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 Cybertronic 2021-11-03 10:11

PI_15(10^22)

It tooks me 3 weeks to calculate all prime 15-tuplets up to 10^22.

There are 676 exists. Up to 10^21, no missing number was found.

[url]https://oeis.org/A257169[/url]

 Cybertronic 2021-11-05 16:13

PI_k(X)

A "Recent additions" for PI_k(X)-tables was added
[URL]http://www.pzktupel.de/Tables.html[/URL]

 Cybertronic 2021-11-06 06:43

PI_7(10^17)

Is done after 1day.
There are 93,940,829 7-tuplets (both pattern) up to 10^17.

[url]http://www.pzktupel.de/counting/PI_07.html[/url]

Next PI_6(10^17)
Estimate time: 60h

 Cybertronic 2021-11-07 09:19

PI_6(10^17)

It's done ,calculation tooks me 16h.

There are 570,735,178 up to 10^17

[URL]http://www.pzktupel.de/counting/PI_06.html[/URL]

Sieving up to ~751000 then Rabin-Miller-Test with base=2.

Final result was reduce by 3, I found with the pseudoprime base_2 - list (up to 2^64) 3 false prime sextuplets.

12202902616309133 6th number
12658530383462153 6th number
12893382792577873 3rd number

 Cybertronic 2021-11-07 13:24

new section added

[URL]http://www.pzktupel.de/Tables10X.html[/URL]

This table show, how many prime k-tuplets are up to 10^n

Note, maby PI_6(10^17) ist not correct....must see, why

 Cybertronic 2021-11-07 15:58

:rant:

Bug found, Pi_6(10^17) is done tomorrow.
Upper limit was not 10^17,it was ~ 9.9879e16

 Cybertronic 2021-11-08 09:13

PI_6(10^17) correction

The calculation is done: There are 571314626 prime sextuplets up to 10^17.
The sum was reduce by 3 (pseudo prime 6-tuplets).

Numbers are
12202902616309117+16
12658530383462137+16
12893382792577867+6

PI_6(10^17)=571314626
LI_6(10^17)=571290398

Looks better now :smile:
Next: PI_5(10^16) .... estimated time 21h per pattern.

 Cybertronic 2021-11-08 10:36

PI_5(10^16)

A first appoximation after 1h gave me for PI_5(10^16) and pattern d=0,2,6,8,12:

53175713/32*899+PI_5(10^15) ~ 1736450170
LI_5(10^15)=1736513588

Tomorrow, I will see what the real value is.

 Cybertronic 2021-11-09 06:41

PI_5(1e16) pattern d=0,2,6,8,12

Value is 1,736,614,143 and LI=1,736,513,588
Sieving up 8,960,453

There are 10 false prime quintuplet with factors > 8,960,453
1414744276484177, 2043183817242019 ,2591106911415857 ,2762007330795523 ,3650579292309623 ,5459403435729829 ,6612111624056921
6829219377998653 ,6949430519779333 ,7595018731158409 ,

2nd pattern done in 12h
There will be 15 false prime quintuplets
1186031063218877, 1199012316059017, 3031646959069873, 5138327769220273, 5156031002809789, 5596084581347179, 5857980051959809
6860390003895949, 6944760326240833, 7060112777135767, 7180054501495873, 8492448456384889, 8861685807262037, 8962939623342589
9511159909417093

 Cybertronic 2021-11-09 18:39

PI_5(1e16) pattern d=0,4,6,10,12

PI_5(1e16)=1,736,521,682, for 2nd pattern
So there are 3,473,135,825 prime quintuplets up to 10^16.

Next PI_8(10^18) for d=0,2,6,8,12,18,20,26
Estimated time: 18h

 Cybertronic 2021-11-11 13:11

Update PI_8(10^18)

[url]http://www.pzktupel.de/counting/PI_08.html[/url]

3rd pattern is done tomorrow

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