- **And now for something completely different**
(*https://www.mersenneforum.org/forumdisplay.php?f=119*)

- - **new prime k-tuplet page**
(*https://www.mersenneforum.org/showthread.php?t=27091*)

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] |

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

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 |

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 |

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 |

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

PI_6(10^17) correctionThe 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. |

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. |

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

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

Update PI_8(10^18)[url]http://www.pzktupel.de/counting/PI_08.html[/url]
3rd pattern is done tomorrow |

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