Prime numbers and primality testing
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AP19 starting with 19

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Jaroslaw Wroblewski     Message 1 of 6  Feb 25, 2013
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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
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mikeoakes2     Message 2 of 6  Feb 26, 2013
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--- In primenumbers@yahoogroups.com, Jaroslaw Wroblewski <jaroslaw.wroblewski@...> wrote:
>
> Wojciech Izykowski has discovered AP19 with the smallest possible start of 19:
> 
> 19 + 13234551541698967679 * 17# * n, n=0,...,18
> (27 digits)
> 

An amazing and highly nontrivial discovery - many congratulations!

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
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Jens Kruse Andersen     Message 3 of 6  Feb 27, 2013
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Jaroslaw Wroblewski wrote:
> 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.

Congratulations to Wojciech!

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
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Jaroslaw Wroblewski     Message 4 of 6  Apr 5, 2013
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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 
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Jaroslaw Wroblewski     Message 5 of 6  Apr 10, 2013
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2013/4/5 Jaroslaw Wroblewski <jwr@...>:
> 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)

Wojciech has completed his computations and confirmed that the above
AP19 has the smallest possible diffrence among all AP19 starting with
19.

Jarek
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Jens Kruse Andersen     Message 6 of 6  Apr 10, 2013
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Jaroslaw Wroblewski wrote:
>> 19 + 4244193265542951705 * 17# * n, n=0,...,18
>
> Wojciech has completed his computations and confirmed that the above
> AP19 has the smallest possible diffrence among all AP19 starting with
> 19.

Congratulations to Wojciech.
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
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