Guess the number of digits in the LAST GFN-17-LOW prime

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

As you know from another (currently pinned) thread in this subforum, GFN-17-LOW is about to end.

The "LOW" means we are looking at primes with less than 1'000'000 digits.

This thread is about betting/guessing on the number of digits of the last GFN-17-LOW prime. The winner will receive all kinds of congratulations and nice words in this thread.

Note: When I say "last", I mean the largest one (which is "last" when sorting in size order). I do not care about whether a smaller GFN-17 is found at a later time.

Of course, if nobody guesses the exact number of digits, the honor goes to the person who comes closest.

I shall start. I say the last GFN-17-LOW prime will have:

999'248 digits.

/JeppeSN

ID: 152878 |

robish

Volunteer moderator
Volunteer tester
Avatar

Send message
Joined: 7 Jan 12
Posts: 2223
ID: 126266
Credit: 7,990,315,060
RAC: 5,325,758

My guess 999983.
____________
My lucky number 1059094^1048576+1

ID: 152879 |

tng

Send message
Joined: 29 Aug 10
Posts: 500
ID: 66603
Credit: 50,989,008,495
RAC: 24,086,538

998712
____________

ID: 152880 |

Monkeydee

Volunteer tester
Avatar

Send message
Joined: 8 Dec 13
Posts: 548
ID: 284516
Credit: 1,735,055,462
RAC: 3,098,297

999937
____________
My Primes
Badge Score: 4*2 + 6*2 + 7*1 + 8*11 + 9*1 + 11*3 + 12*1 = 169

ID: 152881 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

Will start sorting the bets:

998'712 tng 999'248 JeppeSN 999'937 Monkeydee 999'983 robish

/JeppeSN

ID: 152883 |

Scott Brown

Volunteer moderator
Project administrator
Volunteer tester
Project scientist
Avatar

Send message
Joined: 17 Oct 05
Posts: 2420
ID: 1178
Credit: 20,271,239,211
RAC: 24,553,657

999741

ID: 152887 |

Yves Gallot

Volunteer developer
Project scientist
Send message
Joined: 19 Aug 12
Posts: 846
ID: 164101
Credit: 306,572,235
RAC: 5,460

50/50 for one prime in [42,452,750; 42,597,772].
42452750^2¹⁷ + 1 => 999,805 digits.

ID: 152888 |

composite
Volunteer tester
Send message
Joined: 16 Feb 10
Posts: 1174
ID: 55391
Credit: 1,233,038,099
RAC: 2,043,404

1076 44'085'096*2^131'072 + 1 1'001'953 1078 44'049'878*2^131'072 + 1 1'001'908 1100 43'165'206*2^131'072 + 1 1'000'753 1101 43'163'894*2^131'072 + 1 1'000'751 1120 42'654'182*2^131'072 + 1 1'000'075 999'983 robish 999'937 Monkeydee 999'922 composite <-------- 999'805 Yves Gallot 999'741 Scott Brown 999'248 JeppeSN 998'712 tng 1194 38'734'748*2^131'072 + 1 994'588 (288larsson) 1196 38'310'998*2^131'072 + 1 993'962 1197 38'196'496*2^131'072 + 1 993'791 1198 38'152'876*2^131'072 + 1 993'726 1199 37'909'914*2^131'072 + 1 993'363

ID: 152892 |

Grebuloner

Volunteer tester
Avatar

Send message
Joined: 2 Nov 09
Posts: 526
ID: 49572
Credit: 3,608,933,101
RAC: 2,661,039

999,942
____________
Eating more cheese on Thursdays.

ID: 152895 |

dannyridel
Volunteer tester

Send message
Joined: 3 Feb 19
Posts: 1004
ID: 1097922
Credit: 101,544,058
RAC: 362,842

998,990
____________
My lucky number is 6219*2^3374198+1

ID: 152896 |

Michael Millerick

Volunteer tester
Send message
Joined: 4 Feb 09
Posts: 958
ID: 35074
Credit: 1,082,397,217
RAC: 1,133,025

999,500
____________

ID: 152897 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

Stealing the idea of composite and starting from the output of https://primes.utm.edu/primes/search.php?Description=%25%5E131072%2B1&MinDigits=990000&MaxDigits=1002000&OnList=all&Number=200&Style=Text:

1076 44085096^131072+1 1'001'953 L4482 2016 1078 44049878^131072+1 1'001'908 L4466 2016 1100 43165206^131072+1 1'000'753 L4309 2016 1101 43163894^131072+1 1'000'751 L4334 2016 1120 42654182^131072+1 1'000'075 L4208 2015 999'983 robish 999,942 Grebuloner 999'937 Monkeydee 999'922 composite 999'805 Yves Gallot 999'741 Scott Brown 999,500 Michael Millerick 999'248 JeppeSN 998,990 dannyridel 998'712 tng 1194 38734748^131072+1 994'588 L4249 2021 1196 38310998^131072+1 993'962 L4737 2021 1197 38196496^131072+1 993'791 L4861 2021 1198 38152876^131072+1 993'726 L4245 2021 1199 37909914^131072+1 993'363 L4249 2021 1201 36531196^131072+1 991'254 L4249 2021 1203 36422846^131072+1 991'085 L4245 2021 1204 36416848^131072+1 991'076 L5202 2021 1205 36038176^131072+1 990'481 L4245 2021 1206 35997532^131072+1 990'416 L4245 2021 1207 35957420^131072+1 990'353 L4245 2021

Let me know if there are any errors.

Note that you can also get a list at https://www.primegrid.com/primes/primes.php?project=GFN131072&dc=yes.

/JeppeSN

ID: 152898 |

Volunteer moderator
Project administrator

Send message
Joined: 21 Jan 10
Posts: 14045
ID: 53948
Credit: 485,564,848
RAC: 673,873

999,821
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

ID: 152899 |

dthonon

Volunteer tester

Send message
Joined: 6 Dec 17
Posts: 435
ID: 957147
Credit: 1,764,717,803
RAC: 59,628

999,600

ID: 152900 |

Pooh Bear 27

Send message
Joined: 10 May 09
Posts: 809
ID: 39821
Credit: 2,114,986,843
RAC: 1,537,905

999'727
____________
My lucky numbers are 121*2^4553899-1 and 3756801695685*2^666669±1
My movie https://vimeo.com/manage/videos/502242

ID: 152901 |

composite
Volunteer tester
Send message
Joined: 16 Feb 10
Posts: 1174
ID: 55391
Credit: 1,233,038,099
RAC: 2,043,404

Stealing the idea of composite
/JeppeSN

You get credit for not messing up the primes like I did.
All we need now is an API so that we can write bots to create these kinds of pages without a lengthy message thread.

ID: 152902 |

Hans Sveen
Send message
Joined: 18 Aug 05
Posts: 55
ID: 423
Credit: 2,043,923,150
RAC: 2,333,769

Hi!

999 876
____________
MyStats

My Badges

ID: 152903 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

999,997

ID: 152904 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

I'll probably regret asking this question.
GFN-low will go to where GFN-Mega started?
Is there any chance GFN-Mega missed a Mega?

ID: 152905 |

Volunteer moderator
Project administrator

Send message
Joined: 21 Jan 10
Posts: 14045
ID: 53948
Credit: 485,564,848
RAC: 673,873

I'll probably regret asking this question.
GFN-low will go to where GFN-Mega started?
Is there any chance GFN-Mega missed a Mega?

GFN-17-MEGA started exactly at one million digits in length, so, no, it could not have missed any mega primes.

17-low's last candidate is the largest candidate with 999,999 digits, and 17-mega's first candidate was the smallest candidate with 1,000,000 digits.

If you're asking whether there could have been any calculation errors resulting in a missed prime, the answer is effectively no. You would need a double error with exactly the same mistake in both calculations, and the odds of that of beyond astronomical.
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

ID: 152906 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

I'll probably regret asking this question.
GFN-low will go to where GFN-Mega started?
Is there any chance GFN-Mega missed a Mega?

GFN-17-MEGA started exactly at one million digits in length, so, no, it could not have missed any mega primes.

17-low's last candidate is the largest candidate with 999,999 digits, and 17-mega's first candidate was the smallest candidate with 1,000,000 digits.

If you're asking whether there could have been any calculation errors resulting in a missed prime, the answer is effectively no. You would need a double error with exactly the same mistake in both calculations, and the odds of that of beyond astronomical.

No I wasn't asking something 'sensible' like a double error.
I think I should try to learn something about what my computers are actually doing, apart from in general looking for primes.
Edit: It isn't any 1,000,000 digit number - it is a number 1,000,000 digits long that can be proven prime by how we look for GFN17? I think I can get this one. Sorry I am clogging up this thread.

ID: 152907 |

composite
Volunteer tester
Send message
Joined: 16 Feb 10
Posts: 1174
ID: 55391
Credit: 1,233,038,099
RAC: 2,043,404

I guess it's my turn to update the list of guesses.

1076 44085096^131072+1 1'001'953 L4482 2016 1078 44049878^131072+1 1'001'908 L4466 2016 1100 43165206^131072+1 1'000'753 L4309 2016 1101 43163894^131072+1 1'000'751 L4334 2016 1120 42654182^131072+1 1'000'075 L4208 2015 999'997 Nick 999'983 robish 999'942 Grebuloner 999'937 Monkeydee 999'922 composite 999'876 Hans Sveen 999'821 Michael Goetz 999'805 Yves Gallot 999'741 Scott Brown 999'727 Pooh Bear 27 999'600 dthonon 999'500 Michael Millerick 999'248 JeppeSN 998'990 dannyridel 998'712 tng 1194 38734748^131072+1 994'588 L4249 2021 1196 38310998^131072+1 993'962 L4737 2021 1197 38196496^131072+1 993'791 L4861 2021 1198 38152876^131072+1 993'726 L4245 2021 1199 37909914^131072+1 993'363 L4249 2021 1201 36531196^131072+1 991'254 L4249 2021 1203 36422846^131072+1 991'085 L4245 2021 1204 36416848^131072+1 991'076 L5202 2021 1205 36038176^131072+1 990'481 L4245 2021 1206 35997532^131072+1 990'416 L4245 2021 1207 35957420^131072+1 990'353 L4245 2021

ID: 152909 |

DeleteNull

Volunteer tester
Avatar

Send message
Joined: 6 Apr 06
Posts: 268
ID: 2663
Credit: 14,319,710,481
RAC: 9,558,429

999779 my guess.
____________
DeleteNull

ID: 152913 |

KylePolansky

Volunteer tester
Send message
Joined: 23 Oct 15
Posts: 18
ID: 425956
Credit: 384,043,008
RAC: 0

999,999 - I think it would be neat to find a prime at the very end of the search.

I suppose this guess isn't the smartest in the "closest" category.

ID: 152915 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

999,999 - I think it would be neat to find a prime at the very end of the search.

I suppose this guess isn't the smartest in the "closest" category.

It would be so cool if this happened. Perfection.

ID: 152916 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

1080 44085096^131072+1 1'001'953 L4482 2016 1082 44049878^131072+1 1'001'908 L4466 2016 1104 43165206^131072+1 1'000'753 L4309 2016 1105 43163894^131072+1 1'000'751 L4334 2016 1124 42654182^131072+1 1'000'075 L4208 2015 999'999 KylePolansky 999'997 Nick 999'983 robish 999'942 Grebuloner 999'937 Monkeydee 999'922 composite 999'876 Hans Sveen 999'821 Michael Goetz 999'805 Yves Gallot 999'779 DeleteNull 999'741 Scott Brown 999'727 Pooh Bear 27 999'600 dthonon 999'500 Michael Millerick 999'248 JeppeSN 998'990 dannyridel 998'712 tng 1198 38824296^131072+1 994'719 L4245 2021 1199 38734748^131072+1 994'588 L4249 2021 1201 38310998^131072+1 993'962 L4737 2021 1202 38196496^131072+1 993'791 L4861 2021 1203 38152876^131072+1 993'726 L4245 2021 1204 37909914^131072+1 993'363 L4249 2021 1206 36531196^131072+1 991'254 L4249 2021 1208 36422846^131072+1 991'085 L4245 2021 1209 36416848^131072+1 991'076 L5202 2021 1210 36038176^131072+1 990'481 L4245 2021 1211 35997532^131072+1 990'416 L4245 2021 1212 35957420^131072+1 990'353 L4245 2021

/JeppeSN

ID: 152931 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

Someone needs to take 999,998 and join the optimistic club
Edit: I am seeing this 999'998 and not 999,998. I'm all ears.

ID: 152940 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

Someone needs to take 999,998 and join the optimistic club
Edit: I am seeing this 999'998 and not 999,998. I'm all ears.

To me, the problem with 999,998 is that in some traditions, it means 999.998. Then 999.998, on the other hand, means 999,998. I sometimes use apostrophe to try to avoid that ambiguity. /JeppeSN

ID: 152950 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

Someone needs to take 999,998 and join the optimistic club
Edit: I am seeing this 999'998 and not 999,998. I'm all ears.

To me, the problem with 999,998 is that in some traditions, it means 999.998. Then 999.998, on the other hand, means 999,998. I sometimes use apostrophe to try to avoid that ambiguity. /JeppeSN

Cheers that makes sense. It will take me a little while to get used to it. I can see it would be very useful to see numbers at a glance. Yep that is a grouping of three. That is a decimal point.

ID: 152951 |

Vato

Volunteer tester
Avatar

Send message
Joined: 2 Feb 08
Posts: 863
ID: 18447
Credit: 884,218,235
RAC: 1,191,709

might as well dive in with 999899
____________

ID: 152952 |

Margus

Send message
Joined: 5 Feb 18
Posts: 57
ID: 974681
Credit: 618,717,466
RAC: 162,758

999925

ID: 152954 |

288larsson

Volunteer tester
Avatar

Send message
Joined: 17 Apr 10
Posts: 136
ID: 58815
Credit: 6,001,345,135
RAC: 3,137,957

Hi 999951

ID: 152959 |

Bur

Volunteer tester
Avatar

Send message
Joined: 25 Feb 20
Posts: 515
ID: 1241833
Credit: 415,654,067
RAC: 24,560

999,909 digits.

Should correspond to a base between 42518334 and 42519078. If my PARI game isn't way off.
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

ID: 152968 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

It is good to see we have some proper gamblers joining in.
I mean it could be pretty much any number less than a Meg?
And above what is happening now - knowing that a few primes will be found?

ID: 152969 |

reiner
Send message
Joined: 29 Jun 15
Posts: 13
ID: 410433
Credit: 245,662,635
RAC: 69,124

My guess 999 000 digits.

ID: 152972 |

composite
Volunteer tester
Send message
Joined: 16 Feb 10
Posts: 1174
ID: 55391
Credit: 1,233,038,099
RAC: 2,043,404

Is it mathematically guaranteed that there's another sub-mega prime, or is it just highly unlikely that there isn't another one?

ID: 152975 |

Michael Millerick

Volunteer tester
Send message
Joined: 4 Feb 09
Posts: 958
ID: 35074
Credit: 1,082,397,217
RAC: 1,133,025

Is it mathematically guaranteed that there's another sub-mega prime, or is it just highly unlikely that there isn't another one?

There could be none, but the last I saw on discord from a week or so ago was that there are about 15 expected between the leading edge at the time and the 1 million digit cut off.
____________

ID: 152976 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

Is it mathematically guaranteed that there's another sub-mega prime, or is it just highly unlikely that there isn't another one?

There could be none, but the last I saw on discord from a week or so ago was that there are about 15 expected between the leading edge at the time and the 1 million digit cut off.

I like that Kyle and I have made a ridiculous prediction.
Kind of 100 to 1 odds.

ID: 152979 |

matzetoni
Send message
Joined: 25 Nov 17
Posts: 69
ID: 952510
Credit: 47,537,478
RAC: 0

999666 digits

:)

ID: 152980 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

999666 digits

:)

Satan mirror man - nice

ID: 152984 |

dannyridel
Volunteer tester

Send message
Joined: 3 Feb 19
Posts: 1004
ID: 1097922
Credit: 101,544,058
RAC: 362,842

Just as a reference, the smallest GFN17MEG is 1000075 digits.
____________
My lucky number is 6219*2^3374198+1

ID: 152985 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

Is it mathematically guaranteed that there's another sub-mega prime, or is it just highly unlikely that there isn't another one?

No guarantee, the most recent one with 994'719 digits could be the last one. In that case the winner is going to be the person closest to 994'719. But it would be really rare with such a huge primefree region. /JeppeSN

ID: 152986 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

Just as a reference, the smallest GFN17MEG is 1000075 digits.

Yes! This is also what you can see if you understand our weird new way of presenting the summary of bets. /JeppeSN

ID: 152987 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

1080 44085096^131072+1 1'001'953 L4482 2016 1082 44049878^131072+1 1'001'908 L4466 2016 1104 43165206^131072+1 1'000'753 L4309 2016 1105 43163894^131072+1 1'000'751 L4334 2016 1124 42654182^131072+1 1'000'075 L4208 2015 999'999 KylePolansky 999'997 Nick 999'983 robish 999'951 288larsson 999'942 Grebuloner 999'937 Monkeydee 999'925 Margus 999'922 composite 999'909 Bur 999'899 Vato 999'876 Hans Sveen 999'821 Michael Goetz 999'805 Yves Gallot 999'779 DeleteNull 999'741 Scott Brown 999'727 Pooh Bear 27 999'666 matzetoni 999'600 dthonon 999'500 Michael Millerick 999'248 JeppeSN 999'000 reiner 998'990 dannyridel 998'712 tng 1198 38824296^131072+1 994'719 L4245 2021 1199 38734748^131072+1 994'588 L4249 2021 1201 38310998^131072+1 993'962 L4737 2021 1202 38196496^131072+1 993'791 L4861 2021 1203 38152876^131072+1 993'726 L4245 2021 1204 37909914^131072+1 993'363 L4249 2021 1206 36531196^131072+1 991'254 L4249 2021 1208 36422846^131072+1 991'085 L4245 2021 1209 36416848^131072+1 991'076 L5202 2021 1210 36038176^131072+1 990'481 L4245 2021 1211 35997532^131072+1 990'416 L4245 2021 1212 35957420^131072+1 990'353 L4245 2021

/JeppeSN

ID: 152988 |

Scott Cox
Send message
Joined: 3 Aug 16
Posts: 54
ID: 453662
Credit: 39,050,075
RAC: 6

999,998

ID: 152990 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

999,998

Excellent

ID: 152991 |

lunchboxkwdm
Send message
Joined: 22 Nov 14
Posts: 8
ID: 374284
Credit: 91,867,500
RAC: 30,240

I'll take 999,939.

ID: 152996 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

I imagine a Mathematician would be considering the rate of primes (sorry for my terminology) and knowing the gap between LOW and MEGA could get a good handle of how many primes in that gap and a very good guess as to where?
1'000'000 is an arbitrary thing - nothing special about it. It would be kind of fun if something weird happened around that number. Someone correctly guessing a strange moment in the distribution of primes is cool

ID: 153005 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

I imagine a Mathematician would be considering the rate of primes (sorry for my terminology) and knowing the gap between LOW and MEGA could get a good handle of how many primes in that gap and a very good guess as to where?
1'000'000 is an arbitrary thing - nothing special about it. It would be kind of fun if something weird happened around that number. Someone correctly guessing a strange moment in the distribution of primes is cool

Go to the page http://yves.gallot.pagesperso-orange.fr/primes/stat.html by Yves Gallot who posted above. In the form Computation of the expected number of GF primes in a fixed range and of the associated Poisson distribution, pick N = 131072, and type in stuff like bMin = 38824296 and bMax = 42597772. You can calculate how many Generalized Fermat primes of that N are "expected". Chance of 0 primes may be too small t be shown (but it is nonzero). /JeppeSN

ID: 153007 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

I imagine a Mathematician would be considering the rate of primes (sorry for my terminology) and knowing the gap between LOW and MEGA could get a good handle of how many primes in that gap and a very good guess as to where?
1'000'000 is an arbitrary thing - nothing special about it. It would be kind of fun if something weird happened around that number. Someone correctly guessing a strange moment in the distribution of primes is cool

Go to the page http://yves.gallot.pagesperso-orange.fr/primes/stat.html by Yves Gallot who posted above. In the form Computation of the expected number of GF primes in a fixed range and of the associated Poisson distribution, pick N = 131072, and type in stuff like bMin = 38824296 and bMax = 42597772. You can calculate how many Generalized Fermat primes of that N are "expected". Chance of 0 primes may be too small t be shown (but it is nonzero). /JeppeSN

And let us say we wanted to calculate the chance KylePolansky's 999'999 guess was accurate, you would need bMin as 10^(999998/131072) and bMax as 10^(999999/131072). You can calculate these two bounds on a calculator. The result is:

Chance of no prime: 99.64% (100%) Chance of 1 prime: 0.36% (0%)

This does not take into account how many numbers actually survived the sieving, so should probably not be attempted with extremely short intervals.

/JeppeSN

ID: 153008 |

Yves Gallot

Volunteer developer
Project scientist
Send message
Joined: 19 Aug 12
Posts: 846
ID: 164101
Credit: 306,572,235
RAC: 5,460

I imagine a Mathematician would be considering the rate of primes (sorry for my terminology) and knowing the gap between LOW and MEGA could get a good handle of how many primes in that gap and a very good guess as to where?

The expected number of primes in [38,824,296; 42,597,772] is 18. The mean gap is about Δb ~ 220,000 or 190 digits.
But this is a mean value and we have the consecutive GFN-17:
58447642¹³¹⁰⁷² + 1 1018006 digits
58447816¹³¹⁰⁷² + 1 1018006 digits
and
47179704¹³¹⁰⁷² + 1 1005815 digits
48273828¹³¹⁰⁷² + 1 1007120 digits
Mathematically, the distribution of b-gaps is expected to be close to an exponential distribution.

Alea iacta est.

ID: 153011 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

I imagine a Mathematician would be considering the rate of primes (sorry for my terminology) and knowing the gap between LOW and MEGA could get a good handle of how many primes in that gap and a very good guess as to where?

The expected number of primes in [38,824,296; 42,597,772] is 18. The mean gap is about Δb ~ 220,000 or 190 digits.
But this is a mean value and we have the consecutive GFN-17:
58447642¹³¹⁰⁷² + 1 1018006 digits
58447816¹³¹⁰⁷² + 1 1018006 digits
and
47179704¹³¹⁰⁷² + 1 1005815 digits
48273828¹³¹⁰⁷² + 1 1007120 digits
Mathematically, the distribution of b is expected to be close to an exponential distribution.

Alea iacta est.

Veritas communicans est pulchritudo imaginari.

ID: 153012 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

58447642¹³¹⁰⁷² + 1 1018006 digits
58447816¹³¹⁰⁷² + 1 1018006 digits

Is this the first case of two GFN-17 primes having the same number of digits?

For what n do we know explicit GFN-n primes with the same number of digits? How soon (in b) would you expect it to occur?

/JeppeSN

ID: 153024 |

Yves Gallot

Volunteer developer
Project scientist
Send message
Joined: 19 Aug 12
Posts: 846
ID: 164101
Credit: 306,572,235
RAC: 5,460

58447642¹³¹⁰⁷² + 1 1018006 digits
58447816¹³¹⁰⁷² + 1 1018006 digits

Is this the first case of two GFN-17 primes having the same number of digits?

This is the first known case but it will be first case when GFN-17low is completed.

Δb = 174 is the smallest known gap. The next ones are 1312 (43163894/43165206) and 1546 (24641166/24642712) and the gap in digits is 2.

For what n do we know explicit GFN-n primes with the same number of digits? How soon (in b) would you expect it to occur?

Consecutive GF primes are a better criterion than the number of digits (see message 150295 and 150300).
There are ten GFN-13 pairs in [2; 2G] and one GFN-14 pair in [2; 400M] (56414914/56414916). A lucky GFN-15 pair was found 87888966/87888968 [260,307 digits].
For GFN-16, the smallest gap in [2; 100M] is 104 (92914140/92914244) [522,197 digits].

If Bateman and Horn conjecture is true, since ∫dx/(log x)² is divergent, for each n the number of consecutive GF-n primes is infinite.

ID: 153033 |

mexico
Send message
Joined: 6 Jan 13
Posts: 11
ID: 188081
Credit: 8,635,181
RAC: 0

999973
____________
My lucky number is: 129448306^65536+1

ID: 153035 |

composite
Volunteer tester
Send message
Joined: 16 Feb 10
Posts: 1174
ID: 55391
Credit: 1,233,038,099
RAC: 2,043,404

1080 44085096^131072+1 1'001'953 L4482 2016 1082 44049878^131072+1 1'001'908 L4466 2016 1104 43165206^131072+1 1'000'753 L4309 2016 1105 43163894^131072+1 1'000'751 L4334 2016 1124 42654182^131072+1 1'000'075 L4208 2015 999'999 KylePolansky 999'998 Scott Cox 999'997 Nick 999'983 robish 999'973 mexico 999'951 288larsson 999'942 Grebuloner 999'939 lunchboxkwdm 999'937 Monkeydee 999'925 Margus 999'922 composite 999'909 Bur 999'899 Vato 999'876 Hans Sveen 999'821 Michael Goetz 999'805 Yves Gallot 999'779 DeleteNull 999'741 Scott Brown 999'727 Pooh Bear 27 999'666 matzetoni 999'600 dthonon 999'500 Michael Millerick 999'248 JeppeSN 999'000 reiner 998'990 dannyridel 998'712 tng 39134382^131072+1 995'172 leading edge 1198 38824296^131072+1 994'719 L4245 2021 1199 38734748^131072+1 994'588 L4249 2021 1201 38310998^131072+1 993'962 L4737 2021 38221298^131072+1 993'828 min remaining 1202 38196496^131072+1 993'791 L4861 2021 1203 38152876^131072+1 993'726 L4245 2021 1204 37909914^131072+1 993'363 L4249 2021 1206 36531196^131072+1 991'254 L4249 2021 1208 36422846^131072+1 991'085 L4245 2021 1209 36416848^131072+1 991'076 L5202 2021 1210 36038176^131072+1 990'481 L4245 2021 1211 35997532^131072+1 990'416 L4245 2021 1212 35957420^131072+1 990'353 L4245 2021

Looking at tasks completed per day,
at the current rate there are 44 days of work left in this subproject,
and at the maximum rate, it could be as little as 3 days.

ID: 153036 |

Chara34122
Send message
Joined: 11 Feb 17
Posts: 100
ID: 490242
Credit: 20,375,187
RAC: 5,706

999996
____________

ID: 153040 |

pschoefer

Volunteer developer
Volunteer tester
Avatar

Send message
Joined: 20 Sep 05
Posts: 686
ID: 845
Credit: 3,027,797,032
RAC: 1,372,732

999 924
____________

ID: 153041 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

For what n do we know explicit GFN-n primes with the same number of digits? How soon (in b) would you expect it to occur?

Consecutive GF primes are a better criterion than the number of digits [...]

It must be admitted that it would have been more "scientific" if I had let this thread be about guessing b, instead of guessing the number of decimal digits. But after all, the cutoff between GFN-17-LOW and -MEGA is based on the number of digits, so I guess that was my reason.

I found the first time two primes of form b^N+1 had the same number of digits, for N up to 1024. 2, 6, 17, 36, 66, 195, 520, 852, 1870, 4876, ...

Thank you for your answer.

/JeppeSN

ID: 153043 |

dthonon

Volunteer tester

Send message
Joined: 6 Dec 17
Posts: 435
ID: 957147
Credit: 1,764,717,803
RAC: 59,628

Looking at tasks completed per day,
at the current rate there are 44 days of work left in this subproject,
and at the maximum rate, it could be as little as 3 days.

Most probably, the subproject will run out of tasks in 14 days, shortly after the start of Heptadecagenarian challenge.

ID: 153046 |

composite
Volunteer tester
Send message
Joined: 16 Feb 10
Posts: 1174
ID: 55391
Credit: 1,233,038,099
RAC: 2,043,404

The leading edge is advancing at over 5 digits per hour now => about 37 days left.
As dthonon says, the subproject won't last that long.

1080 44085096^131072+1 1'001'953 L4482 2016 1082 44049878^131072+1 1'001'908 L4466 2016 1104 43165206^131072+1 1'000'753 L4309 2016 1105 43163894^131072+1 1'000'751 L4334 2016 1124 42654182^131072+1 1'000'075 L4208 2015 999'999 KylePolansky 999'998 Scott Cox 999'997 Nick 999'996 Chara34122 999'983 robish 999'973 mexico 999'951 288larsson 999'942 Grebuloner 999'939 lunchboxkwdm 999'937 Monkeydee 999'925 Margus 999'924 pschoefer 999'922 composite 999'909 Bur 999'899 Vato 999'876 Hans Sveen 999'821 Michael Goetz 999'805 Yves Gallot 999'779 DeleteNull 999'741 Scott Brown 999'727 Pooh Bear 27 999'666 matzetoni 999'600 dthonon 999'500 Michael Millerick 999'248 JeppeSN 999'000 reiner 998'990 dannyridel 998'712 tng 39242650^131072+1 995'330 leading edge 1198 38824296^131072+1 994'719 L4245 2021 1199 38734748^131072+1 994'588 L4249 2021 1201 38310998^131072+1 993'962 L4737 2021 38221298^131072+1 993'828 min remaining 1202 38196496^131072+1 993'791 L4861 2021 1203 38152876^131072+1 993'726 L4245 2021 1204 37909914^131072+1 993'363 L4249 2021 1206 36531196^131072+1 991'254 L4249 2021 1208 36422846^131072+1 991'085 L4245 2021 1209 36416848^131072+1 991'076 L5202 2021 1210 36038176^131072+1 990'481 L4245 2021 1211 35997532^131072+1 990'416 L4245 2021 1212 35957420^131072+1 990'353 L4245 2021

ID: 153052 |

composite
Volunteer tester
Send message
Joined: 16 Feb 10
Posts: 1174
ID: 55391
Credit: 1,233,038,099
RAC: 2,043,404

1083 44085096^131072+1 1'001'953 L4482 2016 1085 44049878^131072+1 1'001'908 L4466 2016 1107 43165206^131072+1 1'000'753 L4309 2016 1108 43163894^131072+1 1'000'751 L4334 2016 1127 42654182^131072+1 1'000'075 L4208 2015 999'999 KylePolansky 999'998 Scott Cox 999'997 Nick 999'996 Chara34122 999'983 robish 999'973 mexico 999'951 288larsson 999'942 Grebuloner 999'939 lunchboxkwdm 999'937 Monkeydee 999'925 Margus 999'924 pschoefer 999'922 composite 999'909 Bur 999'899 Vato 999'876 Hans Sveen 999'821 Michael Goetz 999'805 Yves Gallot 999'779 DeleteNull 999'741 Scott Brown 999'727 Pooh Bear 27 999'666 matzetoni 999'600 dthonon 999'500 Michael Millerick 999'248 JeppeSN 999'000 reiner 998'990 dannyridel 998'712 tng 39329840^131072+1 995'456 leading edge 1201 39100746^131072+1 995'123 L5441 2022 1202 38824296^131072+1 994'719 L4245 2021 1203 38734748^131072+1 994'588 L4249 2021 1205 38310998^131072+1 993'962 L4737 2021 38221298^131072+1 993'828 min remaining 1206 38196496^131072+1 993'791 L4861 2021 1207 38152876^131072+1 993'726 L4245 2021 1208 37909914^131072+1 993'363 L4249 2021 1210 36531196^131072+1 991'254 L4249 2021 1212 36422846^131072+1 991'085 L4245 2021 1213 36416848^131072+1 991'076 L5202 2021 1214 36038176^131072+1 990'481 L4245 2021 1215 35997532^131072+1 990'416 L4245 2021 1216 35957420^131072+1 990'353 L4245 2021

ID: 153079 |

TeeVeeEss

Send message
Joined: 19 Jul 08
Posts: 12
ID: 25852
Credit: 388,302,591
RAC: 0

999 888

ID: 153096 |

Pilgrim

Send message
Joined: 22 Dec 06
Posts: 125
ID: 4240
Credit: 144,552,766
RAC: 0

999,249 digits

ID: 153099 |

Jay

Send message
Joined: 27 Feb 10
Posts: 136
ID: 56067
Credit: 65,857,807
RAC: 9,485

998,264

ID: 153109 |

composite
Volunteer tester
Send message
Joined: 16 Feb 10
Posts: 1174
ID: 55391
Credit: 1,233,038,099
RAC: 2,043,404

1083 44085096^131072+1 1'001'953 L4482 2016 1085 44049878^131072+1 1'001'908 L4466 2016 1107 43165206^131072+1 1'000'753 L4309 2016 1108 43163894^131072+1 1'000'751 L4334 2016 1127 42654182^131072+1 1'000'075 L4208 2015 999'999 KylePolansky 999'998 Scott Cox 999'997 Nick 999'996 Chara34122 999'983 robish 999'973 mexico 999'951 288larsson 999'942 Grebuloner 999'939 lunchboxkwdm 999'937 Monkeydee 999'925 Margus 999'924 pschoefer 999'922 composite 999'909 Bur 999'899 Vato 999'888 TeeVeeEss 999'876 Hans Sveen 999'821 Michael Goetz 999'805 Yves Gallot 999'779 DeleteNull 999'741 Scott Brown 999'727 Pooh Bear 27 999'666 matzetoni 999'600 dthonon 999'500 Michael Millerick 999'249 Pilgrim 999'248 JeppeSN 999'000 reiner 998'990 dannyridel 998'712 tng 998'264 Jay 39581832^131072+1 995'819 leading edge 1200 39502358^131072+1 995'705 L5453 2022 1201 39324372^131072+1 995'448 L5202 2022 1203 39100746^131072+1 995'123 L5441 2022 1204 38824296^131072+1 994'719 L4245 2021 1205 38734748^131072+1 994'588 L4249 2021 38585220^131072+1 994'368 min remaining 1207 38310998^131072+1 993'962 L4737 2021 1208 38196496^131072+1 993'791 L4861 2021 1209 38152876^131072+1 993'726 L4245 2021 1210 37909914^131072+1 993'363 L4249 2021 1212 36531196^131072+1 991'254 L4249 2021 1214 36422846^131072+1 991'085 L4245 2021 1215 36416848^131072+1 991'076 L5202 2021 1216 36038176^131072+1 990'481 L4245 2021 1217 35997532^131072+1 990'416 L4245 2021 1218 35957420^131072+1 990'353 L4245 2021

ID: 153112 |

GDB
Send message
Joined: 15 Nov 11
Posts: 304
ID: 119185
Credit: 4,294,761,435
RAC: 1,548,248

999,877
____________

ID: 153116 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

I am itching to see what happens.
I really hope someone has guessed the number.

ID: 153120 |

vaughan

Send message
Joined: 11 Aug 05
Posts: 352
ID: 224
Credit: 14,320,855,396
RAC: 31,857,308

999,995
____________

ID: 153137 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

999,995

Nice - a number at the optimistic range of choice.
As far as I know, the distribution of primes over a large expanse of numbers is predictable, but what is being considered here - who knows what may happen?
Sorry that sounds so stupid.

ID: 153145 |

composite
Volunteer tester
Send message
Joined: 16 Feb 10
Posts: 1174
ID: 55391
Credit: 1,233,038,099
RAC: 2,043,404

Someone is throwing a lot of gerbils at this subproject.
The tasks in progress doubled today, and my percentage of firsts climbed dramatically,
changing from 0% firsts to 40% firsts.

1084 44085096^131072+1 1'001'953 L4482 2016 1086 44049878^131072+1 1'001'908 L4466 2016 1108 43165206^131072+1 1'000'753 L4309 2016 1109 43163894^131072+1 1'000'751 L4334 2016 1128 42654182^131072+1 1'000'075 L4208 2015 999'999 KylePolansky 999'998 Scott Cox 999'997 Nick 999'996 Chara34122 999'995 vaughan 999'983 robish 999'973 mexico 999'951 288larsson 999'942 Grebuloner 999'939 lunchboxkwdm 999'937 Monkeydee 999'925 Margus 999'924 pschoefer 999'922 composite 999'909 Bur 999'899 Vato 999'888 TeeVeeEss 999'877 GDB 999'876 Hans Sveen 999'821 Michael Goetz 999'805 Yves Gallot 999'779 DeleteNull 999'741 Scott Brown 999'727 Pooh Bear 27 999'666 matzetoni 999'600 dthonon 999'500 Michael Millerick 999'249 Pilgrim 999'248 JeppeSN 999'000 reiner 998'990 dannyridel 998'712 tng 998'264 Jay 39812596^131072+1 996'150 leading edge 1201 39597790^131072+1 995'842 L4737 2022 1202 39502358^131072+1 995'705 L5453 2022 1203 39324372^131072+1 995'448 L5202 2022 1205 39100746^131072+1 995'123 L5441 2022 39093836^131072+1 995'113 min remaining 1206 38824296^131072+1 994'719 L4245 2021 1207 38734748^131072+1 994'588 L4249 2021 1209 38310998^131072+1 993'962 L4737 2021 1210 38196496^131072+1 993'791 L4861 2021 1211 38152876^131072+1 993'726 L4245 2021 1212 37909914^131072+1 993'363 L4249 2021 1214 36531196^131072+1 991'254 L4249 2021 1216 36422846^131072+1 991'085 L4245 2021 1217 36416848^131072+1 991'076 L5202 2021 1218 36038176^131072+1 990'481 L4245 2021 1219 35997532^131072+1 990'416 L4245 2021 1220 35957420^131072+1 990'353 L4245 2021

ID: 153149 |

Aaron

Send message
Joined: 19 Feb 17
Posts: 3
ID: 493492
Credit: 48,354,850
RAC: 0

997945

ID: 153150 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

composite, thank you for all your updates.

I wonder if we should close the bet soon? It would be silly if you could win by mentioning some digit count simply taken from an already discovered prime.

/JeppeSN

ID: 153180 |

Ravi Fernando
Project administrator
Volunteer tester
Project scientist
Send message
Joined: 21 Mar 19
Posts: 211
ID: 1108183
Credit: 14,604,950
RAC: 10,112

I wonder if we should close the bet soon?

I guess that's my cue to stop lurking. I'll go with 999848.

ID: 153182 |

composite
Volunteer tester
Send message
Joined: 16 Feb 10
Posts: 1174
ID: 55391
Credit: 1,233,038,099
RAC: 2,043,404

I wonder if we should close the bet soon?

I guess that's my cue to stop lurking. I'll go with 999848.

Good strategy, wait as long as possible.

The leading edge is currently at 40013074^131072+1 (996,436 digits long).
The pit boss is watching. Last call for bets.

ID: 153188 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

OK, I made the thread, so I declare (unilaterally) that no bets will be accepted after January 13 at 00:00 UTC. So there is about 40 hours 43 minutes left to place bets. /JeppeSN

ID: 153191 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

REMINDER: In less than eight hours, this thread will accept no more bets! /JeppeSN

ID: 153225 |

Honza

Volunteer moderator
Volunteer tester
Project scientist
Send message
Joined: 15 Aug 05
Posts: 1963
ID: 352
Credit: 6,426,580,351
RAC: 2,445,603

999765
____________
My stats

ID: 153226 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

We passed the deadline. The final list of bets:

999'999 KylePolansky 999'998 Scott Cox 999'997 Nick 999'996 Chara34122 999'995 vaughan 999'983 robish 999'973 mexico 999'951 288larsson 999'942 Grebuloner 999'939 lunchboxkwdm 999'937 Monkeydee 999'925 Margus 999'924 pschoefer 999'922 composite 999'909 Bur 999'899 Vato 999'888 TeeVeeEss 999'877 GDB 999'876 Hans Sveen 999'848 Ravi Fernando 999'821 Michael Goetz 999'805 Yves Gallot 999'779 DeleteNull 999'765 Honza 999'741 Scott Brown 999'727 Pooh Bear 27 999'666 matzetoni 999'600 dthonon 999'500 Michael Millerick 999'249 Pilgrim 999'248 JeppeSN 999'000 reiner 998'990 dannyridel 998'712 tng 998'264 Jay 997'945 Aaron

/JeppeSN

ID: 153232 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

In less than a week, we should have a good indication of who will win.

The leading edge according to the front page right now is at 997'268, so we are getting closer to the smallest guesses. And a 17-challenge is coming up.

/JeppeSN

ID: 153257 |

dthonon

Volunteer tester

Send message
Joined: 6 Dec 17
Posts: 435
ID: 957147
Credit: 1,764,717,803
RAC: 59,628

The leading edge is starting to move up the list : 998,059 digits long. But the largest prime : 997,196 digits long, is still smaller than the smallest guess...

ID: 153321 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

The leading edge is starting to move up the list : 998,059 digits long. But the largest prime : 997,196 digits long, is still smaller than the smallest guess...

Yes! Let us say I post actual GFN-17 discoveries with digit counts between 997'500 and 1'000'000 here, together with the list of guesses. Relevant challenge starts in less than one hour! /JeppeSN

ID: 153327 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

Very soon we will have an indication of the winner, although clean-up tasks will mean that it can take several days, or weeks, before we have absolute certainty.

The actual primes with at least 997'500 digits will be shown together with the guesses:

999'999 KylePolansky
999'998 Scott Cox
999'997 Nick
999'996 Chara34122
999'995 vaughan
999'983 robish
999'973 mexico
999'951 288larsson
999'942 Grebuloner
999'939 lunchboxkwdm
999'937 Monkeydee
999'925 Margus
999'924 pschoefer
999'922 composite
999'909 Bur
999'899 Vato
999'888 TeeVeeEss
999'877 GDB
999'876 Hans Sveen
999'848 Ravi Fernando
999'821 Michael Goetz
999'805 Yves Gallot
999'779 DeleteNull
999'765 Honza
999'741 Scott Brown
999'727 Pooh Bear 27
999'666 matzetoni
999'600 dthonon
999'500 Michael Millerick
999'249 Pilgrim
999'248 JeppeSN
999'000 reiner
998'990 dannyridel
998'712 tng
998'327 actual prime 41364744^131072+1
998'264 Jay
998'152 actual prime 41237116^131072+1
997'965 actual prime 41102236^131072+1
~~997'945 Aaron~~
997'834 actual prime 41007562^131072+1
997'825 actual prime 41001148^131072+1

/JeppeSN

ID: 153373 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

Could we place a wager (non-monetary) on who may get it?
Just another level of fun.
I suspect no, but I like the idea of 2 levels of guessing.
To me this makes sense - we have a distribution of guesses that have a range of connection/understanding with what may happen.
Now that we have these guesses, we could now guess the result from those options?
This is probably why I shouldn't be near maths.

ID: 153377 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

Could we place a wager (non-monetary) on who may get it?
Just another level of fun.
I suspect no, but I like the idea of 2 levels of guessing.
To me this makes sense - we have a distribution of guesses that have a range of connection with what may happen.
Now that we have these guesses, we could now guess the result from those options?
This is probably why I shouldn't be near maths.

People whose bets are "sandwiched" by other bets really near, like yourself, need a lot of luck to win! /JeppeSN

ID: 153379 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

Could we place a wager (non-monetary) on who may get it?
Just another level of fun.
I suspect no, but I like the idea of 2 levels of guessing.
To me this makes sense - we have a distribution of guesses that have a range of connection with what may happen.
Now that we have these guesses, we could now guess the result from those options?
This is probably why I shouldn't be near maths.

People whose bets are "sandwiched" by other bets really near, like yourself, need a lot of luck to win! /JeppeSN

But if it happens it would be awesome.
I wish anyone to have guessed correctly - which I think is very unlikely. About 1% chance? I think it is less than that, but as maths and I have a mutual understanding to not get too close, I have no idea how likely it is for someone to have guessed it.

ID: 153381 |

dthonon

Volunteer tester

Send message
Joined: 6 Dec 17
Posts: 435
ID: 957147
Credit: 1,764,717,803
RAC: 59,628

Could we place a wager (non-monetary) on who may get it?
Just another level of fun.
I suspect no, but I like the idea of 2 levels of guessing.
To me this makes sense - we have a distribution of guesses that have a range of connection with what may happen.
Now that we have these guesses, we could now guess the result from those options?
This is probably why I shouldn't be near maths.

People whose bets are "sandwiched" by other bets really near, like yourself, need a lot of luck to win! /JeppeSN

But if it happens it would be awesome.
I wish anyone to have guessed correctly - which I think is very unlikely. About 1% chance? I think it is less than that, but as maths and I have a mutual understanding to not get too close, I have no idea how likely it is for someone to have guessed it.

There are around 3 primes per thousand digits, so probability is about 0.3%, if I am not mistaken.

ID: 153382 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

Could we place a wager (non-monetary) on who may get it?
Just another level of fun.
I suspect no, but I like the idea of 2 levels of guessing.
To me this makes sense - we have a distribution of guesses that have a range of connection with what may happen.
Now that we have these guesses, we could now guess the result from those options?
This is probably why I shouldn't be near maths.

People whose bets are "sandwiched" by other bets really near, like yourself, need a lot of luck to win! /JeppeSN

But if it happens it would be awesome.
I wish anyone to have guessed correctly - which I think is very unlikely. About 1% chance? I think it is less than that, but as maths and I have a mutual understanding to not get too close, I have no idea how likely it is for someone to have guessed it.

There are around 3 primes per thousand digits, so probability is about 0.3%, if I am not mistaken.

Cool

ID: 153383 |

Volunteer moderator
Project administrator

Send message
Joined: 21 Jan 10
Posts: 14045
ID: 53948
Credit: 485,564,848
RAC: 673,873

How is the winner determined? It's unlikely someone will guess the exact number of digits, so is it whomever is closest to the last prime? Or something else?

EDIT: The latest (not yet public) prime is between Pilgrim's and Michael Millerick's guesses. That means everyone with a guess lower than Pilgrim's (999,249) is officially out of the running.
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

ID: 153422 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

Update.

Some strikethroughs based on info I heard on our Discord server (and in above post) about primes not public yet.

999'999 KylePolansky
999'998 Scott Cox
999'997 Nick
999'996 Chara34122
999'995 vaughan
999'983 robish
999'973 mexico
999'951 288larsson
999'942 Grebuloner
999'939 lunchboxkwdm
999'937 Monkeydee
999'925 Margus
999'924 pschoefer
999'922 composite
999'909 Bur
999'899 Vato
999'888 TeeVeeEss
999'877 GDB
999'876 Hans Sveen
999'848 Ravi Fernando
999'821 Michael Goetz
999'805 Yves Gallot
999'779 DeleteNull
999'765 Honza
999'741 Scott Brown
999'727 Pooh Bear 27
999'666 matzetoni
999'600 dthonon
999'500 Michael Millerick
~~999'249 Pilgrim~~
~~999'248 JeppeSN~~
~~999'000 reiner~~
~~998'990 dannyridel~~
998'772 actual prime 41688706^131072+1
~~998'712 tng~~
998'327 actual prime 41364744^131072+1
~~998'264 Jay~~
998'152 actual prime 41237116^131072+1
997'965 actual prime 41102236^131072+1
~~997'945 Aaron~~
997'834 actual prime 41007562^131072+1
997'825 actual prime 41001148^131072+1

/JeppeSN

ID: 153424 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

How is the winner determined? It's unlikely someone will guess the exact number of digits, so is it whomever is closest to the last prime? Or something else?

Precisely, I think I said the person who is closest in the first post! /JeppeSN

ID: 153425 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

Update.

999'999 KylePolansky
999'998 Scott Cox
999'997 Nick
999'996 Chara34122
999'995 vaughan
999'983 robish
999'973 mexico
999'951 288larsson
999'942 Grebuloner
999'939 lunchboxkwdm
999'937 Monkeydee
999'925 Margus
999'924 pschoefer
999'922 composite
999'909 Bur
999'899 Vato
999'888 TeeVeeEss
999'877 GDB
999'876 Hans Sveen
999'848 Ravi Fernando
999'821 Michael Goetz
999'805 Yves Gallot
999'779 DeleteNull
999'765 Honza
999'741 Scott Brown
999'727 Pooh Bear 27
999'666 matzetoni
999'600 dthonon
999'500 Michael Millerick
999'424 actual prime 42168978^131072+1
~~999'249 Pilgrim~~
~~999'248 JeppeSN~~
~~999'000 reiner~~
~~998'990 dannyridel~~
998'772 actual prime 41688706^131072+1
~~998'712 tng~~
998'327 actual prime 41364744^131072+1
~~998'264 Jay~~
998'152 actual prime 41237116^131072+1
997'965 actual prime 41102236^131072+1
~~997'945 Aaron~~
997'834 actual prime 41007562^131072+1
997'825 actual prime 41001148^131072+1

/JeppeSN

ID: 153428 |

Volunteer moderator
Project administrator

Send message
Joined: 21 Jan 10
Posts: 14045
ID: 53948
Credit: 485,564,848
RAC: 673,873

All of the 17-low tasks have been sent out.

As of right now, Monkeydee would win, with an exact match on the the number of digits.

However, there's 2267 candidates with more digits that are still in progress, and 233 of those don't have any results yet. So it's not over yet!
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

ID: 153432 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

Update. A lot of primes (that I do not know) are in the pipeline; they will be posted in this thread later.

999'999 KylePolansky
999'998 Scott Cox
999'997 Nick
999'996 Chara34122
999'995 vaughan
999'983 robish
999'973 mexico
999'951 288larsson
999'942 Grebuloner
999'939 lunchboxkwdm
999'937 Monkeydee <--- probable winner
~~999'925 Margus~~
~~999'924 pschoefer~~
~~999'922 composite~~
~~999'909 Bur~~
~~999'899 Vato~~
~~999'888 TeeVeeEss~~
~~999'877 GDB~~
~~999'876 Hans Sveen~~
~~999'848 Ravi Fernando~~
~~999'821 Michael Goetz~~
~~999'805 Yves Gallot~~
~~999'779 DeleteNull~~
~~999'765 Honza~~
~~999'741 Scott Brown~~
~~999'727 Pooh Bear 27~~
~~999'666 matzetoni~~
~~999'600 dthonon~~
~~999'500 Michael Millerick~~
999'424 actual prime 42168978^131072+1
~~999'249 Pilgrim~~
~~999'248 JeppeSN~~
~~999'000 reiner~~
~~998'990 dannyridel~~
998'772 actual prime 41688706^131072+1
~~998'712 tng~~
998'327 actual prime 41364744^131072+1
~~998'264 Jay~~
998'152 actual prime 41237116^131072+1
997'965 actual prime 41102236^131072+1
~~997'945 Aaron~~
997'834 actual prime 41007562^131072+1
997'825 actual prime 41001148^131072+1

/JeppeSN

ID: 153443 |

Jay

Send message
Joined: 27 Feb 10
Posts: 136
ID: 56067
Credit: 65,857,807
RAC: 9,485

Dang it! I was really counting on winning this thing to turn my life around.

ID: 153444 |

firedrakes
Avatar

Send message
Joined: 7 Feb 09
Posts: 80
ID: 35268
Credit: 219,718,198
RAC: 160,758

999,9969

ID: 153446 |

Send message
Joined: 11 Jul 11
Posts: 2301
ID: 105020
Credit: 10,430,478,791
RAC: 36,050,541

Dang it! I was really counting on winning this thing to turn my life around.

I'd be worried if I manage to guess it, I have used up all my turning-my-life-around potential.

ID: 153447 |

Grebuloner

Volunteer tester
Avatar

Send message
Joined: 2 Nov 09
Posts: 526
ID: 49572
Credit: 3,608,933,101
RAC: 2,661,039

SO CLOSE! :-)
____________
Eating more cheese on Thursdays.

ID: 153449 |

Monkeydee

Volunteer tester
Avatar

Send message
Joined: 8 Dec 13
Posts: 548
ID: 284516
Credit: 1,735,055,462
RAC: 3,098,297

Total fluke to have nailed it. If I couldn't get the last prime then I'm happy to have been able to guess its size!
____________
My Primes
Badge Score: 4*2 + 6*2 + 7*1 + 8*11 + 9*1 + 11*3 + 12*1 = 169

ID: 153451 |

Aaron

Send message
Joined: 19 Feb 17
Posts: 3
ID: 493492
Credit: 48,354,850
RAC: 0

Congratulations on the guess! Even though my guess was wrong I'm happy to have found a prime (my first).

I took a long shot on the guess because even though there are usually a few primes per thousand digits, there have been some larger gaps in the past.

ID: 153475 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

999'999 KylePolansky
999'998 Scott Cox
999'997 Nick
999'996 Chara34122
999'995 vaughan
999'983 robish
999'973 mexico
999'951 288larsson
999'942 Grebuloner
999'939 lunchboxkwdm
999'937 actual prime 42550702^131072+1
999'937 Monkeydee <--- probable winner
~~999'925 Margus~~
~~999'924 pschoefer~~
~~999'922 composite~~
~~999'909 Bur~~
~~999'899 Vato~~
~~999'888 TeeVeeEss~~
~~999'877 GDB~~
~~999'876 Hans Sveen~~
~~999'848 Ravi Fernando~~
~~999'821 Michael Goetz~~
~~999'805 Yves Gallot~~
~~999'779 DeleteNull~~
~~999'765 Honza~~
999'753 actual prime 42414020^131072+1
~~999'741 Scott Brown~~
~~999'727 Pooh Bear 27~~
~~999'666 matzetoni~~
~~999'600 dthonon~~
999'539 actual prime 42254832^131072+1
999'524 actual prime 42243204^131072+1
999'506 actual prime 42230406^131072+1
~~999'500 Michael Millerick~~
999'424 actual prime 42168978^131072+1
~~999'249 Pilgrim~~
~~999'248 JeppeSN~~
~~999'000 reiner~~
~~998'990 dannyridel~~
998'772 actual prime 41688706^131072+1
~~998'712 tng~~
998'327 actual prime 41364744^131072+1
~~998'264 Jay~~
998'152 actual prime 41237116^131072+1
997'965 actual prime 41102236^131072+1
~~997'945 Aaron~~
997'834 actual prime 41007562^131072+1
997'825 actual prime 41001148^131072+1

/JeppeSN

ID: 153479 |

robish

Volunteer moderator
Volunteer tester
Avatar

Send message
Joined: 7 Jan 12
Posts: 2223
ID: 126266
Credit: 7,990,315,060
RAC: 5,325,758

Congrats Monkeydee, well played ▶️
____________
My lucky number 1059094^1048576+1

ID: 153480 |

Send message
Joined: 5 Apr 14
Posts: 1853
ID: 306875
Credit: 52,643,606
RAC: 27,348

If the largest two prime had not existed, Michael Millerick would have the last four primes closer to his bet than to anybody else's. /JeppeSN

ID: 153481 |

Volunteer moderator
Project administrator

Send message
Joined: 21 Jan 10
Posts: 14045
ID: 53948
Credit: 485,564,848
RAC: 673,873

With regards to the "largest 17-Low prime", all of the candidates greater than 999,937 digits now have at least one task completed. While there are still 167 candidates lacking a second, verifying task, the odds that one of them both is prime and has an erroneous result is exceedingly small. It's therefore extremely likely that 42550702^131072+1 is the largest GFN-17 prime with fewer than a million digits. Since some tasks are likely to time out more than once, it's likely that it will be a couple of weeks until this is proven conclusively.
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

ID: 153492 |

Volunteer moderator
Project administrator

Send message
Joined: 21 Jan 10
Posts: 14045
ID: 53948
Credit: 485,564,848
RAC: 673,873

And we are done!

All of the candidates with more than 999,937 digits have now been double checked, and 42550702^131072+1 is the largest GFN-17-Low prime.

This makes Monkeydee officially the winner of the guessing contest! Congratulations!!!
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

ID: 153594 |