Problems & Puzzles: Puzzles

 

 

Problems & Puzzles: Puzzles

Puzzle 1276 A new visit to Puzzle 49

Around 20 years ago, my friend Jaime Ayala and me created this Puzzle 49 and gave some solutions apart from the given by Anurag Sahay.

In short this puzzle ask you to determine what are the maximum quantity of primes you can form using once all the k sets of digits if each set is composed by the ten decimal digits {0,1,2,3,4,5,6,7,8,9}.

In those times we got the following results (please see the list of primes in the Puzzle 49):

k Maximum quantity of primes(4k+2) Quantity of Primes gotten %
1 6 {2, 3, 5, 7, 41, 89} 6 100
2 10 {2, 3, 5, 7, 23, 41, 47, 59, 61, 89} 10 100
3 14 ... 14 100
4 18... 18 100
5 22... 22 100
6 26... 26 100
7 30... 29 96.66
8 34... 33 97.05
9 38... 36 94.74
10 42... 39 92.86
20 82... 73 (J.A) 89.02
50 202... 159(J.A) 78.91
100 402... 285 70.89
150 602... 420 (A.S) 69.77



Q1. Can you confirm or improve the Quantity of primes gotten (column2)?
Q2. It seems that the % decreases as k increases. What do you think about the lower limit of this quantity (%), is it asymptotic to zero or to another grater value?



 

 

 
 




Records   |  Conjectures  |  Problems  |  Puzzles