- Yesterday I started a search aimed at 18 Simultaneous Primes (BiTwin).

So far I failed to improve SP18 record, but I have determined that the

number

112511682470782472978100 = 1.12512*10^23

is the only number N below 1.23056*10^23 which produces 18 primes by

the formula

N * 2^n +/- 1, n=0,...,8

Jarek - Jarek wrote:
> 112511682470782472978100 = 1.12512*10^23

Congratulations on another great result!

> is the only number N below 1.23056*10^23 which produces 18 primes by

> the formula

> N * 2^n +/- 1, n=0,...,8

The first BiTwin with 8 links as defined at

http://www.primenumbers.net/Henri/fr-us/BiTwinRec.htm

It also beats the largest known with 7 links by Hans Rosenthal and I.

--

Jens Kruse Andersen - 2008/12/4 Jens Kruse Andersen <jens.k.a@...>:
> Jarek wrote:

Thanks.

>> 112511682470782472978100 = 1.12512*10^23

>> is the only number N below 1.23056*10^23 which produces 18 primes by

>> the formula

>> N * 2^n +/- 1, n=0,...,8

>

> Congratulations on another great result!

Another LUCKY result, I would say :-) At the moment I have the

following solution count:

5 links or longer: 1022

6 links or longer: 42

7 links or longer: 3

8 links: 1

Given that the additional link appears in 4-5% of solutions, the

expected nuber of 7-linked solutions is 2 and the expected number of

8-linked solutions is around (or even slightly below) 0.1.

Jarek - --- In primenumbers@yahoogroups.com, "jarek372000"

<jaroslaw.wroblewski@...> wrote:>

Fantastic find, so jealous.

> Yesterday I started a search aimed at 18 Simultaneous Primes (BiTwin).

> So far I failed to improve SP18 record, but I have determined that the

> number

> 112511682470782472978100 = 1.12512*10^23

> is the only number N below 1.23056*10^23 which produces 18 primes by

> the formula

> N * 2^n +/- 1, n=0,...,8

>

> Jarek

>

And which, in its elemental form k=N/4=28127920617695618244525

has 2^4+k and 2^6+k prime.

Robert