mersenneforum.org  

Go Back   mersenneforum.org > Fun Stuff > Puzzles

Reply
 
Thread Tools
Old 2008-08-14, 19:04   #1
davar55
 
davar55's Avatar
 
May 2004
New York City

108B16 Posts
Default Triangle of Primes

A variation on a recent puzzle:

Draw 21 congruent circles in rows of 1,2,3,4,5 & 6, to form the shape
of an equilateral triangle.
Now fill in each circle with a different 2-digit prime (there just happen
to be 21 of these) such that the concatenation of primes in any row
of circles in either direction is prime (that's 33 primes).
Don't reverse the digits of the 2-digit primes.

Is this possible?
davar55 is offline   Reply With Quote
Old 2008-08-27, 20:08   #2
davar55
 
davar55's Avatar
 
May 2004
New York City

5×7×112 Posts
Default

If this problem was poorly stated or has no solution,
then the following is just an attempt to save the problem:

(a) Fill in the circles so as to create as many primes as possible,
instead of all rows, backward and forward, in three directions
giving prime concatenations. (I think expecting to find 33 primes
of average length ~7 digits was far too unlikely among the 21!
different configurations.)

(b) Instead of a triangle, construct a 3x7 rectangle using all the
2-digit primes such that the rows and columns by concatenation
are prime.
davar55 is offline   Reply With Quote
Old 2008-09-05, 14:33   #3
davieddy
 
davieddy's Avatar
 
"Lucan"
Dec 2006
England

647410 Posts
Default

I miss Mally if only for his provision of a less number-theoretic
type of problem.

Last fiddled with by davieddy on 2008-09-05 at 14:34
davieddy is offline   Reply With Quote
Old 2008-09-15, 12:52   #4
ckdo
 
ckdo's Avatar
 
Dec 2007
Cleves, Germany

2·5·53 Posts
Default

Quote:
Originally Posted by davar55 View Post
A variation on a recent puzzle:

Draw 21 congruent circles in rows of 1,2,3,4,5 & 6, to form the shape
of an equilateral triangle.
Now fill in each circle with a different 2-digit prime (there just happen
to be 21 of these) such that the concatenation of primes in any row
of circles in either direction is prime (that's 33 primes).
Don't reverse the digits of the 2-digit primes.

Is this possible?
At the risk of being proven wrong: no.

I wrote a program to fill the triangle from the bottom up and had it dump all partial solutions with the last number (the top one) still missing. It came up with only 21 of these. However, I had previously invested some thought into pruning the search space so that no full solutions would be reported multiple times, so there may be more than just 21.

I then manually added the last number and checked the four 12-digit primes along the left and right edges for factors. In 16 cases, neither was prime. In four cases, one was prime. In one case, two were prime:

Code:
          37
        89  23
      31  73  71
    19  67  41  13
  97  53  79  61  83
47  43  59  11  17  29
378931199747 and 479719318937 are both prime, however 372371138329 = 409 * 910442881 and 298313712337 = 116707 * 2556091.

So what I have I'd like to call a "31-prime, 35-factor" solution. A better solution in the spirit of post #2 (a) may exist, but I seriously doubt it.

Cheers,
Carsten
ckdo is offline   Reply With Quote
Old 2009-07-02, 20:16   #5
davar55
 
davar55's Avatar
 
May 2004
New York City

5×7×112 Posts
Default

Quote:
Originally Posted by davieddy View Post
I miss Mally if only for his provision of a less number-theoretic
type of problem.
Yes, his interest in old math did help some of us
learn from the past.
davar55 is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Triangle puzzle MattcAnderson Homework Help 12 2016-11-08 12:10
A triangle problem MattcAnderson Puzzles 6 2014-08-25 21:53
Triangle davieddy Puzzles 2 2010-06-29 13:18
Triangle puzzle Zeta-Flux Puzzles 12 2007-03-16 19:05
Triangle puzzle dsouza123 Puzzles 16 2006-05-26 01:58

All times are UTC. The time now is 13:02.


Sat Oct 16 13:02:41 UTC 2021 up 85 days, 7:31, 0 users, load averages: 2.49, 2.05, 1.82

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.