prime formula

meeztamike · 2005-10-09, 22:21

i have found that 2 with any exponet minus one of these four numbers 11,13,17,19 will be prime 2>1 thur 2>20 is a pattern depending on what number the answer ends with. The pattern changes every 20 times I have not found a way to find the right pattern for each set but if you minus all of the four numbers one will be prime. To find out what number your answer will end with 2 with a exponet follows a pattern of 2,4,8,6 for 20 times therefore 2>12 will end with a 6, 2>234 will end with 4 ect. Can anyone help me find the pattern changes and when they repeat I am sure they will.
thank you.mike

ewmayer · 2005-10-09, 22:38

2^n-p is composite for n=14 and p=11,13,17,19. Similarly for n=23,25,26,27,28,29,30,33,34,35,...

I believe you've encountered yet another example of the strong law of small numbers ("3, 5 and 7 are prime, therefore every odd number must be prime.")

meeztamike · 2005-10-10, 01:02

I don't think so if you do the math you will find that it works every time but after 2>20 the pattern changes and I don't have a list of primes big enough to find the pattern changes and when they will repeat. I have tried this with the list of primes online and it works to that point but I need a bigger list to find out when the pattern repeats so that a true formula can be written. Do the math you will find out I am right.

Prime95 · 2005-10-10, 01:09

Quote:

Originally Posted by meeztamike

I don't think so if you do the math you will find that it works every time but after 2>20 the pattern changes.

The most common mistake of amateurs is seeing a pattern work for a few cases and assuming that it will work forever.

In your case, you've found that your pattern doesn't hold up, but rather than saying "Oh, my theory didn't work", you've assumed that you just need to tweak the pattern some more.

ewmayer · 2005-10-10, 02:11

Quote:

Originally Posted by Prime95

The most common mistake of amateurs is seeing a pattern work for a few cases and assuming that it will work forever.

That would be quite forgivable (even luminaries of number theory like Fermat are guilty of the above), but here our original poster continues to assert that his formula works "for all cases" even when presented with clear evidence to the contrary. It's easy to show that e.g.

7 divides 2^14-11
3 divides 2^14-13
13 divides 2^14-17
3 divides 2^14-19

...but presented with such our thread author cleverly replies "I don't think so." Brilliant stuff there. I hereby refer our readers to Bob Silverman's criterion of "willful ignorance", rest my case, and exit thread left.

meeztamike · 2005-10-11, 00:34

I told you the numbers were11,13.17.19 and I should have told you that they were 13,15,17,19 please try the math again. thank you, mike

Numbers · 2005-10-11, 06:52

Your theory breaks down when n = 25. 2^25 = 33 554 432 but there are no prime numbers >33 554 393 <33 554 467 so neither -11, -13, -15, -17, or -19 will give you a prime number.

Looking for patterns can often be a fun thing to do, and there is no shame in thinking you have found one when you haven’t. But when a serious professional mathematician like ewmayer tells you that you have not found a pattern it really doesn’t do you any favours to argue with him unless you can present a compelling proof of your pattern. A few trivially low examples does not constitute proof.

If you want to learn something from this, instead of looking for bigger examples try looking at the prime numbers as being of the form 6q + r and look at your examples in light of this and try to figure out why it happened so often before it broke down.

3.14159 · 2010-07-15, 18:52

Bowdlerized,

!

bsquared · 2010-07-15, 20:44

This thread is six. years. old.

science_man_88 · 2010-07-17, 20:18

Quote:

Originally Posted by bsquared

This thread is six. years. old.

2010-2005 = 5 years at best

3.14159 · 2010-07-18, 03:15

Quote:

This thread is six. years. old.

5 years*

2005-10-09, 22:21	#1
meeztamike Oct 2005 2² Posts	prime formula i have found that 2 with any exponet minus one of these four numbers 11,13,17,19 will be prime 2>1 thur 2>20 is a pattern depending on what number the answer ends with. The pattern changes every 20 times I have not found a way to find the right pattern for each set but if you minus all of the four numbers one will be prime. To find out what number your answer will end with 2 with a exponet follows a pattern of 2,4,8,6 for 20 times therefore 2>12 will end with a 6, 2>234 will end with 4 ect. Can anyone help me find the pattern changes and when they repeat I am sure they will. thank you.mike

2005-10-11, 00:34	#6
meeztamike Oct 2005 2² Posts	I am sorry I made a mistake I told you the numbers were11,13.17.19 and I should have told you that they were 13,15,17,19 please try the math again. thank you, mike

2010-07-15, 18:52	#8
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	Bowdlerized, ! Last fiddled with by xilman on 2010-07-15 at 20:42 Reason: This should be enough of a warning...

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2005-10-09, 22:38	#2
ewmayer ∂²ω=0 Sep 2002 República de California 5·2,351 Posts	2^n-p is composite for n=14 and p=11,13,17,19. Similarly for n=23,25,26,27,28,29,30,33,34,35,... I believe you've encountered yet another example of the strong law of small numbers ("3, 5 and 7 are prime, therefore every odd number must be prime.")

2005-10-10, 01:02	#3
meeztamike Oct 2005 2² Posts	I don't think so if you do the math you will find that it works every time but after 2>20 the pattern changes and I don't have a list of primes big enough to find the pattern changes and when they will repeat. I have tried this with the list of primes online and it works to that point but I need a bigger list to find out when the pattern repeats so that a true formula can be written. Do the math you will find out I am right.

2005-10-11, 06:52	#7
Numbers Jun 2005 Near Beetlegeuse 388₁₀ Posts	Your theory breaks down when n = 25. 2^25 = 33 554 432 but there are no prime numbers >33 554 393 <33 554 467 so neither -11, -13, -15, -17, or -19 will give you a prime number. Looking for patterns can often be a fun thing to do, and there is no shame in thinking you have found one when you haven’t. But when a serious professional mathematician like ewmayer tells you that you have not found a pattern it really doesn’t do you any favours to argue with him unless you can present a compelling proof of your pattern. A few trivially low examples does not constitute proof. If you want to learn something from this, instead of looking for bigger examples try looking at the prime numbers as being of the form 6q + r and look at your examples in light of this and try to figure out why it happened so often before it broke down.

2010-07-15, 20:44	#9
bsquared "Ben" Feb 2007 111010010100₂ Posts	This thread is six. years. old.