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• If one multiplies prime numbers add one (or minus one). It seams to turn out to be always a prime. And even other tricks seams to apply to turn out a prime My
Message 1 of 5 , Oct 30, 2002
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If one multiplies prime numbers add one (or minus one).
It seams to turn out to be always a prime.
And even other tricks seams to apply to turn out a prime
My math knowledge is average.
Hhave these 3 types of geting prime numbers a name?

Is 2*3*5*7*11*13* ..... +1 always prime ?
2*3+1=7
2*3*5+1=31
2*3*5*7=211
...
.

Also 2*3*5*7*22*13*.... -1 seams to be alaway prime (not sure yet).
2*3-1=5
2*3*5-1=29
2*3*5*7-1=209
..
.

playing with the set a bit more.
This might work just because there are a lot of low primes.
It also doesn't always produce primes sometime near primes.
Well I didn't tested it with big sets since i only had a simple
calculator wgen writing this Email.

multiply prime set - same set whitout one element Z + 1
(z = one prime of the same set replaced by number 1 )

2*3*5 - 2*3*z +1 = (10) not a prime
2*3*5 - 2*z*5 +1 = 11
2*3*5 - z*3*5 +1 = 16 not a prime (*>> -part has no 2

2*3*5*7 - 2*3*5*z +1 = 281 prime
2*3*5*7 - 2*3*z*7 +1 = 269 prime
2*3*5*7 - 2*z*5*7 +1 = 141 near prime -1 instead of +1 is prime
2*3*5*7 - z*3*5*7 +1 = 106 not a prime (*>> -part has no 2

2*3*5*7*11 -2*3*5*7*z +1 = 2101 near prime -1 instead of +1 is prime
2*3*5*7*11 -2*3*5*z*11+1 = 2081 prime
2*3*5*7*11 -2*3*z*7*11+1 = 1849 near prime -1 instead of +1 is prime
2*3*5*&*11 -2*z*5*7*11+1 = 1901 prime
2*3*5*&*11 -z*3*5*7*11+1 = 1156 not a prime (*>> -part has no 2

*>> part has no 2 will never be prime since numbers multiply will
always resurl in even numbers, so 2 is required.
• ... Wrong. ... The product of all the primes up to and including p is generally known as p#, or p primorial (by analogy with factorial). ... No. ...
Message 2 of 5 , Oct 30, 2002
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> If one multiplies prime numbers add one (or minus one).
> It seams to turn out to be always a prime.

Wrong.

> And even other tricks seams to apply to turn out a prime
> My math knowledge is average.
> Hhave these 3 types of geting prime numbers a name?

The product of all the primes up to and including p is generally known as p#, or p primorial (by analogy with factorial).

> Is 2*3*5*7*11*13* ..... +1 always prime ?

No.

> 2*3+1=7
> 2*3*5+1=31
> 2*3*5*7=211

2*3*5*7*11*13 + 1 = 59 * 509

> Also 2*3*5*7*22*13*.... -1 seams to be alaway prime (not sure yet).
> 2*3-1=5
> 2*3*5-1=29
> 2*3*5*7-1=209

209 = 11 * 19

Nice try, but you don't win the prize.

Paul
• Paul what do you think about the 3th type?. It produces a remarkable list i think. Later I used a internet list of the first 10000 primes. I should have tested
Message 3 of 5 , Oct 30, 2002
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Paul what do you think about the 3th type?.
It produces a remarkable list i think.

Later I used a internet list of the first 10000
primes.
I should have tested the first 2 types also :(
So far I have not tested larger sets then the previous
post. If I have time perhaps I can program it in VB
but now i have not much time anymore.

--- Paul Leyland <pleyland@...> wrote:
> > If one multiplies prime numbers add one (or minus
> one).
> > It seams to turn out to be always a prime.
>
> Wrong.
>
> > And even other tricks seams to apply to turn out a
> prime
> > My math knowledge is average.
> > Hhave these 3 types of geting prime numbers a
> name?
>
> The product of all the primes up to and including p
> is generally known as p#, or p primorial (by analogy
> with factorial).
>
> > Is 2*3*5*7*11*13* ..... +1 always prime ?
>
> No.
>
> > 2*3+1=7
> > 2*3*5+1=31
> > 2*3*5*7=211
>
> 2*3*5*7*11*13 + 1 = 59 * 509
>
> > Also 2*3*5*7*22*13*.... -1 seams to be alaway
> prime (not sure yet).
> > 2*3-1=5
> > 2*3*5-1=29
> > 2*3*5*7-1=209
>
> 209 = 11 * 19
>
> Nice try, but you don't win the prize.
>
>
> Paul
>

=====
Kind regards Peter Booshttp://www.geocities.com/Peter_Boos

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• ... Peter, Download a copy of PFGW from http://groups.yahoo.com/group/primeform/files/20020515_OpenPFGW.zip This is a very fast primality prover for many types
Message 4 of 5 , Oct 30, 2002
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> Paul what do you think about the 3th type?.
> It produces a remarkable list i think.

Peter,

http://groups.yahoo.com/group/primeform/files/20020515_OpenPFGW.zip

This is a very fast primality prover for many types of number, this included.
The product of the primes up to n, called the "primorial" (like the
factorial), and is conveniently written as n#. To use PFGW, enter something
like

pfgw -q"13#+1"

which will test 2x3x5x7x11x13+1 for (probably) primality.

You can investigate your third form using ABC2 files - see the documentation.
Basically you create a file called (say) 37test.txt containing something like
this:

ABC2 37#/\$a+1
a: primes from 3 to 37

then you call PFGW giving it the parameter 37test.txt:

P:\pfgw>pfgw 37test.txt
PFGW Version 20021007.Win_Dev (Alpha software, 'caveat utilitor') (Woltman
22.7lib w/P4 fixes)

Recognized ABC Sieve file: ABC2 File
Switching to Exponentiating using GMP
37#/2+1 is composite: [21B7D0D749F] (0.000000 seconds)
37#/3+1 is composite: [1412642F4E8] (0.000000 seconds)
37#/5+1 is composite: [D5B2EC019A] (0.000000 seconds)
37#/7+1 is 3-PRP! (0.000000 seconds)
37#/11+1 is composite: [5010B73FC9] (0.000000 seconds)
37#/13+1 is composite: [3732BC9436] (0.000000 seconds)
37#/17+1 is composite: [6E91841F2] (0.000000 seconds)
37#/19+1 is 3-PRP! (0.000000 seconds)
37#/23+1 is 3-PRP! (0.000000 seconds)
37#/29+1 is composite: [22D547146F] (0.000000 seconds)
37#/31+1 is 3-PRP! (0.000000 seconds)
37#/37+1 is 3-PRP! (0.000000 seconds)

Oh - I spy a bug! Why did it test 37#/2+1???

Regards,

Paul (another one).

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• Hi Paul, How can I (we) get pfgw Version 20021007 ? Greetings, Rob
Message 5 of 5 , Oct 31, 2002
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Hi Paul,

How can I (we) get pfgw Version 20021007 ?

Greetings, Rob
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