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 Primed and Ready whodat Junior Member  Posts: 31 Threads: 4 Joined: Oct 2005 10-14-2005, 07:41 PM How many prime numbers can you find that are 1 less than a perfect square? Antoni Gual Posting Freak     Posts: 1,407 Threads: 117 Joined: Dec 2002 10-15-2005, 12:16 AM Funny challenge! If Mr Caldwell does enter you're lost..... :wink: Antoni rpgfan3233 Senior Member    Posts: 500 Threads: 7 Joined: Jun 2005 10-15-2005, 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(n-1) + (a(n-1) - a(n-2)) + 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 non-prime numbers), the only possible prime number that fits your criterion is the number 3. 974277320612072617420666C61696C21 (Hexadecimal for those who don't know) whodat Junior Member  Posts: 31 Threads: 4 Joined: Oct 2005 10-15-2005, 12:39 AM Quote:Funny challenge! If Mr Caldwell does enter you're lost..... :wink: I don't know Mr. Caldwell, but you had better post your code before he beats you to it!  whodat Junior Member  Posts: 31 Threads: 4 Joined: Oct 2005 10-15-2005, 12:48 AM Quote: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(n-1) + (a(n-1) - a(n-2)) + 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 non-prime numbers), the only possible prime number that fits your criterion is the number 3. 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)*(N-1). 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: Antoni Gual Posting Freak     Posts: 1,407 Threads: 117 Joined: Dec 2002 10-15-2005, 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 rpgfan3233 Senior Member    Posts: 500 Threads: 7 Joined: Jun 2005 10-15-2005, 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) « Next Oldest | Next Newest »

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