025303038079835479877190289631640250889417325517360526822004037166559595833373545081201533456667326717244754058156866313102720668337785735523213374418933780267085847731441131646783734282382026888566190859947369071339203752307037823982765686606116810496498400500831792697383650409814354309432990915988249213952145419643054072557205187975497633901417779944914352553689998866949563500653804695584455804439178530705791578972065873683664923178708868256986592481613851621055203
(11:06) gp > ispseudoprime(%)
%2 = 1

So, I must conclude: It is prime!

[CRGreathouse]

Pari certifies this as prime (4.9 seconds) with Pocklington-Lehmer:

> isprime(9238 * 619^619 + 1, 1)
[2 2 1]

[31 2 1]

[149 2 1]

[619 2 1]