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

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 mensanator Posts: 5,039 Registered: 12/6/04
Re: Largest primeproduct with 2 as factor?
Posted: Aug 15, 2007 7:44 PM

On Aug 15, 6:00 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.

Oh, you want all composites of exactly two prime factors where
one of the factos is 2.

>>> import gmpy
>>> p = 3
>>> for i in xrange(30):

print '2*%d=%d' % (p,2*p)
p = gmpy.next_prime(p)

2*3=6
2*5=10
2*7=14
2*11=22
2*13=26
2*17=34
2*19=38
2*23=46
2*29=58
2*31=62
2*37=74
2*41=82
2*43=86
2*47=94
2*53=106
2*59=118
2*61=122
2*67=134
2*71=142
2*73=146
2*79=158
2*83=166
2*89=178
2*97=194
2*101=202
2*103=206
2*107=214
2*109=218
2*113=226
2*127=254

> and for three
> 6=3*2,15=3*5,21=3*7,33=3*11,39=3*13....

>>> p = 2
>>> for i in xrange(30):

print '3*%d=%d' % (p,3*p)
p = gmpy.next_prime(p)

3*2=6
3*3=9
3*5=15
3*7=21
3*11=33
3*13=39
3*17=51
3*19=57
3*23=69
3*29=87
3*31=93
3*37=111
3*41=123
3*43=129
3*47=141
3*53=159
3*59=177
3*61=183
3*67=201
3*71=213
3*73=219
3*79=237
3*83=249
3*89=267
3*97=291
3*101=303
3*103=309
3*107=321
3*109=327
3*113=339

>
> So forget my question

Why? It's too interesting. As I noted earlier, Randy's number has
two factors of 2, so the next even number 7924720394820394812478
would have one.

Alas, it has more than two prime factors.

C:\python25\user>factor! 7924720394820394812478
PRIME_FACTOR 2
PRIME_FACTOR 13
PRIME_FACTOR 29
PRIME_FACTOR 91283
PRIME_FACTOR 115139064781229

But if we grab the next prime after that

>>> print gmpy.next_prime(7924720394820394812478)
7924720394820394812487

and multiply it by 2, we should get a prime product:
>>> print gmpy.next_prime(7924720394820394812478)*2
15849440789640789624974

Of course, we should verify that the number was actually prime,
just in case next_prime() only gave us a probable prime:

C:\python25\user>factor! 15849440789640789624974
PRIME_FACTOR 2
PRIME_FACTOR 7924720394820394812487

>
>
>

> > I guarantee that has 2 as a factor.
>
> > - Randy