Prev: number example to show how Infinitude of Twin Primes works #651 Correcting Math
Next: method only works for Twin Primes?? and not for N+4 nor N+6 or beyond? #653 Correcting Math
From: Archimedes Plutonium on 12 Jul 2010 14:12


Archimedes Plutonium wrote:
(snipped)
>
> There maybe a sticking point about this proof procedure for large even
> numbered
> prime pairs such as say p_n and p_n+1000, that we may have to have
> some
> more qualifiers to impose the Square Root Patch, due to the large
> spread between
> the n and even numbered n_
>

Let me write a list of the first few primes:

2, 3, 5, 7, 11, 13, 17, 19, 23, . .

The first twin primes is 3, 5

The first quad primes (n+4) is 3, 7

The first (n + 6) primes is 5, 11

The first (n +8) primes is 3, 11

etc etc

And so it matters not, how large the N+2k becomes, because the square-
root
patch on the last prime in the successive prime list captures all the
primes
of that succession, that finite succession, for example, doing the
N +4 primes proof would go like this:

Proof of the Infinitude of N+4 Primes:

(1) Definition of prime
(2) Hypothetical Assumption, suppose set of all N+4 Primes is finite
with
3,7 being the last two n+4 primes of the sequence set S = 3, 5, 7
where
7 is the last and largest of the N+4 primes. Note we can either use
2 in the S list or delete 2, depending on convenience.
(3) Multiply the lot and add 2 and subtract 2, yielding  W+2 =
(3x5x7)
+2 = 107 and
W-2 = (3x5x7) -2 = 103
(4) Take the square root of W+2 and I get 10.3.... I do not need
square root of W-2, and there cannot be any
regular primes
for consideration of being a prime factor of this W+2 that is greater
than 10
(5) Successively divide all the primes in the sequence S into W+2
and
W-2 and
they all leave a remainder
(6) The two new numbers W+2 and W-2 are necessarily two new N+4
primes
(7) Contradiction to 3 and 7 with 7 the largest and last N + 4
primes
(8) Set of N+4 Primes are infinite.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
 | 
Pages: 1
Prev: number example to show how Infinitude of Twin Primes works #651 Correcting Math
Next: method only works for Twin Primes?? and not for N+4 nor N+6 or beyond? #653 Correcting Math