Problems & Puzzles:
Puzzle 823. String of
digits 1379 full of primes
Here we will ask for strings S composed of L
digits from these four: 1, 3, 7 & 9. In particular we will
ask for that S of L digits such that a maximal of K primes
are embedded in S, reading S only from left to right.
Example: For L=20, I found that
for S=19717393139337391999 K=68. But I'm not sure that 68 is the
maximal K value for L=20.
confirm that for L=20, K=68 is maximal, or get another S
with a larger K, for the same L=20.
Q2. Redo Q1
for L=40 and L=80.
Contribution came from Emmanuel Vantieghem and Dmitry Kamenetsy
About Q1 : S
= 91131179719337391999 gives 73 underlying primes.
But I'm not sure this is the
About Q2 : S = 7139971933199733313711131179719337391999
(40 digits) gives 156 underlying primes.
I'm almost 100% sure this is NOT
L=20, 74 primes:
L=40, 166 primes: 391997391117113173331399793373971719
L=80, 354 primes: 19133139391911371797171391397919391117191773
I don't think the results are maximal. Even for
L=20, there are 4^20 possibilities to check.
On March 29, 2016 T. D. Noe wrote:
This appears to be a hard problem. I decided to
solve it (completely) for
n digit-numbers for n = 1 to 14. The results are on
three consecutive web
pages beginning with http://www.integersequences.org/s000857.html Using
Mathematica, the 14-digit case took about 15 hours;
The 20-digit case will
take about a year using my current approach.
Michael Hürter wrote on April 17, 2017:
I have the
L = 40: 183 primes
L = 80: 431 primes