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Message boards : General discussion : A new Mersenne prime was found (50th known)

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serge

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Message 112732 - Posted: 28 Dec 2017 | 16:11:28 UTC
A day after Christmas a computer has reported a new Mersenne prime.

...finished (first) double-check:
Mxxxxxxxx is prime!

Congratulations to all GIMPS participants on their 20+ years of continuing team effort!

Luigi R.

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Message 112735 - Posted: 28 Dec 2017 | 16:20:56 UTC

I was just reading at this moment and going to post here. Congratz!

What score would it get a so large prime number here at Primegrid?

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Message 112736 - Posted: 28 Dec 2017 | 17:03:08 UTC - in response to Message 112735.

I was just reading at this moment and going to post here. Congratz!

What score would it get a so large prime number here at Primegrid?

They haven't made the actual number public yet, but here are some other numbers...

The largest non-Mersenne, the SoB we found last year, has a score of 1.13 million.

M49, the previous (assuming the new Mersenne is larger) world record, has a score of 16.03 million.

If the new prime has 25 million digits (pure speculation there -- I have no actual information), the score would be about 24 million.

For those who are interested, the formula is:

score = X^3 * ln(X) / Q

X is the size of the number expressed in base e -- i.e., it's similar to the standard length calculation LOG10(k) + LOG10(b)*n, except using the natural logarithm instead of the base 10 logarithm. So X = ln(k) + ln(b)*n.

Q is a scaling factor equal to 150732545640984000.

Furthermore, if you're the double checker, the score is reduced by 50%.

It's very similar to the scoring function used at T5K, but with a different scaling factor.
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Message 112737 - Posted: 28 Dec 2017 | 17:06:03 UTC

Thanks Michael.

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Message 112957 - Posted: 3 Jan 2018 | 20:31:02 UTC

Well, we know the discovered prime now!

2^77232917-1

It is 23,249,425 digits long.

Press release: https://www.mersenne.org/primes/press/M77232917.html

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Message 112958 - Posted: 3 Jan 2018 | 20:39:06 UTC

Incredible!

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Message 112963 - Posted: 3 Jan 2018 | 20:54:28 UTC - in response to Message 112958.

Would a potential GFN-23 be larger than the newest Mersenne prime?

Yes.

It's doable, but...
A) It would be really big tests (4 times as long as GFN-22)
B) Lots of sieving needs to be done first
C) The chance of finding a prime is significantly less than finding one at n22, and we haven't found one yet at 22 after 5 years of searching. Or any at 21. The odds of success are not good.

When we first started, it wasn't even feasible because the state of the art GPUs had 1 GB of video memory. That's enough for GFN22, but not GFN23. If we did actually do this, I'd certainly restrict it to the faster video cards. You might want to think about tripling your GPU budget; a GT 1030 is not going to work on tests like that.

Items A and B we can overcome, but C makes it hard to justify the effort.
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Message 112964 - Posted: 3 Jan 2018 | 20:58:06 UTC - in response to Message 112963.

You might want to think about tripling your GPU budget; a GT 1030 is not going to work on tests like that.

Unfortunately, the computer I'm putting the GPU in is a small-form-factor Dell Optiplex which has limited power and space.

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Message 112966 - Posted: 3 Jan 2018 | 21:07:39 UTC - in response to Message 112735.

I was just reading at this moment and going to post here. Congratz!

What score would it get a so large prime number here at Primegrid?

Actual score:

18113181.97418924980940051180381
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Message 112976 - Posted: 4 Jan 2018 | 0:00:31 UTC - in response to Message 112963.

Would a potential GFN-23 be larger than the newest Mersenne prime?

Yes.

It's doable, but...
A) It would be really big tests (4 times as long as GFN-22)
B) Lots of sieving needs to be done first
C) The chance of finding a prime is significantly less than finding one at n22, and we haven't found one yet at 22 after 5 years of searching. Or any at 21. The odds of success are not good.

When we first started, it wasn't even feasible because the state of the art GPUs had 1 GB of video memory. That's enough for GFN22, but not GFN23. If we did actually do this, I'd certainly restrict it to the faster video cards. You might want to think about tripling your GPU budget; a GT 1030 is not going to work on tests like that.

Items A and B we can overcome, but C makes it hard to justify the effort.

Item B is a good reason to start GFN-23 sieving NOW. It would be good to get 5+ years of sieving in before starting GFN-23 tasks.

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Message 112977 - Posted: 4 Jan 2018 | 0:03:43 UTC - in response to Message 112963.

Would a potential GFN-23 be larger than the newest Mersenne prime?

GFN-22 is sufficient: 349218^(2^22)+1 > 2^77232917-1

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Message 112979 - Posted: 4 Jan 2018 | 0:43:34 UTC - in response to Message 112977.

Would a potential GFN-23 be larger than the newest Mersenne prime?

GFN-22 is sufficient: 349218^(2^22)+1 > 2^77232917-1

Aka vote for GFN-WR. C'mon, we run 2 GFN 17 already, no reason NOT to run 2 GFN 22.

jk :)

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Message 112981 - Posted: 4 Jan 2018 | 2:38:22 UTC - in response to Message 112979.

Would a potential GFN-23 be larger than the newest Mersenne prime?

GFN-22 is sufficient: 349218^(2^22)+1 > 2^77232917-1

Aka vote for GFN-WR. C'mon, we run 2 GFN 17 already, no reason NOT to run 2 GFN 22.

jk :)

For those who weren't around back then, you might want to look up the discussion from when M49 was discovered. The same question was asked. The answer would be the same today. (It's actually not a bad question.)
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Message 113043 - Posted: 5 Jan 2018 | 22:05:34 UTC - in response to Message 112977.

Would a potential GFN-23 be larger than the newest Mersenne prime?

GFN-22 is sufficient: 349218^(2^22)+1 > 2^77232917-1

Good! This also means that a GFN-23 would need the square root of that base to be big enough. I mean, iff

b > 2^(77232917/2^23) = 590.9

then b^(2^23) will exceed the new Mersenne prime M77232917.

/JeppeSN

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Message 113464 - Posted: 16 Jan 2018 | 16:06:17 UTC

Reading this, I found that any finder of a Mersenne Prime is awarded a \$3000 Discovery Award (no matter what the size is). I assume there's no such award for anything found on PrimeGrid??

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Message 113469 - Posted: 16 Jan 2018 | 16:49:58 UTC - in response to Message 113464.

Reading this, I found that any finder of a Mersenne Prime is awarded a \$3000 Discovery Award (no matter what the size is). I assume there's no such award for anything found on PrimeGrid??

Correct. At least not unless we are the first to find a 100 million digit prime.

GIMPS' prize money comes from an anonymous EFF prize for the first 10 million digit prime (I think -- it may have been the first 1 million digit prime). GIMPS put that prize in the bank and uses that to fund the small prizes they give out for finding each new Mersenne.

There's another prize for the first 100 million digit prime.

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Message 113472 - Posted: 16 Jan 2018 | 17:09:39 UTC - in response to Message 113469.

Reading this, I found that any finder of a Mersenne Prime is awarded a \$3000 Discovery Award (no matter what the size is). I assume there's no such award for anything found on PrimeGrid??

Correct. At least not unless we are the first to find a 100 million digit prime.

GIMPS' prize money comes from an anonymous EFF prize for the first 10 million digit prime (I think -- it may have been the first 1 million digit prime). GIMPS put that prize in the bank and uses that to fund the small prizes they give out for finding each new Mersenne.

There's another prize for the first 100 million digit prime.

I think (may be wrong) when GIMPS found the first 1 million digit prime (first megaprime), the EFF prizes had just been announced. I actually think the work unit that led to the discovery of the first megaprime, was sent to the GIMPS user before the EFF prizes had been published, but nobody knew at that time, then when the result was returned, the prize was there. If I recall correctly, the entire amount went to that one lucky GIMPS user.

After that, GIMPS made a policy that in the future the money should be split, with some going to the user who finds the relevant prime, some going to finders of other (Mersenne) primes, and some going to the GIMPS project itself. Which seems fair enough to me.

By the time the first 10 M digit prime was found, the prize was split according to their policy. If they are first at 100 M digits, it will be the same.

I suppose PrimeGrid needs no EFF prize policy because we will most probably lose the "battle" to GIMPS.

/JeppeSN

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Message 113506 - Posted: 17 Jan 2018 | 11:03:51 UTC - in response to Message 113472.

I suppose PrimeGrid needs no EFF prize policy because we will most probably lose the "battle" to GIMPS.

Having it and not needing it is better than needing it and not having it.

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Message 123276 - Posted: 10 Dec 2018 | 20:23:04 UTC

Now, less than a year later, they find yet another one (the 51st known Mersenne)!? /JeppeSN

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Message 123280 - Posted: 10 Dec 2018 | 20:32:56 UTC

Yeah, 80M-90M digits.
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Message 123283 - Posted: 10 Dec 2018 | 20:45:17 UTC - in response to Message 123280.

Yeah, 80M-90M digits.

I imagine it's bits.
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Message 123285 - Posted: 10 Dec 2018 | 20:49:04 UTC - in response to Message 123280.

Yeah, 80M-90M digits.
(Edit: Ah, Michael Goetz already said this aboveÃ¢â‚¬Â¦)

I think that means the exponent is between 80M and 90M.

Then the number of digits in the world record prime would be between 24,082,400 and 27,092,700.

/JeppeSN

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Message 123307 - Posted: 11 Dec 2018 | 6:39:26 UTC

Ahh, good old GIMPS ways:

As usual, the automatic email notification to myself and past Mersenne prime discoverers failed. Yes, the automatic email was debugged and tested after its last failure. Apparently bit rot set in. Fortunately the backup notification plan worked.

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Message 123868 - Posted: 21 Dec 2018 | 16:10:53 UTC

The new Mersenne prime is 282589933-1.

This prime is 24862048 digits long.

For those that are curious, the GFN that would be greater than this would be:
846398222+1 or 8463984194304+1
The current leading edge is 1393404194304+1, after almost 7 years.

If we were testing GFN23 the equivalent candidate would be:
920223+1 or 9208388608+1

SoB, even if we were done with the double check and were back processing leading edge candidates, would only be about 9 million digits. Even if we tested the entire contents of the SoB sieve file, that would only bring us to about 15 million digits.

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Message 123870 - Posted: 21 Dec 2018 | 17:57:28 UTC - in response to Message 123868.

The new Mersenne prime is 282589933-1.

The number of "huge" Mersenne primes is completely abnormal.

Pomerance conjectured that the expected number of Mersenne primes 2p-1 with p between n and 2n is about egamma, where gamma is Euler's constant.

egamma ~ 1.78 then the number of Mersenne primes with p in [n; 10n[ is expected to be 5.9. We have
# digits of p exp. found 1 5.9 4 2 5.9 6 3 5.9 4 4 5.9 8 5 5.9 6 6 5.9 5 7 5.9 5 8 5.9 > 13

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Message 123899 - Posted: 22 Dec 2018 | 4:15:32 UTC

Re:

The number of "huge" Mersenne primes is completely abnormal.

The simulation is breaking down! "They" never expected us to be using 100M bit numbers! ;)

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Message 123911 - Posted: 22 Dec 2018 | 12:21:48 UTC - in response to Message 123899.

Re:
The number of "huge" Mersenne primes is completely abnormal.

The simulation is breaking down! "They" never expected us to be using 100M bit numbers! ;)

This is not a simulation but a strong conjecture.
We can "simulate" the number of Mersenne primes with p in [x; 10x[ as being a Poisson distribution where the average number of events in the interval is ÃŽÂ» = 5.9165945. We have:
n prob = n prob >= n 0 0.27 % 100.00 % 1 1.59 % 99.73 % 2 4.72 % 98.14 % 3 9.30 % 93.42 % 4 13.76 % 84.12 % 5 16.28 % 70.36 % 6 16.05 % 54.08 % 7 13.57 % 38.03 % 8 10.03 % 24.46 % 9 6.60 % 14.43 % 10 3.90 % 7.83 % 11 2.10 % 3.93 % 12 1.04 % 1.83 % 13 0.47 % 0.79 % 14 0.20 % 0.32 % 15 0.08 % 0.12 % 16 0.03 % 0.04 % 17 0.01 % 0.01 %

The chance that the number of Mersenne primes with 108 <= p < 109 is 13 or more is 1 in 126!
When this sort of thing is the result of one experiment in physics you start to look for the reason for the measurement error...

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Message 123923 - Posted: 22 Dec 2018 | 15:38:40 UTC - in response to Message 123911.

Re:
The number of "huge" Mersenne primes is completely abnormal.

The simulation is breaking down! "They" never expected us to be using 100M bit numbers! ;)

This is not a simulation but a strong conjecture.

My joke was obtuse, but I like your excellent ripost, effectively "reality is a strong conjecture".

Some people like to imagine that our reality is a big simulation (like the Matrix). With unlimited time, a finite-size computer with sufficient memory could simulate something as big as our "universe" with a finite precision in agreement with quantum theory. Since software is rarely bug-free, we have strong grounds to believe that reality is not a simulation. But finding unexpected results in the realm of pure math hints at an overflow condition in the simulation.

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Message 123944 - Posted: 23 Dec 2018 | 10:10:13 UTC - in response to Message 123923.

Re:
The number of "huge" Mersenne primes is completely abnormal.

The simulation is breaking down! "They" never expected us to be using 100M bit numbers! ;)

This is not a simulation but a strong conjecture.

My joke was obtuse, but I like your excellent ripost, effectively "reality is a strong conjecture".

Some people like to imagine that our reality is a big simulation (like the Matrix). With unlimited time, a finite-size computer with sufficient memory could simulate something as big as our "universe" with a finite precision in agreement with quantum theory. Since software is rarely bug-free, we have strong grounds to believe that reality is not a simulation. But finding unexpected results in the realm of pure math hints at an overflow condition in the simulation.

you forgot, there are bugs in "the matrix" ^^
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Message 126041 - Posted: 2 Feb 2019 | 18:36:46 UTC

With Mersenne 51(?) The gauntlet was thrown down, and we have accepted the challenge!

Do You Feel Lucky?

We may not win (i.e., find the next world record prime), in fact, it's rather unlikely, but the fun is in the journey, not the destination!

Good luck to everyone, including our friends at GIMPS!

____________
My lucky number is 75898524288+1

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Message 126260 - Posted: 5 Feb 2019 | 13:47:30 UTC - in response to Message 112732.

Now we already have the 51st Mersenne prime discovered by Patrick Laroche also around Christmas!
Onward, BOINC and GIMPS users!

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Message 126261 - Posted: 5 Feb 2019 | 13:49:16 UTC - in response to Message 112977.

Actually, GFN-22 won't, since M82539933 was discovered.
GFN-23 will.
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Message 126262 - Posted: 5 Feb 2019 | 13:53:35 UTC - in response to Message 126261.

Actually, GFN-22 won't, since M82539933 was discovered.
GFN-23 will.

Welcome to Primegrid Danny, see http://www.primegrid.com/forum_thread.php?id=8434
For update.
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Message 126263 - Posted: 5 Feb 2019 | 13:55:42 UTC - in response to Message 126041.

With Mersenne 51(?) The gauntlet was thrown down, and we have accepted the challenge!

Do You Feel Lucky?

We may not win (i.e., find the next world record prime), in fact, it's rather unlikely, but the fun is in the journey, not the destination!

Good luck to everyone, including our friends at GIMPS!

The GIMPS guys are focusing on trial factoring, not doing Lucas-Lehmer tests on the 100 million primes or PRPs.
I hope that they will upgrade Prime95 becase it is so hard to use!
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GFN-14: 50103906^16384+1
Proth "SoB": 44243*2^440969+1

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Message 126264 - Posted: 5 Feb 2019 | 13:57:56 UTC - in response to Message 126262.

hi robish, thx
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Message 126274 - Posted: 5 Feb 2019 | 15:19:52 UTC - in response to Message 126263.

The GIMPS guys are focusing on trial factoring, not doing Lucas-Lehmer tests on the 100 million primes or PRPs.
I hope that they will upgrade Prime95 because it is so hard to use!

Opposite!
Prime95 is most optimized and very easy usable program !
And can be configured in many ways.

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Message 126311 - Posted: 5 Feb 2019 | 19:38:22 UTC

If GFN 23 aka "lucky" take only 23-24 hours on todays gf cards generation like 2080Ti..remind me relative short..
just if i compare to older times when was new nvidia 5xx or 6xx generations. take days to finnish one task..
maybe is time for bigger app .. i have no problem 7 day long task days on 2080Ti)). of course there is other factors what can complicated this big app ,,
For users wiht V100 nvidia is it just ..piece of cake..)
Problem is bigger app cannot by more lucky on prime.. but if try this many users.. i dont know.. i am not math spec..

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Message 126312 - Posted: 5 Feb 2019 | 19:59:59 UTC - in response to Message 126311.

If GFN 23 aka "lucky" take only 23-24 hours on todays gf cards generation like 2080Ti..remind me relative short..
just if i compare to older times when was new nvidia 5xx or 6xx generations. take days to finnish one task..
maybe is time for bigger app .. i have no problem 7 day long task days on 2080Ti)). of course there is other factors what can complicated this big app ,,
For users wiht V100 nvidia is it just ..piece of cake..)
Problem is bigger app cannot by more lucky on prime.. but if try this many users.. i dont know.. i am not math spec..

Except there's no reason to, at least not just yet. If you can test GFN 23, you can test it's 22 equivalent, which will run faster by nature, so you're better off exausting the 22 range (either by checking everything or having GIMPS find something too large) before moving to 23.

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Message 126333 - Posted: 5 Feb 2019 | 22:57:28 UTC - in response to Message 126311.

If GFN 23 aka "lucky" ...

Lucky is GFN-22, not GFN-23.
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Message 129365 - Posted: 12 May 2019 | 10:00:50 UTC - in response to Message 126333.

will the GFN-23 ever come out as a Primegrid subproject?
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Message 129371 - Posted: 12 May 2019 | 10:35:05 UTC - in response to Message 129365.

will the GFN-23 ever come out as a Primegrid subproject?

You can always try

ABC \$a^\$b+1 // 2210062663681
4 8388608
6 8388608
10 8388608
12 8388608
14 8388608
16 8388608
18 8388608
22 8388608
24 8388608
26 8388608
28 8388608
36 8388608
38 8388608
44 8388608

but number size increase rapidly!

while for 4^8388608+1 is 5050446 digits , for 10000^8388608+1 is already 33554436 digits , and for 1000000^8388608+1 is 50331654 digits.

And since you have NVIDIA GeForce GT 440 (993MB), it is far away from your reach .
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Message 129374 - Posted: 12 May 2019 | 11:07:28 UTC - in response to Message 129366.

will the GFN-23 ever come out as a Primegrid subproject?

Maybe at some time, but not now.

Every time we've considered it (usually after GIMPS finds another Mersenne prime) the numbers just didn't make a lot of sense.

Please see my earlier explanation in this same thread. Just scroll up, or down, depending on which way you have your forum preferences set.
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Message 129384 - Posted: 12 May 2019 | 13:50:00 UTC - in response to Message 129365.

will the GFN-23 ever come out as a Primegrid subproject?

In the (distant) future when we have found primes in GFN-21 and GFN-22, it is going to be natural to include also GFN-23. /JeppeSN

JeppeSN

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Message 129385 - Posted: 12 May 2019 | 14:09:05 UTC - in response to Message 129371.

You can always try

ABC \$a^\$b+1 // 2210062663681
4 8388608

GF(23, 4) = GF(24, 2) = F(24) is a known composite.

6 8388608

GF(23, 6) has two known factors on prothsearch.com.

10 8388608

You were right to leave out GF(23, 8) since 8 is a cube.
GF(23, 10) is a known composite ("S. Batalov").

12 8388608

GF(23, 12) has a known factor.

14 8388608
16 8388608

GF(23, 16) = GF(25, 2) = F(25) has three known factors.

18 8388608
22 8388608

Why did you skip exactly GF(23, 20)? Personal sieving (it has the really small factor 5*2^25+1)?

And so on.

/JeppeSN

Crun-chi
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Message 129389 - Posted: 12 May 2019 | 15:28:48 UTC - in response to Message 129385.

You can always try

ABC \$a^\$b+1 // 2210062663681
4 8388608

GF(23, 4) = GF(24, 2) = F(24) is a known composite.

6 8388608

GF(23, 6) has two known factors on prothsearch.com.

10 8388608

You were right to leave out GF(23, 8) since 8 is a cube.
GF(23, 10) is a known composite ("S. Batalov").

12 8388608

GF(23, 12) has a known factor.

14 8388608
16 8388608

GF(23, 16) = GF(25, 2) = F(25) has three known factors.

18 8388608
22 8388608

Why did you skip exactly GF(23, 20)? Personal sieving (it has the really small factor 5*2^25+1)?

And so on.

/JeppeSN

I give output of GFNsieve program. As you can see sieve depth is very low.So it is ok to have more factors...and they will be eliminate while sieve progress. Or it is bug in GFNsieve program for such big exponent
____________
92*10^1439761-1 REPDIGIT PRIME :) :) :)
314187728^131072+1 GENERALIZED FERMAT
31*332^367560+1 CRUS PRIME
Proud member of team Aggie The Pew. Go Aggie!

JeppeSN

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Message 129403 - Posted: 12 May 2019 | 22:24:12 UTC - in response to Message 129389.

I give output of GFNsieve program. As you can see sieve depth is very low.So it is ok to have more factors...and they will be eliminate while sieve progress. Or it is bug in GFNsieve program for such big exponent

Cool enough. That is probably the natural thing to do. Those very small b values are just so "interesting" that a lot is known already, but GFNsieve starts from "scratch". /JeppeSN

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