20181231, 18:11  #67  
Nov 2008
2·3^{3}·43 Posts 
Quote:
The likely CK for this base is 1429458644604553 which has covering set {19, 37, 61, 307, 1051, 39916801} with period 18. The reason it's so big is that the primes that can appear in the covering set with period d are the primes p such that b has order d mod p; these are prime factors of the cyclotomic number Φ_{d}(b). If for small d these numbers have lots of small prime factors then there are lots of primes that are likely to appear as factors and so the CK will be small. If there are few small factors then we will either need a big prime in the covering set (making the CK big as well) or a lot of small primes with longer periods (which will probably also make the CK big). For b = 11!, there are very few small factors: Φ_{2}(b) = b+1 = 39916801 Φ_{3}(b) = b^2+b+1 = 61*26120507576341 Φ_{4}(b) = b^2+1 = 1593350922240001 Φ_{5}(b) = b^4+b^3+b^2+b+1 = 761*3336093593961274918315629641 Φ_{6}(b) = b^2b+1 = 1051*1516033189651 So it's not a surprise that the CK is huge. Quote:
Last fiddled with by 10metreh on 20181231 at 18:18 Reason: small correction 

20190101, 18:24  #68 
Jul 2003
3·197 Posts 
hi,
i am starting R2019 CK 304 
20190107, 10:14  #69  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2·2,861 Posts 
Quote:


20190107, 10:59  #70 
Nov 2008
2×3^{3}×43 Posts 

20190107, 18:47  #71 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2×2,861 Posts 

20190108, 17:32  #72 
Dec 2011
After milion nines:)
1343_{10} Posts 

20190108, 22:01  #73 
Dec 2011
After milion nines:)
17×79 Posts 

20190109, 11:30  #74 
Jul 2003
3·197 Posts 

20190109, 14:21  #75 
Dec 2011
After milion nines:)
2477_{8} Posts 

20190201, 15:05  #76 
Jul 2003
24F_{16} Posts 
hi,
status update for R2019 range n=1 to 100k done 10 k´s remain for more info visit lalera.alotspace.com continuing 
20190202, 09:47  #77  
Nov 2016
2249_{10} Posts 
Quote:
Odd n has factor of 5 Even n has algebra factors For k=100: Odd n has factor of 101 Even n has algebra factors Thus R2019 has only 6 k’s remain at n=100K: 84, 114, 204, 242, 296, 302 

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