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Topic: Largest primeproduct with 2 as factor?
Replies: 19   Last Post: Aug 16, 2007 1:06 PM

 Messages: [ Previous | Next ]
 Randy Poe Posts: 5,658 Registered: 12/6/04
Re: Largest primeproduct with 2 as factor?
Posted: Aug 16, 2007 11:30 AM

On Aug 16, 3:20 am, jonas.thornv...@hotmail.com wrote:
> On 16 Aug, 05:23, Randy Poe <poespam-t...@yahoo.com> wrote:
>
>
>

> > On Aug 15, 7:00 pm, jonas.thornv...@hotmail.com wrote:
>
> > > On 16 Aug, 00:42, Randy Poe <poespam-t...@yahoo.com> wrote:
>
> > > > On Aug 15, 6:36 pm, jonas.thornv...@hotmail.com wrote:
>
> > > > > On 16 Aug, 00:18, stephane.fr...@gmail.com wrote:
>
> > > > > > On Aug 15, 3:03 pm, jonas.thornv...@hotmail.com wrote:
>
> > > > > > > On 16 Aug, 00:00, stephane.fr...@gmail.com wrote:
>
> > > > > > > > On Aug 15, 2:53 pm, jonas.thornv...@hotmail.com wrote:
>
> > > > > > > > > I do not know much math, i just wonder if there is a largest
> > > > > > > > > primeproduct with two as one of the factors.
> > > > > > > > > Same i wonder for three.

>
> > > > > > > > > If not..., but if so is it true for any primefactor used in
> > > > > > > > > primeproduct that they will have a range?
> > > > > > > > > Do every factor have a range in primeproducts?

>
> > > > > > > > > A pure guess tell me that the numbers of primeproducts with 2 or 3
> > > > > > > > > used as one of the factor is infinite but i am not sure.

>
> > > > > > > > > JT
>
> > > > > > > > You guess is right. This is because there is infinity prime number
> > > > > > > > then if N is the bigger prime product, you will find A your biggest
> > > > > > > > prime with A = N/2. You can find a prime number A' with A'> A, then N'
> > > > > > > > = A x 2 > N. Same rules with 3 or any prime numbers.

>
> > > > > > > > SF
>
> > > > > > > Could anyone tell me the biggest "known" primeproduct that has two as
> > > > > > > factor?- Hide quoted text -

>
> > > > > > > - Show quoted text -
>
> > > > > > Well dude , you can suppose you got one and then prove that you can a
> > > > > > bigger one .- D?lj citerad text -

>
> > > > > > - Visa citerad text -
>
> > > > > Ok an easy question i do not have any primeproduct algorithm going, so
> > > > > i would be interested in a list of primeproducts less than a million
> > > > > that has two as factor?

>
> > > > > Can not be that many or?
>
> > > > > If not that many would be nice for 10 000 000 and for 100 000 000?
>
> > > > > Well if already a million would have couple of 100 i am not that
> > > > > interested in the bigger numbers.

>
> > > > What do you mean by "primeproduct"? Do you mean any
> > > > number that has 2 as a factor?

>
> > > > For instance, does 2^20 = 1048576 qualify as a "primeproduct"?
>
> > > > If you just mean any number that has two as a factor,
> > > > these are called "even numbers", and any number that
> > > > ends in 0, 2, 4, 6, or 8 is such a number. Thus, here
> > > > is a large even number: 7924720394820394812476

>
> > > Sorry i am tired, it is of course
> > > 6=2*3,10=2*5,14=2*7,22=2*11,26=2*13,34=2*17,38=2*19 and so son.
> > > and for three
> > > 6=3*2,15=3*5,21=3*7,33=3*11,39=3*13....

>
> > > So forget my question
>
> > Ah. Well, these days primes far > 10^6 are easily
> > turned out in milliseconds by computer software.

>
>
> > Not exactly what you're looking for, but if you
> > try various values of n you'll find a prime of the
> > size you want. Then obviously just multiply by 2.

>
> > For instance, the billionth prime is:
> > 22,801,763,489

>
>
> Is the computional effort for primality test for x bigger or less than
> checking that a composit only have two factors x*2?
> (Maybe actually is effort*2, i do not remember much about log
> notation)

question (checking if a number is of the form 2*prime)
just involves dividing by 2 and then doing prime testing
on the result.

> But if the composit primeproduct of x*2="y" have two other factors we
> know that x not prime either?

Yes. If y = 2*p1*p2 = 2*x, then we know x is not prime.

> Is this the main idea behind JSH pseudoprime rantings?

It's hard to follow JSH's rantings. The history I know
is that he thought he had a proof of Fermat's Last
Theorem that was contradicted by number theory, so he
concluded that number theory was wrong and was a hoax
perpetrating by lying mathematicians for centuries.

- Randy