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41 replies to this topic

#11 brhan

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Posted 17 March 2008 - 11:20 AM

Master=45
Sage=477
Death=?

Hmm... well, seems like it's either, 4*prime, 9*prime, 25*prime, 49*prime, 121*prime, 169*prime, blah blah blah...
Anyways, since i've only found two, there's no pattern really, but what it was was... for master, it was a 4*11, 9*5 and for sage is was 25*19, 4*119, 9*53...
Maybe for death it will be something with 49*prime, 4*prime, 9*prime, 25*prime?

Well done PhoenixTears, you got the first one. Lyrans become masters at 45.

The sage is not correct because you assumed that 119 is a prime number (22*119=476), but actually it is not a prime number: 7*17=119.
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#12 unreality

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Posted 17 March 2008 - 01:51 PM

For people that say -1 is not prime, they are wrong as far as I know.

-1 is only divisible by itself and 1 (-1*1 and 1*-1 are its only two factor pairs)

therefore -1 is prime

but I'm not sure if Primes are allowed to be negative, but even if they are, you can't have a negative age ;D

if primes were allowed to be negative, -1 would be the only prime. Take -2 for example:
(-2, 1)
(1, -2)
(2, -1)
(-1, 2)

a prime number only has 2 factor pairs (itself and 1, 1 and itself), but -2 has four cuz its negative. -3 is the same. etc.

So if negative primes were allowed (not sure if they are), -1 would be the only negative prime. Just thought I'd point that out
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#13 brhan

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Posted 17 March 2008 - 02:15 PM

For people that say -1 is not prime, they are wrong as far as I know.

-1 is only divisible by itself and 1 (-1*1 and 1*-1 are its only two factor pairs)

therefore -1 is prime

but I'm not sure if Primes are allowed to be negative, but even if they are, you can't have a negative age ;D

if primes were allowed to be negative, -1 would be the only prime. Take -2 for example:
(-2, 1)
(1, -2)
(2, -1)
(-1, 2)

a prime number only has 2 factor pairs (itself and 1, 1 and itself), but -2 has four cuz its negative. -3 is the same. etc.

So if negative primes were allowed (not sure if they are), -1 would be the only negative prime. Just thought I'd point that out

Well, negative numbers are not involved with primes. Otherwise, the definition of prime numbers need to be modified ...
We know that 2 is prime, because it has two factors -- 1 and 2. But if consider negative numbers, -1*-2 is 2. So the factors of 2 will be {1,2,-1,-2} ...

Some people may argue that 1 is also prime number. But in this puzzle, I didn't consider 1 as a prime.
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#14 Noct

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Posted 17 March 2008 - 05:02 PM

For people that say -1 is not prime, they are wrong as far as I know.

-1 is only divisible by itself and 1 (-1*1 and 1*-1 are its only two factor pairs)

therefore -1 is prime

A prime number has to be a natural number, so -1 is out, along with all other negatives.
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#15 zoris

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Posted 17 March 2008 - 05:30 PM

For people that say -1 is not prime, they are wrong as far as I know.

-1 is only divisible by itself and 1 (-1*1 and 1*-1 are its only two factor pairs)

therefore -1 is prime

but I'm not sure if Primes are allowed to be negative, but even if they are, you can't have a negative age ;D

if primes were allowed to be negative, -1 would be the only prime. Take -2 for example:
(-2, 1)
(1, -2)
(2, -1)
(-1, 2)

a prime number only has 2 factor pairs (itself and 1, 1 and itself), but -2 has four cuz its negative. -3 is the same. etc.

So if negative primes were allowed (not sure if they are), -1 would be the only negative prime. Just thought I'd point that out

By definition prime numbers can only be positive. The number 1 used to be considered prime until the 19th century, but now it is not considered prime, otherwise the fundamental theorem of arithmetic would not be true. This theorem states that every non-prime number greater than 1 can be factorized in a unique (apart from the order) product of prime numbers. E.g. 15 = 3x5 (or 5x3). If the number 1 would be considered prime, then we could also write:
15 = 3x5x1 = 3x5x1x1 = 3x5x1x1x1.... and so on indefinitely, and the factorization would not be unique.
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#16 jword

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Posted 17 March 2008 - 06:05 PM

How did you come up with 8 being a special number?

Yeah I goofed on that when I re-read the prime numbers are different, thats also why I did´nt use it "8" in my guesstimation, hey it was 4 in the morning ! ! and I´m still looking for the cat.
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#17 Duh Puck

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Posted 17 March 2008 - 06:08 PM

After trying for a bit to find a pattern in the numbers, I gave up and retreated to my old habits ... programming. Using a pretty simple brute force approach, I quickly solved the first two, but as for how long these Lyran's live? Wow. Apparently a really long time ....

Spoiler for two of three solutions

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#18 jword

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Posted 17 March 2008 - 06:19 PM

A prime number has to be a natural number, so -1 is out, along with all other negatives.

A Prime Number is a positive integer divisible by no integers other than unity and itself.

Example: 2, 3, 5, 7, 11, etc.

Twin Primes
A pair of prime numbers that differ by 2 (successive odd numbers that are both Prime numbers).

Examples: (3,5), (5,7), (11,13), ...

It is not known whether the set of twin prime numbers ends or not.

Co-primes or Relatively prime numbers
A pair of numbers not having any common factors other than 1 or -1. (Or alternatively their greatest common factor is 1 or -1)

Example: 15 and 28 are co-prime, because the factors of 15 (1,3,5,15), and the factors of 28 (1,2,4,7,14,28) are not in common (except for 1).

Mersenne's Primes
Prime numbers of the form 2n-1 where n must itself be prime.

3, 7, 31, 127 etc. are Mersenne primes.
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#19 Duh Puck

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Posted 18 March 2008 - 02:51 AM

... unless there's a bug in my program, over 21,000,000 and counting.

Yep, there was a bug in my program (discovered by my subconscious while sleeping, I think, because I thought of it as soon as I woke up). I correctly identified that I could exit the age-checking loop if (p*p*2) > age, but I failed to populate my list of prime numbers all the way to (limit/2^2), which meant that I would have overlooked special years where q > (p*p*2). Ugh. I fixed it and started it over, but since this requires that the prime number list I work with be much, much larger, it will run significantly slower. I set the age limit at 10,000,000 and restarted it before leaving for work this morning. I'll find out if it worked when I get home.
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#20 Noct

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Posted 18 March 2008 - 02:52 AM

What prime number algorithm are you working with? Or is it a preset list?
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