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Old 2022-09-12, 12:40   #78
Puzzle-Peter
 
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Default Addition for your Octuplet table

5586218959960365309179*757#/1768767+1+d, d=0, 2, 6, 8, 12, 18, 20, 26


I have the primo certificates if like, but it is super fast to recreate them.
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Old 2022-09-12, 14:48   #79
Cybertronic
 
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Default Updated

Congratulation Peter !
Pages was updated !
https://pzktupel.de/ktuplets.php

Last fiddled with by Cybertronic on 2022-09-12 at 14:49
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Old 2022-09-30, 09:31   #80
Puzzle-Peter
 
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Default more octuplets

4869586684665128135306*757#/1768767+1+d, d=0, 2, 6, 8, 12, 18, 20, 26


530956818040688210255681*757#/1768767+1+d, d=0, 2, 6, 8, 12, 18, 20, 26


531258360785860208657753*757#/1768767+1+d, d=0, 2, 6, 8, 12, 18, 20, 26



Again, I will gladly provide PRIMO certificates but they are so fast to recreate...
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Old 2022-09-30, 11:10   #81
Cybertronic
 
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Thumbs up Congratulations ...

Peter, for a new prime octuplet world record !
...and few top-10 septuplets.
All primes true by Primo.


Pages was updated: https://pzktupel.de/ktuplets.php


Norman
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Old 2022-10-24, 18:47   #82
Cybertronic
 
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Default Riecoin

All prime octuplets, found by Riecoin are separated here: (click blue line)

https://pzktupel.de/ktuplets.php#largest8
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Old 2022-11-04, 10:47   #83
Cybertronic
 
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Default prime k-tuplet page got a new update

From now, "Record Gap Tables of prime k-tuplets", k= 1..15 are available, incl. merits.



Link: https://pzktupel.de/Rectables.php


Hope, it is correct.


greetings
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Old 2022-11-27, 13:12   #84
sweety439
 
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I have an idea for a sequence for prime k-tuples, see https://pzktupel.de/smarchive.php, this sequence seems not to be in OEIS

Smallest k such that there exists all kinds of prime n-tuples <= k

a(1) = 2, the smallest prime is 2
a(2) = 5, the smallest twin prime pair is {3,5}
a(3) = 13, the smallest prime 3-tuple for d = {0,2,6} is {5,7,11}, and the smallest prime 3-tuple for d = {0,4,6} is {7,11,13}
a(4) = 13, the smallest prime quadruple (d = {0,2,6,8}) is {5,7,11,13}
a(5) = 19, the smallest prime 5-tuple for d = {0,2,6,8,12} is {5,7,11,13,17}, and the smallest prime 5-tuple for d = {0,4,6,10,12} is {7,11,13,17,19}
a(6) = 23, the smallest prime 6-tuple (d = {0,4,6,10,12,16}) is {7,11,13,17,19,23}
a(7) = 5659, the smallest prime 7-tuple for d = {0,2,6,8,12,18,20} is {11,13,17,19,23,29,31}, and the smallest prime 7-tuple for d = {0,2,8,12,14,18,20} is {5639,5641,5647,5651,5653,5657,5659}
a(8) = 88819, the smallest prime 8-tuple for d = {0,2,6,8,12,18,20,26} is {11,13,17,19,23,29,31,37}, and the smallest prime 8-tuple for d = {0,6,8,14,18,20,24,26} is {88793,88799,88801,88807,88811,88813,88817,88819}, and the smallest prime 8-tuple for d = {0,2,6,12,14,20,24,26} is {17,19,23,29,31,37,41,43}

@Cybertronic, your page has error, for the 8-tuple, "d = 0, 2, 8, 12, 14, 18, 20, 26" should be "d = 0, 2, 6, 8, 12, 18, 20, 26"
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Old 2022-11-27, 13:26   #85
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Thank you sweety439, is corrected.
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