Digit strings containing primes - Page 2

henryzz · 2018-02-01, 14:33

Quote:

Originally Posted by davar55

So it's not hard to specify some digit string that contains all the, say , three-digit
primes, and the OP puzzle did ask for a minimal length such string. If that's too
hard to find and prove minimal at this point, how short a digit string can we find
ignoring the minimality condition?

Shorter than 3*(number of 3 digit primes) should be possible but here is an upper bound.

henryzz · 2018-02-10, 17:58

For three digit primes there were 57 possible double overlaps. There were no cases where there wasn't enough ends for primes to go onto for double overlaps.
There were then 35 possible single overlaps. All were possible.
This produced a 280 digit number as predicted by axn above.

An example number:

Code:

2233137392277307229347924191157127197107251631491991092577263499726916735359367728181151010383892839401409421131144317334494574613977463467487750350952152395415475575635696758760160727619375743964164337983647016536599661797096838094182182382782907853857695385929478638818838878751

davar55 · 2018-03-15, 14:46

Excellent. Is it just a coincidence that axn's bound was achievable for n = 2, 3, or are
these bounds always achievable?

2018-02-10, 17:58	#13
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 2³×3×5×7² Posts	For three digit primes there were 57 possible double overlaps. There were no cases where there wasn't enough ends for primes to go onto for double overlaps. There were then 35 possible single overlaps. All were possible. This produced a 280 digit number as predicted by axn above. An example number: Code: 2233137392277307229347924191157127197107251631491991092577263499726916735359367728181151010383892839401409421131144317334494574613977463467487750350952152395415475575635696758760160727619375743964164337983647016536599661797096838094182182382782907853857695385929478638818838878751

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2018-03-15, 14:46	#14
davar55 May 2004 New York City 108A₁₆ Posts	Excellent. Is it just a coincidence that axn's bound was achievable for n = 2, 3, or are these bounds always achievable?