- 1. A prime is a positive integer that cannot be expressed by the even number of sums of

any single number except 1 and itself.

2. A prime is a positive integer that cannot be expressed by the product of any of its

smaller positive integers >1. Implication: if a number has no smaller numbers >1, the

definition would not apply to that number.

3. A prime is a positive integer that has only two divisors. Implication: For primes

greater than 2, only two divisors means we have tested and confirmed that other smaller

numbers are non-divisors. For the number 2, however, only two divisors means we have

not tested other smaller numbers as divisors or we have nothing available to test. So, only

two divisors means opposite things to the real primes versus the number 2. It is sloppy

logic to use this definition to slip 2 into the class of real primes.

4. A prime is a positive integer that can be proven to be non-dividable by a smaller

number >1.

5. A prime is an odd positive integer that has only two divisors.

6. The essence of prime is non-dividability by any smaller number >1.

7. A number is not a prime unless it can be proven to be non-dividable by a smaller

number >1.

8. A thing is unique if it is not an inherent part of something else. A prime is a positive

integer with the property of uniqueness. Such property is not an inherent part of any

single smaller number. The property of a number is an inherent part of a smaller number

either because the number is needed for the smaller number to have meaning or its

property of non-uniqueness can be expressed as a pattern or sums of a single smaller

number >1. The number 2 is an inherent part of the creation of the number 1, as

evidenced by the existence of civilizations that had invented only 1 and 2 but no numbers

beyond 2 and by the absence of civilizations that invented only 1 but not 2. We need 2 to

invent 1 or for 1 to have any meaning. We need both 1 and 2 in order to invent the

concept of number. However, we do not need 3 to invent 1 and 2. All numbers are

inherent in the number 1 as patterns of 1s but the property of uniqueness is not inherent

in the pattern of 1s. The uniqueness of 11 cannot be expressed as a pattern of 1 that

would in itself say that 11 is unique but 12 is not. The non-uniqueness of a non-prime

number is inherently associated with at least one single smaller number. The number 12

is inherently associated with 3 as a pattern of 3, and this association reveals that 12 is not

unique.

Prime has meaning and value only with regard to odd numbers. Why make an exception to

accommodate one number while disregard the many fundamental differences between this

one number and the rest? Only left-handed amino acids are relevant to life on earth while

right-handed amino acids are not. Only odd numbers are relevant to the concept of

primes while even numbers are not.

The essence of Prime is about uniqueness and no even numbers can claim to be unique.

Dividability is a way of measuring uniqueness but is not the essence of primes. A number

can be non-dividable but still lacks uniqueness, such as 2. The present conventional view

of 2 as a prime mistook a secondary property (non-dividability) of a primary property

(uniqueness) as the primary property. Uniqueness cannot exist without something else

serving as the contrasting background of non-uniqueness. Odd cannot exist without the

concept of even. 1 cannot exist without 2. Uniqueness is oneness and No numbers could

be more unique than 1. The uniqueness of 1 demands 1 to be a prime and 2 a non-prime

by default.

"317 is a prime, not because we think so, or because our minds are shaped in one way

rather than another, but *because it is so*, because mathematical reality is built that way."

--G. H. Hardy, "A Mathematician's Apology"

Cambridge University Press, 1940.

I doubt very much that Hardy or any mathematician in his right mind would say the same

thing about the number 2. 2 may be a prime today but it was not viewed as a prime at

least once in human history and is most likely not a prime in the objective truth of a

supernatural reality of God. 317 is a prime no matter how you define prime. But 2 does

not qualify as a prime in many definitions as I listed above. 317 is an objective prime

whereas 2 is an artificial prime invented by human conventions of today that will surely be

proven to be misguided.

Can any one offer a list of definitions that would include 2 as a prime? - --- shuangtheman <shuangtheman@...> wrote:
> 1. A prime is a positive integer that cannot be expressed by the even number

How is 2 expressible as an even number of sums of a single number that isn't 1

> of sums of any single number except 1 and itself.

or 2? It can't. So your definition of prime that excludes 2 includes 2.

Does this depend on what the meaning on of 'is' is, or something?

Or have your just shot yourself in the foot _really_ badly.

I think the latter, and I recommend retreating.

Phil

() ASCII ribbon campaign () Hopeless ribbon campaign

/\ against HTML mail /\ against gratuitous bloodshed

[stolen with permission from Daniel B. Cristofani]

__________________________________________________

Do You Yahoo!?

Tired of spam? Yahoo! Mail has the best spam protection around

http://mail.yahoo.com