First titanic septuplet

Puzzle-Peter · 2021-01-27, 16:13

Hi folks,

Code:

6527857976181824068992954643835694152758237019621735794948630093353336346444314578259582354585710855994307682737795442832125943401558879429194267031660381989716139241076371879146441315760418319872828561352677668767
1053723486511718558339089252445263773938186288150981580244335287683233068859938146588878476184881280868412424826182271496440436727784955105445771221485902895990027424280489401038701236414000872718491439818091469396
7304022822631528546780463820548491458411079145254080730147373094640929014344061934952856686212476868492409708996478326911807622536628173799515250408676132841379612953085777057056143813041528304824344397034074951630
7849117807594366497569182520540434297558948186914404301799722681684515676195709095022274970314090528557131542557895182774819105217442760710517443049165534373742055263087492019855106882576413414056168714720625018176
8437441603278644196375616672481894410777389981443144241700543513545788015856486646285507126439158806149011698515665493114050189281
+1984419776555481*

(779335438037760160496591507183907769655856062999157556185939042593867827082091682481915363252420707043997349878578830309827188551771729543839005051107813891838035145375992949256064827070099991791479702094701476704
981442982291994293141771303874449576320219094208869801645463893226762267578243532564011056079611811860250461944113550775186726229991886965067672281675661441566894667464674398174394287003279554694237312956499172449
231931403376943570561885941668250654443056598233820766743806885392135242023171851812491738030323595846283298894505608970091375282873125077679924289474552940063830695017245881769845421776462807174597476947220731806
896503488271568278727091992063681108887922290146260410039855596704571630002796908632898154383539527668412881349229422969207362850867073216433419806135035650097846083962056375611351006095997577879489878679184413085
16512423315733977854074167299139642606490536607385570837818017825394467317266921734988640613075687125125595165728201546828770680483130)+d

with d=0, 2, 6, 8, 12, 18, 20 should be the first known septuplet with more than 1000 decimal digits. I did not find a shorter way to describe the numbers.

Batalov · 2021-01-27, 17:38

Quote:

Originally Posted by Puzzle-Peter

...with d=0, 2, 6, 8, 12, 18, 20 should be the first known septuplet with more than 1000 decimal digits.
I did not find a shorter way to describe the numbers.

It is easy.
113225039190926127209 * 2339#/57057 + 1 + d

Congratulations!

Puzzle-Peter · 2021-01-27, 17:59

Thanks!
How do you find the short description?

Batalov · 2021-01-27, 18:23

You do a few gcd()'s of the base number +- 100 or so, with the usual suspects (primorials, I took a guess that it would be based around 2341#), and then cancel unneeded terms.

Did you use rieMiner or something like it?

You should submit to UTM. 1000 digits - and you are in :-)

Puzzle-Peter · 2021-01-27, 19:07

I'll give it a better try next time. Chris Caldwell does not like unnecessarily long descriptions.

I used a tweaked version of Robert Gerbicz' Polysieve for sieving and PFGW for testing. Primo for the final certification.

mart_r · 2021-01-27, 19:11

Contfracs on p/q# with q# ~ p should also work wonders in finding a shorter representation.

Congrats on the titanic septuplet!

Does anyone have an ETA on the first 24-tuplet?

Cybertronic · 2021-01-31, 08:36

Herzlichen Glückwunsch , lieber Peter !!!

Wahnsinn, da kam er doch noch relativ vorzeitig !

rudy235 · 2021-01-31, 09:26

Quote:

Originally Posted by Puzzle-Peter

I'll give it a better try next time. Chris Caldwell does not like unnecessarily long descriptions.

I used a tweaked version of Robert Gerbicz' Polysieve for sieving and PFGW for testing. Primo for the final certification.

The description given By Sergei is very concise. Why don't you present it to UTM with that description?

Ahh! Congratulations BTW.

rudy235 · 2021-01-31, 09:30

Quote:

Originally Posted by mart_r

Contfracs on p/q# with q# ~ p should also work wonders in finding a shorter representation.

Congrats on the titanic septuplet!

Does anyone have an ETA on the first 24-tuplet?

12 12 2121 @12:21 GMT (I meant Titanic 24-tuplet)

Puzzle-Peter · 2021-02-01, 17:40

Quote:

Originally Posted by rudy235

The description given By Sergei is very concise. Why don't you present it to UTM with that description?

Ahh! Congratulations BTW.

I did upload the septuplet in Sergeis notation.

Thanks

2021-01-27, 17:59	#3
Puzzle-Peter Jun 2009 2³·3·29 Posts	Thanks! How do you find the short description? Last fiddled with by Puzzle-Peter on 2021-01-27 at 17:59

2021-01-27, 19:11	#6
mart_r Dec 2008 you know...around... 2²·11·17 Posts	Contfracs on p/q# with q# ~ p should also work wonders in finding a shorter representation. Congrats on the titanic septuplet! Does anyone have an ETA on the first 24-tuplet? Last fiddled with by mart_r on 2021-01-27 at 19:14

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2021-01-27, 18:23	#4
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,829 Posts	You do a few gcd()'s of the base number +- 100 or so, with the usual suspects (primorials, I took a guess that it would be based around 2341#), and then cancel unneeded terms. Did you use rieMiner or something like it? You should submit to UTM. 1000 digits - and you are in :-)

2021-01-27, 19:07	#5
Puzzle-Peter Jun 2009 2³·3·29 Posts	I'll give it a better try next time. Chris Caldwell does not like unnecessarily long descriptions. I used a tweaked version of Robert Gerbicz' Polysieve for sieving and PFGW for testing. Primo for the final certification.

2021-01-31, 08:36	#7
Cybertronic Jan 2007 Germany 111011110₂ Posts	Herzlichen Glückwunsch , lieber Peter !!! Wahnsinn, da kam er doch noch relativ vorzeitig !