A "prime triangle" is made up of rows of numbers. Row number n contains the integers 1 through n. The first row is just "1", the second row is "1 2", the third row is "1 2 3" and so on. The tricky part is that the numbers have to be arranged so that if you add a number to its neighbor, that sum must be a prime number. So when you get to "1 2 3 4 5", you have to reorder the numbers because 4+5 is 9, which isn't prime. "1 4 3 2 5" works.
Here's a 10 row prime triangle:
1 1 2 1 2 3 1 2 3 4 1 4 3 2 5 1 4 3 2 5 6 1 4 3 2 5 6 7 1 2 3 4 7 6 5 8 1 2 3 4 7 6 5 8 9 1 2 3 4 7 6 5 8 9 10
Question: Is there a (really long) row for which there is no solution?
Answer: I dunno. If you have any insights into the answer, please drop me a line at Acuff@Dr-Amy.com.
Joke
My wonderful wife Amy's undergraduate degree is in English Lit, so in her honor:
The mathematician says, "3 is prime, 5 is prime, 7 is prime, therefore, by induction, the answer is yes."
The physicist says, "3 is prime, 5 is prime, 7 is prime, 9 is experimental error, 11 is prime; that's a large enough sample; the answer is yes."
The engineer says, ""3 is prime, 5 is prime, 7 is prime, 9 is not prime, so the answer is no."
The English major says, "What's a prime?"
Christopher Lane got me interested in prime triangles when he used them as an example in a class he's teaching. (See Prime Spiral for another prime number plaything he introduced me to.)
In order to play with prime triangles and learn more about Java, I wrote the following Applet. Drop me a line to let me know if you enjoy it. You can see the source here.
Here are some tips on using it.
Last updated on 6-19-2002 by Rich Acuff