## AP19, AP20 with difference 19#

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• Searching for an AP19 with difference 19# I have determined that there are exactly 2 AP19 with the first term below 1522399116794903040 = 1.5224*10^18 and
Message 1 of 4 , Dec 1, 2008
Searching for an AP19 with difference 19# I have determined that there
are exactly 2 AP19 with the first term below
1522399116794903040 = 1.5224*10^18
and difference 19#.
They are both part of AP20 starting with
1424014323012131633 = 1.42401*10^18.

I have used 41 64-bit computers for over 11 hours.

Jarek
• ... Congratulations on a two-for-one! http://hjem.get2net.dk/jka/math/aprecords.htm#minimal is updated with two new blue entries instead of red. If anyone is
Message 2 of 4 , Dec 2, 2008
Jarek wrote:
> Searching for an AP19 with difference 19# I have determined that there
> are exactly 2 AP19 with the first term below
> 1522399116794903040 = 1.5224*10^18
> and difference 19#.
> They are both part of AP20 starting with
> 1424014323012131633 = 1.42401*10^18.

Congratulations on a two-for-one!
http://hjem.get2net.dk/jka/math/aprecords.htm#minimal is updated
with two new blue entries instead of red.
If anyone is in doubt, 1424014323012131633 is a base 10 number!

--
Jens Kruse Andersen
• I have changed my program searching for AP with difference 19# from AP19 exhaustive to AP21 exhaustive, which allowed me to move much faster. I have found:
Message 3 of 4 , Dec 2, 2008
I have changed my program searching for AP with difference 19# from
AP19 exhaustive to AP21 exhaustive, which allowed me to move much
faster.

I have found:

AP21: 28112131522731197609+19#*n, n=0..20

This is:
The smallest EXISTING AP21 with difference 19#.
The first KNOWN case of 21 simultaneous primes according to JKA rules.
The first KNOWN AP21 with any difference and terms above 2^64.

I have used 42 computers yesterday during the day and total of 58
overnight, making something like 50 computers on average times 24
hours since the program was restarted after change.

After the restart I found one AP19, and the above AP21 was the second AP19+.

With 5 AP18 (for a total of 7 AP18+) I think I fully deserved to find
one AP19, perhaps two with some luck. I shouldn't really expect any
AP20, so AP21 is a miracle.

Jarek
• ... Big congratulations! An AP21 with the minimal difference 19# is amazing. http://hjem.get2net.dk/jka/math/aprecords.htm and
Message 4 of 4 , Dec 3, 2008
Jaroslaw Wroblewski wrote:
> AP21: 28112131522731197609+19#*n, n=0..20
>
> This is:
> The smallest EXISTING AP21 with difference 19#.
> The first KNOWN case of 21 simultaneous primes according to JKA rules.
> The first KNOWN AP21 with any difference and terms above 2^64.

Big congratulations!
An AP21 with the minimal difference 19# is amazing.

http://hjem.get2net.dk/jka/math/aprecords.htm and
http://hjem.get2net.dk/jka/math/simultprime.htm are updated.

--
Jens Kruse Andersen
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