10142005, 07:41 PM
How many prime numbers can you find that are 1 less than a perfect square?
Primed and Ready

10142005, 07:41 PM
How many prime numbers can you find that are 1 less than a perfect square?
10152005, 12:32 AM
I have the answer, without much time spent either: there can be only one.
Why? Well, think about it: 4 (perfect square)  1 = 3 (prime) 9 (perfect square)  1 = 8 (not prime) 16 (perfect square)  1 = 15 (not prime) 25 (perfect square)  1 = 24 (not prime) 36 (perfect square)  1 = 35 (not prime) 49 (perfect square)  1 = 48 (not prime) 64 (perfect square)  1 = 63 (not prime) Do you see a pattern here? The results increment like this: a(n) = a(n1) + (a(n1)  a(n2)) + 2 This means that the current result is found by adding to the difference between the previous two results. In other words: 8 + (8  3) + 2 = 8 + (5) + 2 = 15 15 + (15  8) + 2 = 15 + (7) + 2 = 24 24 + (24  15) + 2 = 24 + (9) + 2 = 35 Note the increments shown in parentheses. They have a difference of 2 (because of the +2 at the end). A little math lesson for people who hate it. Because this keeps happening (and rendering nonprime numbers), the only possible prime number that fits your criterion is the number 3.
974277320612072617420666C61696C21 (Hexadecimal for those who don't know)
10152005, 12:39 AM
Quote:Funny challenge! I don't know Mr. Caldwell, but you had better post your code before he beats you to it!
10152005, 12:48 AM
Quote:I have the answer, without much time spent either: there can be only one. It can be made even simpler: Your looking for a prime number of the form N^2 1. This can always be factored into (N+1)*(N1). In the case where N=2, one of the factors is 1, the other one happens to be prime (3). I was hoping someone would start writing code, but no one bit. :bounce:
10152005, 01:50 AM
Mr Caldwell runs the Prime Page http://primes.utm.edu/
You can find there 3 is the only prime that fits the criterion. I modified some code to do the search, but as it did'nt find anything, I checked the Prime Page.... I would give the prize to rpgfan, who actually thinked at the problem....
Antoni
10152005, 03:08 AM
Quote:I would give the prize to rpgfan, who actually thinked at the problem....No, I'm just a maths geek. Prime numbers seem to be a topic for discussion within the QB community right now.
974277320612072617420666C61696C21 (Hexadecimal for those who don't know)

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