- 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. > If one multiplies prime numbers add one (or minus one).

Wrong.

> It seams to turn out to be always a prime.

> And even other tricks seams to apply to turn out a prime

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

> 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 ?

No.

> 2*3+1=7

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

> 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).

209 = 11 * 19

> 2*3-1=5

> 2*3*5-1=29

> 2*3*5*7-1=209

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 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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http://hotjobs.yahoo.com/ > Paul what do you think about the 3th type?.

Peter,

> It produces a remarkable list i think.

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 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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