Relatively Prime Numers

[steve_bank]

I am reading through some proofs on linear congruential random number generators.

A requirement for a condition to exist is that two numbers be relatively prime.

It seems like it is correct say for any odd even number pair are relatively prime?

Coprime integers - Wikipedia

en.wikipedia.org

In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1.<a href="https://en.wikipedia.org/wiki/Coprime_integers#cite_note-1"><span>[</span>1<span>]</span></a> Consequently, any prime number that divides a does not divide b, and vice versa. This is equivalent to their greatest common divisor (GCD) being 1.<a href="https://en.wikipedia.org/wiki/Coprime_integers#cite_note-2"><span>[</span>2<span>]</span></a> One says also a is prime to b or a is coprime with b.

 

[Bomb#20]

Depends on what you mean by "odd even number pair". If you mean any odd number paired with any even number, then no. (3, 6) is the first counterexample. If you mean any pair of adjacent numbers, (N, N+1), then you are correct.

 

[steve_bank]

Thanks, I didn't see it.

 

[Jimmy Higgins]

What a bastardization of the term prime. It is about incompatible divisors not exclusivity of no divisors but 1.

Looks like I need to get a Math degree so I can change this.

 

[bilby]

What a bastardization of the term prime.

Just wait until you hear the way Amazon uses it.

 

[Tigers!]

This place has butchered the term prime.
Great food though. My daughter and son-in-law took me there for my birthday last week.

Carnivores rule!

 

[lpetrich]

"Prime" is borrowed from Old French, and in turn is descended from Latin prîmus "first".

In general, "first" is often used to mean "foremost".

 

[Swammerdami]

The last few posts in this thread were irreverent to the thread topic: primes, whether relative or not. My hijack -- which is a plug for the film Good Thief -- at least actually concerns a prime number.

With an IMDB rating of 6.5, Good Thief is one of only VERY few movies rated below 7 which I've considered for my personal Favorite 80 Movies List. Roger Ebert wrote ""it is clear, that he [Nick Nolte] was born to play Bob. It is one of those performances that flows unhindered from an actor's deepest instincts." Although I DO recommend the movie, it has flaws and may seem like an odd candidate for a Top 80 list. I think the soundtrack is a big part of why I liked the film! Leonard Cohen song(s) and a French version of the Stones' "Black is Black" are among several songs that make the film a pleasure.

Anyway in the opening scene the middle-aged Nick Nolte character meets a 17 year-old girl and explains to her that her age is a prime number. He immediately picks a fight with her would-be pimp to recover her passport. Too young for him, he tries to set her up with a much younger man, but she's not interested. Toward the end of the movie they walk into a casino and Nolte places a large bet on Number 17 at the roulette wheel. She says "Today's my birthday. I'm not a prime anymore," and moves the stack of chips to Number 18 (which wins). Although the huge age gap hasn't changed, a too-young taboo has lifted and the viewer senses their love will soon be consummated.

The movie is silly in several ways, but I liked it anyway.

- - - - - - - - - - - - - - - -

In a (futile?) attempt to avoid Infidels' anger at my hijack of a Mathematics thread, I decided to mention a tidbit from the History Desk. But which one? Perhaps most interesting is that the record for largest known prime number was shattered just a few weeks ago.

2^136,279,841 − 1​

is prime. That number has 41,024,320 digits compared with less than 25 million digits for the previous record-holder.

 

[steve_bank]

What a bastardization of the term prime. It is about incompatible divisors not exclusivity of no divisors but 1.

Looks like I need to get a Math degree so I can change this.

While you are at it alpso take a whack at using the term imaginary numbers.