6*(4x+1)+1

science_man_88 · 2010-06-29, 16:52

is there a pattern that works for 4x+1 in this equation such that it's prime all together? if so I think i have a way to use it to find mersenne primes. I realize this gives the 24x+7 but I found a sequence that if a rule can be applied to it's members may help find mersennes.

NBtarheel_33 · 2010-06-29, 18:09

Quote:

Originally Posted by science_man_88

is there a pattern that works for 4x+1 in this equation such that it's prime all together? if so I think i have a way to use it to find mersenne primes. I realize this gives the 24x+7 but I found a sequence that if a rule can be applied to it's members may help find mersennes.

Are you saying that 24x+7 is always prime, for any x? This is trivially not true, just take x = 7, or x = 7k, for any nonzero integer k. Then 7 | 24x and 7 | 7, hence 7 | 24x + 7, and so 24x + 7 is not prime.

Were you thinking about something else here?

science_man_88 · 2010-06-29, 18:30

Quote:

Originally Posted by NBtarheel_33

Are you saying that 24x+7 is always prime, for any x? This is trivially not true, just take x = 7, or x = 7k, for any nonzero integer k. Then 7 | 24x and 7 | 7, hence 7 | 24x + 7, and so 24x + 7 is not prime.

Were you thinking about something else here?

I'm not saying 24x+7 is prime for all x I'm asking for a pattern so i can apply something I found to possibly work with the sequences A002450 and and
A146768 I think trying to figure something out.

science_man_88 · 2010-06-29, 18:41

Basically what I see is if A139483 has a number 1 less than a member of A002450 then take the n value used to find it and that's a k value for A146768

retina · 2010-06-29, 18:42

Sometimes we see patterns where none exists.

Chasing patterns, that in all likelihood aren't there, is a good way to ~~waste~~ pass time.

science_man_88 · 2010-06-29, 18:45

Quote:

Originally Posted by retina

Sometimes we see patterns where none exists.

Chasing patterns, that in all likelihood aren't there, is a good way to ~~waste~~ pass time.

beats being on facebook etc. all day I'd rather do math some days

henryzz · 2010-06-29, 18:45

Quote:

Originally Posted by science_man_88

I'm not saying 24x+7 is prime for all x I'm asking for a pattern so i can apply something I found to possibly work with the sequences A002450 and and
A146768 I think trying to figure something out.

If your asking for a pattern in primes then think again. To my knowledge there is no known pattern in primes for any sequence.
24x+7 does seem like it is prime for lots of values but this is a combination of the fact that these numbers can't be divisible by 2 or 3 and the law of small numbers.

science_man_88 · 2010-06-29, 18:55

can we come up with a easy way to figure out if 24* (A002450-1)+7 is prime ? could there be a simple way if so then we can find the k just as easy for mersenne primes.

bsquared · 2010-06-29, 18:58

Quote:

Originally Posted by science_man_88

... I'm asking for a pattern so i can apply something I found to possibly work with ...

Here are some patterns which fit your critieria. I'm particularly fond of the third one.

pattern 1:

Code:

jbaoisdhrelkanesadb889adbqerb3e32jbaoisdhrelkanesadb889adbqerb3e32jbaoisdhrelkanesadb889adbqerb3e32jbaoisdhrelkanesadb889adbqerb3e32jbaoisdhrelkanesadb889adbqerb3e32jbaoisdhrelkanesadb889adbqerb3e32...

pattern 2:

Code:

99999999999999999999999999999999999999999999999999999999999999999999999999999999999...

pattern 3:

science_man_88 · 2010-06-29, 19:07

look unless you can help me with the pattern i later listed leave me alone I'm actually trying something.

kar_bon · 2010-06-29, 19:16

It's obvious: pattern is jbaoisdhrelkanesadb889adbqerb3e32

Another pattern:

Read about Ulam Spiral. There you can see a line with represents the primes of n=4x^2-2x+41.
But this is only true for small values and not for all of them.
It's only a special representation of the higher density of primes at low n.

Don't talk about a pattern, if it's only true for the first 5 numbers!

Read about Law of small numbers.
Try higher values of your 'patterns' and you will see there is none.

In 200 years hundreds of mathmaticians searched for such patterns and found none for Mersenne primes! There is none!

2010-06-29, 16:52	#1
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶×131 Posts	*6(4x+1)+1** is there a pattern that works for 4x+1 in this equation such that it's prime all together? if so I think i have a way to use it to find mersenne primes. I realize this gives the 24x+7 but I found a sequence that if a rule can be applied to it's members may help find mersennes. Last fiddled with by science_man_88 on 2010-06-29 at 17:04

2010-06-29, 18:41	#4
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶·131 Posts	Basically what I see is if A139483 has a number 1 less than a member of A002450 then take the n value used to find it and that's a k value for A146768

2010-06-29, 18:42	#5
retina Undefined "The unspeakable one" Jun 2006 My evil lair 1100001010100₂ Posts	Sometimes we see patterns where none exists. Chasing patterns, that in all likelihood aren't there, is a good way to ~~waste~~ pass time.

2010-06-29, 18:55	#8
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶·131 Posts	can we come up with a easy way to figure out if 24* (A002450-1)+7 is prime ? could there be a simple way if so then we can find the k just as easy for mersenne primes.

2010-06-29, 19:07	#10
science_man_88 "Forget I exist" Jul 2009 Dumbassville 2⁶·131 Posts	look unless you can help me with the pattern i later listed leave me alone I'm actually trying something.

2010-06-29, 19:16	#11
kar_bon Mar 2006 Germany 2908₁₀ Posts	It's obvious: pattern is jbaoisdhrelkanesadb889adbqerb3e32 Another pattern: Read about Ulam Spiral. There you can see a line with represents the primes of n=4x^2-2x+41. But this is only true for small values and not for all of them. It's only a special representation of the higher density of primes at low n. Don't talk about a pattern, if it's only true for the first 5 numbers! Read about Law of small numbers. Try higher values of your 'patterns' and you will see there is none. In 200 years hundreds of mathmaticians searched for such patterns and found none for Mersenne primes! There is none!