Last night I came across a pattern in finding prime numbers. In school today, during Biology, I wrote a general rule for it:
y = 2x^2+2x-1 where y is the prime number. Is this equation correct and will it work for any number plugged in for x in the equation?
2006-08-18 13:28:25 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Sorry, my bad, it need parenteses, otherwise:
2(1)^2+2-1
2-1=
1
not a prime number.
It should read:
(2x)^2+2x-1
2006-08-18 13:31:38 · update #1
Oh, and one more thing:
Use NATURAL NUMBERS ONLY!!!
eg (1, 2, 3, 4, 5, 6, 7 etc.)
2006-08-18 13:34:05 · update #2
Yeah...... I guess you're right..... Lol I've been looking for an equation for a while now.... owell I should give up now.
2006-08-18 13:42:18 · update #3
Johnny J came up with an equation, try his:
x^2-x+41=p
2006-08-18 13:52:14 · update #4
There is no such formula (polynomial function) for generating primes and the proof of this available.
Johny J's suggestion of n*n -n +41 fails at n=40 . Have a look at the wikipedia. And yes if you can generate a formula...it cant be non-constant-polynomial...ok?
2006-08-25 00:58:21 · answer #1 · answered by sumits1 2 · 0⤊ 0⤋
(2x)^2 is the same thing as 4x^2. I suggest you use 4x^2.
Any positive integer, it'll work, but not for negative and irrational numbers.
This makes an interesting conjecture... I'll see if I can disprove it.
1: 4 + 2 - 1 = 5
2. 16 + 4 - 1 = 19
3. 36 + 6 - 1 = 41
4. 64 + 8 - 1 = 71
5. 100 + 10 - 1 = 109
6. 144 + 12 - 1 = 155
There... done. It doesn't work with 6...
2006-08-18 14:05:31 · answer #2 · answered by Anonymous · 0⤊ 0⤋
There is a function that generates prime numbers, it is far more complicated than that. It doesn't generate them in any order, though.
When x is 10 in your function, y is 219 (200 + 20 -1) Since the sum of the digits is divisible by three, this number is, too. (3*73). So I have a counterexample.
There are instances like 101, 103, 107, and 109 all being prime, but in general they get further and further apart as the numbers increase, although there is an infinite number of primes.
2006-08-18 13:46:22 · answer #3 · answered by John T 6 · 0⤊ 1⤋
Wow-- quite cool! However, 6 doesn't work.(12)^2+12-1 = 144+12-1 = 155. Which I'm sure you know is divisible by 5. I don't think numbers greater than 6 work. But great try though! I like to do such experiments myself! Keep trying and I hope you find something!
2006-08-18 13:41:11 · answer #4 · answered by flit 4 · 0⤊ 0⤋
For finding all the small primes, say all those less than 10,000,000,000; one of the most efficient ways is by using the Sieve of Eratosthenes (ca 240 BC):
Make a list of all the integers less than or equal to n (greater than one) and strike out the multiples of all primes less than or equal to the square root of n, then the numbers that are left are the primes. (See also our glossary page.)
For example, to find all the odd primes less than or equal to 100 we first list the odd numbers from 3 to 100 (why even list the evens?) The first number is 3 so it is the first odd prime--cross out all of its multiples. Now the first number left is 5, the second odd prime--cross out all of its multiples. Repeat with 7 and then since the first number left, 11, is larger than the square root of 100, all of the numbers left are primes.
2006-08-26 12:44:37 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Look what happens if x=6
144 + 12 -1 = 155,
155 is obviously divisible by 5 sorry,
try x^2-x+41=p
2006-08-18 13:42:49 · answer #6 · answered by jonny j 1 · 0⤊ 0⤋
It's nice that you attempted to make an equation for prime numbers.
If you will let x = 100, y = 40199
and 40199 is 61 * 659
Just an example.
2006-08-18 13:44:59 · answer #7 · answered by ?????????? 2 · 0⤊ 0⤋
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2016-11-30 19:10:31 · answer #8 · answered by ? 3 · 0⤊ 0⤋
What would the unnatural numbers be?
I have heard of a Regular Baptist Church and peope wondered if there was an Irregular Baptist Church. So many years later they have renamed the church.
2006-08-26 12:19:07 · answer #9 · answered by Pepsi 4 · 0⤊ 0⤋
Its going to fail for the following numbers
6,7,8,9,11,16,17,18,20,more
I used maple to find this. The is no know formula to find primes, if you get one every math student wil know your name. Nice try thought.
Good luck
2006-08-18 13:39:10 · answer #10 · answered by pj2024 3 · 0⤊ 0⤋