# A new prime number puzzle

• Sep 29th 2010, 08:51 AM
wonderboy1953
A new prime number puzzle
I did a similar one before but this one is different.

Take the numbers 1 and 14. Multiply them to get 14 and add them to get 15. Now add the results to get 29 which is a prime number. Now take 4 and 11 which yields 44 and 15 for the results. Adding the results gives 59 which is a prime number.

Let's try 1 and 15. The results are 15 and 16 which upon adding yields the prime number 31. With 11 and 5, the results are 55 and 16 which yields the prime number 71 after adding.

At this point you should notice a pattern and the question is how far can this be extended? Would this work with numbers that don't have repeated digits? Would this work with more than two numbers at a time?

Have fun.
• Sep 29th 2010, 08:59 AM
undefined
Quote:

Originally Posted by wonderboy1953
I did a similar one before but this one is different.

Take the numbers 1 and 14. Multiply them to get 14 and add them to get 15. Now add the results to get 29 which is a prime number. Now take 4 and 11 which yields 44 and 15 for the results. Adding the results gives 59 which is a prime number.

Let's try 1 and 15. The results are 15 and 16 which upon adding yields the prime number 31. With 11 and 5, the results are 55 and 16 which yields the prime number 71 after adding.

At this point you should notice a pattern and the question is how far can this be extended? Would this work with numbers that don't have repeated digits? Would this work with more than two numbers at a time?

Have fun.

Not sure I follow. 1*16 + 1 + 16 = 33 which is not prime. What pattern did you want to continue? Are you looking for all pairs (m,n) such that mn+m+n is prime? (perhaps subject to a constraint like 1 <= m <= n <= 10^5.) And for triples are you referring to kmn+m+k+n or kmn+km+kn+mn or kmn+km+kn+mn+k+m+n or something else?
• Sep 29th 2010, 09:16 AM
wonderboy1953
Quote:

Originally Posted by undefined
Not sure I follow. 1*16 + 1 + 16 = 33 which is not prime. What pattern did you want to continue? Are you looking for all pairs (m,n) such that mn+m+n is prime? (perhaps subject to a constraint like 1 <= m <= n <= 10^5.) And for triples are you referring to kmn+m+k+n or kmn+km+kn+mn or kmn+km+kn+mn+k+m+n or something else?

You're overlooking my question: "...how far can this be extended?" Granted I only gave two examples, but what I've given should indicate that the pattern is to get prime numbers for two groups of related numbers in the manner described.

Does anyone out there get what I'm talking about?
• Sep 29th 2010, 09:30 AM
undefined
Quote:

Originally Posted by wonderboy1953
You're overlooking my question: "...how far can this be extended?" Granted I only gave two examples, but what I've given should indicate that the pattern is to get prime numbers for two groups of related numbers in the manner described.

Does anyone out there get what I'm talking about?

So are you asking whether 1*m+1+m=2m+1 is prime if and only if 11*(m-10)+11+m-10=12m-109 is prime, for m > 13?

This is a fallacy of various puzzles in my opinion. Just because there is one pattern doesn't mean it's the ONLY pattern.

And by the way I did not overlook your question, I addressed it directly.