- 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 - Jarek wrote:
> Searching for an AP19 with difference 19# I have determined that there

Congratulations on a two-for-one!

> 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.

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:

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 - Jaroslaw Wroblewski wrote:
> AP21: 28112131522731197609+19#*n, n=0..20

Big congratulations!

>

> 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.

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.

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Jens Kruse Andersen