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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?
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