- I have a quick question. How did Lucas determine s of 0 =4? The book I

am reading says he uses U of n and V of n for (P,Q). IF (P,Q)

determines that s of 0 =4, Which equation did he use or which (P,Q)

did he use? Or, is 4 used because it is the first composite number.

Because if you use 2 or 3, you get prime numbers. Thanks for any help!!

-matt - 2^17 - 1 = 131071. Both 131 and 071 are prime, or 131~071,

or 3~(2^17-1), since it splits at the third position.

I tried to split other Mersenne primes up into two primes,

but found no other examples up to 2^9689 - 1.

What is the largest known splitable prime?

-Ed Pegg Jr - --- In primenumbers@yahoogroups.com, "newjack56" <mrnsigepalum@a...>

wrote:>

book I

> I have a quick question. How did Lucas determine s of 0 =4? The

> am reading says he uses U of n and V of n for (P,Q). IF (P,Q)

help!!

> determines that s of 0 =4, Which equation did he use or which (P,Q)

> did he use? Or, is 4 used because it is the first composite number.

> Because if you use 2 or 3, you get prime numbers. Thanks for any

>

Hi matt,

>

> -matt

>

Take a look at this paper :

http://www.maths.tcd.ie/pub/ims/bull54/M5402.pdf

You will understand that in fact, S0=4 is one possibility but that

there are in fact infinitely many others (look at theorem 4 on page

71).

For example, S0=10 or S0=52 or S0=724 work as well.

Regards,

Jean-Louis. - Ed Pegg Jr wrote:

> 2^17 - 1 = 131071. Both 131 and 071 are prime, or 131~071,

I have not heard of searches for large splitable primes.

> or 3~(2^17-1), since it splits at the third position.

>

> What is the largest known splitable prime?

One way to search them is to concatenate known primes.

27918*10^10000+1 was found in 1999 by Yves Gallot.

58789 is the smallest prime which can be put in front and give a prime:

D:>pfgw -t -q"5878927918*10^10000+1"

PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 5878927918*10^10000+1 [N-1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 3

Calling Brillhart-Lehmer-Selfridge with factored part 69.83%

5878927918*10^10000+1 is prime! (26.4531s+0.0023s)

The form k*10^n+1 was chosen to make the concatenation easily provable.

PrimeForm/GW prp tested and APTreeSieve sieved.

--

Jens Kruse Andersen