- --- In primenumbers@yahoogroups.com, Jaroslaw Wroblewski <jaroslaw.wroblewski@...> wrote:
>

An amazing and highly nontrivial discovery - many congratulations!

> Wojciech Izykowski has discovered AP19 with the smallest possible start of 19:

>

> 19 + 13234551541698967679 * 17# * n, n=0,...,18

> (27 digits)

>

But don't rush to look for an AP23:

heuristics in my NMBRTHRY post of 2001

https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0106&L=NMBRTHRY&F=&S=&P=3812

indicate that a complete search would take many times the age of the Universe.

Mike - Jaroslaw Wroblewski wrote:
> Wojciech Izykowski has discovered AP19 with the smallest possible start of

Congratulations to Wojciech!

> 19:

>

> 19 + 13234551541698967679 * 17# * n, n=0,...,18

> (27 digits)

>

> At the moment it is not known whether the difference of the AP is the

> smallest possible, but Wojciech is working to determine that.

http://users.cybercity.dk/~dsl522332/math/aprecords.htm#minimalstart

is updated with a mixed color entry to show that it has the smallest

possible start but the difference may not be the smallest.

--

Jens Kruse Andersen - Wojciech Izykowski has discovered AP19 with the smallest possible

start of 19 and a smaller difference than in his first example:

19 + 4244193265542951705 * 17# * n, n=0,...,18

(26 digits)

He needs about a week to determine whether this difference is the

smallest possible.

Jarek

2013/2/26 Jaroslaw Wroblewski <jwr@...>:> Wojciech Izykowski has discovered AP19 with the smallest possible start of 19:

>

> 19 + 13234551541698967679 * 17# * n, n=0,...,18

> (27 digits)

>

> At the moment it is not known whether the difference of the AP is the

> smallest possible, but Wojciech is working to determine that.

>

> Although Wojciech was using the ideas I have developed in the past, he

> created brand new implementation of the search program on his own.

>

> Jarek - 2013/4/5 Jaroslaw Wroblewski <jwr@...>:
> Wojciech Izykowski has discovered AP19 with the smallest possible

Wojciech has completed his computations and confirmed that the above

> start of 19 and a smaller difference than in his first example:

>

> 19 + 4244193265542951705 * 17# * n, n=0,...,18

> (26 digits)

AP19 has the smallest possible diffrence among all AP19 starting with

19.

Jarek - Jaroslaw Wroblewski wrote:
>> 19 + 4244193265542951705 * 17# * n, n=0,...,18

Congratulations to Wojciech.

>

> Wojciech has completed his computations and confirmed that the above

> AP19 has the smallest possible diffrence among all AP19 starting with

> 19.

http://users.cybercity.dk/~dsl522332/math/aprecords.htm#minimalstart is

updated so the color is no longer red.

It should also be submitted to http://oeis.org/A061558

--

Jens Kruse Andersen