What is the pattern of twin prime acceleration?

[eminent_youtom]

twin prime acceleration!

few weeks ago while i was doing my physics homework, i thought about the acceleration of prime number, so used the kinematics equations of acceleration on prime numbers. i was amazed to find that the difference of square of two prime numbers(>5) are always divisible by 24. especially if you look into twin primes then you can see a pattern (yet unknown:uhh:)
i mean the differences are reasonable.
how can i prove that,, or m just becoming fool? misunderstanding basic ideas? ( coz once i was glad to find that each and every numbers can be construct out of prime numbers,, which is absolute and universal truth)
help me!
m lost on nothing :grumpy:

here is the list of the few twin prime acceleration

twin prime t. prime acceleration

5,7 1
11,13 2
17,19 3
29,31 5
41,43 7
59,61 10
71,73 12
101,103 17
107,109 18
137,139 23
149,151 25
179,181 30
191,193 32
197,199 33
227,229 38
239,241 40
269,271 45
281,283 47
311,313 52
347,349 58
419,421 70
431,433 72
461,463 77
521,523 87
569,571 95
599,601 100
617,619 103
641,643 107
659,661 110
809,811 135
821,823 137
827,829 138
857,859 143
881,883 147

 

[ramsey2879]

few weeks ago while i was doing my physics homework, i thought about the acceleration of prime number, so used the kinematics equations of acceleration on prime numbers. i was amazed to find that the difference of square of two prime numbers(>5) are always divisible by 24. especially if you look into twin primes then you can see a pattern (yet unknown:uhh:)
i mean the differences are reasonable.
how can i prove that,, or m just becoming fool? misunderstanding basic ideas? ( coz once i was glad to find that each and every numbers can be construct out of prime numbers,, which is absolute and universal truth)
help me!
m lost on nothing :grumpy:

here is the list of the few twin prime acceleration

twin prime t. prime acceleration

5,7 1
11,13 2
17,19 3
29,31 5
41,43 7
59,61 10
71,73 12
...
881,883 147

Check the sequence, http://www.research.att.com/~njas/sequences/A002822 .
To prove it consider looking at prime numbers mod 6 and squares mod 4. There is a pattern that is readily apparant. Think about how to prove that and you are own your way to the proof you are looking for. Easy work for an student with background in algebra who is interested in numbers, because mod considerations are a basic tool of number theorists.

 

[eminent_youtom]

Check the sequence, http://www.research.att.com/~njas/sequences/A002822 .
To prove it consider looking at prime numbers mod 6 and squares mod 4. There is a pattern that is readily apparant. Think about how to prove that and you are own your way to the proof you are looking for. Easy work for an student with background in algebra who is interested in numbers, because mod considerations are a basic tool of number theorists.

thankx for the reply.
by the way is it better to spend my time on that new sequence(for me) or let it go coz its already ...?

how can i do mod consideration? i don't have any idea,( right now m taking calc III).

 

[CRGreathouse]

thankx for the reply.
by the way is it better to spend my time on that new sequence(for me) or let it go coz its already ...?

how can i do mod consideration? i don't have any idea,( right now m taking calc III).

You can spend time looking at this, it will help you understand better. But without a radically new idea and fast computers, you probably won't calculate further than has already been done.

Mods are easy, you know how to do them already. It's clock math -- 11 + 3 = 2 (3 hours past 11 o'clock is 2 o'clock). That's working mod 12 -- you can freely add or subtract 12. It's usually most convenient to put them in the simplest form, that is, between 0 and one less than the modulus. (Clocks instead put the time between 1 and the modulus, which also works.)

All primes other than 2 and 3 are equal to either 1 or 5 mod 6. (Otherwise, they'd be divisible by 2 or 3 -- and of the primes, only 2 and 3 are divisible by 2 and 3.)