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Topic: professors of Stanford endorsing proof of Goldbach to arxiv
Replies: 20   Last Post: Sep 5, 2014 4:14 AM

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 plutonium.archimedes@gmail.com Posts: 18,572 Registered: 3/31/08
Re: professors of Stanford endorsing proof of Goldbach to arxiv
Posted: Aug 27, 2014 1:34 PM

On Tuesday, August 26, 2014 11:22:42 PM UTC-5, Archimedes Plutonium wrote:
(snipped)
> I vaguely recall some mathematician (Euler probably) had a formula that listed all the primes between say 19 and 51, or something of such a nature.
>

Now I am still looking that up, but I ran into Wilson's theorem

So, I wonder if we have a infinity borderline as 1*10^603, does that impact Wilson's theorem and allow for a complete ordering formula for the primes?

--- quoting from Wikipedia on Wilson's theorem ---

In number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if
.
That is, it asserts that the factorial is one less than a multiple of n exactly when n is a prime number.

The following table shows the values of n from 2 to 30, (n - 1)!, and the remainder when (n - 1)! is divided by n. (In the notation of modular arithmetic, the remainder when m is divided by n is written m mod n.) The background color is blue for prime values of n, gold for composite values.
Table of remainder modulo n

2
1
1
3
2
2
4
6
2
5
24
4
6
120
0
7
720
6
8
5040
0
9
40320
0
10
362880
0
11
3628800
10
12
39916800
0
13
479001600
12
14
6227020800
0
15
87178291200
0
16
1307674368000
0
17
20922789888000
16
18
355687428096000
0
19
6402373705728000
18
20
121645100408832000
0
21
2432902008176640000
0
22
51090942171709440000
0
23
1124000727777607680000
22
24
25852016738884976640000
0
25
620448401733239439360000
0
26
15511210043330985984000000
0
27
403291461126605635584000000
0
28
10888869450418352160768000000
0
29
304888344611713860501504000000
28
30
8841761993739701954543616000000
0

--- end quote of Wikipedia on Wilson's theorem ---

AP