Prime numbers are components that can be used to make all the other numbers. You can't make the primes themselves using those components. Primes are kind of fundamental , primitive building blocks that way.
So 2 * 3 makes a 6 for us. 3 * 4 makes a 12, and so on.
What about 1?
Well, 1 * 3 = 3. That does not make anything new for us now does it.
Clearly 1 times anything does not make any new number for us so 1 is not one of those components we can use to make the other numbers. Ergo it is not prime.
Every integerwhich can be written as the sum of two primes, can also be written as the sum of as many primes as one wishes, until all terms are units.
He then proposed a second conjecture in the margin of his letter: Every integer greater than 2 can be written as the sum of three primes.He considered 1 to be a prime number, a convention subsequently abandoned.[6] The two conjectures are now known to be equivalent, but this did not seem to be an issue at the time. A modern version of Goldbach's marginal conjecture is: Every integer greater than 5 can be written as the sum of three primes.Euler replied in a letter dated 30 June 1742, and reminded Goldbach of an earlier conversation they had (" so Ew vormals mit mir communicirt haben "), in which Goldbach remarked his original (and not marginal) conjecture followed from the following statement Every even integer greater than 2 can be written as the sum of two primes,which is, thus, also a conjecture of Goldbach. In the letter dated 30 June 1742, Euler stated:
Dass ein jeder numerus par eine summa duorum primorum sey, halte ich für ein ganz gewisses theorema, ungeachtet ich dasselbe nicht demonstriren kann. ("every even integer is a sum of two primes. I regard this as a completely certain theorem, although I cannot prove it.")[7][8]
Goldbach's third version (equivalent to the two other versions) is the form in which the conjecture is usually expressed today. It is also known as the "strong", "even", or "binary" Goldbach conjecture, to distinguish it from a weaker corollary. The strong Goldbach conjecture implies the conjecture that all odd numbers greater than 7 are the sum of three odd primes, which is known today variously as the"weak" Goldbach conjecture, the "odd" Goldbach conjecture, or the "ternary" Goldbach conjecture. While the weak Goldbach conjecture appears to have been finally proved in 2013,[9][10] the strong conjecture has remained unsolved. If the strong Goldbach conjecture is true, the weak Goldbach conjecture will be true by implication.[8]
Sorry Heater , I am not a mathematic, but it seems you're wrong.
It seems to me that the original conjecture was "every integer" (including odd numbers of course). It also seems to me that someone, after discarding the "1" from primes, needed to add some "even" here and "greater" there to bring the water to their mill.
:P
If we take the P1 to be the unit then the next Prop would be that prime number closest to the Pnew/P1. I am planning to over-clock the next Propeller at 220Mhz.
So, taking the NOP instruction as an example (the only one of which I have full understanding), Pnew/P1 =11, which is prime but not fibronaccian.
This gives us the PROP11, which in Englich can be read "Prop...2" or "Prop-eleven" Or we could use Hex, in which case it would be Prop$B, which I personally prefer.
Comments
Prime numbers are components that can be used to make all the other numbers. You can't make the primes themselves using those components. Primes are kind of fundamental , primitive building blocks that way.
So 2 * 3 makes a 6 for us. 3 * 4 makes a 12, and so on.
What about 1?
Well, 1 * 3 = 3. That does not make anything new for us now does it.
Clearly 1 times anything does not make any new number for us so 1 is not one of those components we can use to make the other numbers. Ergo it is not prime.
Are we thinking about this too hard?
Oh yes. To put Goldbach's Conjecture correctly: "Every even integer greater than 2 can be expressed as the sum of two primes."
Clearly if 1 was considered to be prime the conjecture would not contain that "greater than 2" condition.
Dave
Sorry Heater
It seems to me that the original conjecture was "every integer" (including odd numbers of course). It also seems to me that someone, after discarding the "1" from primes, needed to add some "even" here and "greater" there to bring the water to their mill.
:P
Yep seems you are right.
If I'm reading all that correctly the last version is the "strong" conjecture is not proved even today and anyway mathemeticans regard 1 as not prime.
I don't make the rules here you know:)
That's really going to confuse he marketing:)
So, taking the NOP instruction as an example (the only one of which I have full understanding), Pnew/P1 =11, which is prime but not fibronaccian.
This gives us the PROP11, which in Englich can be read "Prop...2" or "Prop-eleven" Or we could use Hex, in which case it would be Prop$B, which I personally prefer.
Rich