- I got it overnight:

254215977184797362303 + 53#*n, n=0..18

Yes, I was hoping to find it, but not sooner than after a few days.

If I am correct this improves AP19 record:

1.464 -> 8.408 (*10^20)

Jarek - Jaroslaw Wroblewski wrote:
> 254215977184797362303 + 53#*n, n=0..18

Congratulations on improving my AP19 record.

You now have the largest AP19 to AP24, all found since January 18.

http://hjem.get2net.dk/jka/math/aprecords.htm is updated.

I verify submitted AP's and test for extensions, so others will have

to be fast to discover something. No errors or extensions found yet.

--

Jens Kruse Andersen - I was trying to get AP17 with difference 107*61#. The reason why I

didn't use primorial difference is that I needed 9 primes coprime with

the sequence difference and with product below (2^62)/15 and primes 67-103

are the largest 9 consecutive primes with that property, so I had to

avoid them as factors of the sequence difference.

I was rather unlucky sitting there with 10 AP15's and nothing longer than

that (I should have AP16 every 4-5 AP15's).

And right now came the first sequence longer than 15 terms:

62749659973280668140514103 + 107*61#*n, n=0..18

I was expecting to get AP17. I was taking into acount small chance of AP18.

But I was never thinking of AP19 of that size, so I was really surprised

when it has appeared.

Jarek - Jaroslaw Wroblewski wrote:

> I was trying to get AP17 with difference 107*61#.

Congratulations!

> And right now came the first sequence longer than 15 terms:

>

> 62749659973280668140514103 + 107*61#*n, n=0..18

That lucky hit is the first triple record set since the page opened in

January 2005. Back then there was an existing triple record from 2004 to

2006: AP21 to AP23 by Markus Frind, Paul Jobling and Paul Underwood.

They actually searched for AP23!

Jaroslaw now has all the largest from AP17 to AP24:

http://hjem.get2net.dk/jka/math/aprecords.htm#records

--

Jens Kruse Andersen