- **Octoproth Search**
(*https://www.mersenneforum.org/forumdisplay.php?f=63*)

- - **Number of octoproths per n**
(*https://www.mersenneforum.org/showthread.php?t=5344*)

SorryNo, you guys are totally right, and I was totally wrong. I did not notice until this morning as I set my computer on its merry way for what I thought was the last 0.6E15, and realised I was a whole magitude adrift.
But I doubt I have the computer resources to run this much further. Each 1E15 takes about 8 hours, so the whole exercise will take someone 10 days. I will complete to 4E15, and then release this one. Regards Robert Smith |

[QUOTE=robert44444uk]No, you guys are totally right, and I was totally wrong. I did not notice until this morning as I set my computer on its merry way for what I thought was the last 0.6E15, and realised I was a whole magitude adrift.
But I doubt I have the computer resources to run this much further. Each 1E15 takes about 8 hours, so the whole exercise will take someone 10 days. I will complete to 4E15, and then release this one. Regards Robert Smith[/QUOTE] If I put my whole G5 on it I can have n=55 done in a shade under 2 days. I think this may be the limit of computing all Octoproths for a specific n. Let me check Robert's estimation formula:- est(54) = 225950 (actual = 230143) est(55) = 772429 est(56) = 280214 est(57) = 1253015 est(58) = 2335233 est(59) = 2922982 est(60) = 5869985 I might do n=56 as well, since it has fewer Octoproths than n=55. n=57 looks like a step too far. |

[QUOTE=Greenbank]
est(54) = 225950 (actual = 230143) est(55) = 772429 est(56) = 280214 est(57) = 1253015 I might do n=56 as well, since it has fewer Octoproths than n=55. n=57 looks like a step too far.[/QUOTE] n=55 [0,1E16] = 229947 n=55 [1E16,2E16] = 214250 n=55 [2E16,3E16] = 211102 n=55 [3E16,3.61E16] = 131672 Every 3-prp output by your program was indeed a prime! None failed the tests with PARI. 229947 + 214250 + 211102 + 131672 = 786971 est(54) = 225950 (actual = 230143) est(55) = 772429 (actual = 786971) |

OK, n=56 is complete!
Estimate was 280214. Final count after isprime() PARI checking script: 285415 2^n = 72057594037927936 so I used a kmax of 72060T. Output: n=56, kmin=0T, kmax=72060T, version=5.0, here T=10^12 Starting the sieve... Using the first 11 primes to reduce the size of the sieve array [285415 lines removed] The sieving is complete. Number of Prp tests=1503700301 Time=187990 sec. So that's 2 days, 4 hours, 13 minutes, 10 seconds. That's the end of it, not going to start n=57, there are too many of them! |

[QUOTE=Greenbank]OK, n=56 is complete!
Estimate was 280214. Final count after isprime() PARI checking script: 285415 [/QUOTE] That's great! [Code] g(n)=round(f(n)*(1+1/n)) [/CODE] I don't know why but it seems a better formula for large n values! Try it. |

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