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

- - **Dodecaproths**
(*https://www.mersenneforum.org/showthread.php?t=5358*)

Thanks a lot, now is much better :smile:
n=70 to 3E15, was 1970 sec, now 1300 sec (estimate) n=70 3E15-1E16, was 23000sec (est), now 2900 sec! (est) n=71 to 1E15, was 5500sec, now 5000 sec (est) Also confirmed a number of already found DodecaProths. I'm now trying to find more DodecaProths for n=62 which was most prolific so far. ps. To moderators: Please remove my duplicate post #276. |

There are 6 dodecaproths for n=53I've searched the full range for n=53
Here is the full report. On my P4 Celeron 1.7 GHz: C:\>dodeca_2_0 53 1 9007199254740991 You can also find the k n values in results_dodeca.txt file ( These are 3-probable primes ) n=53, kmin=1, kmax=9007199254740991, version=2.0 Starting the sieve... Using the first 11 primes to reduce the size of the sieve array 243175720207035 53 2045619551693025 53 5622222735873975 53 2468433344406645 53 4167419818747185 53 2104470659030355 53 The sieving is complete. Number of Prp tests=1692282 Time=21101 sec. |

27 DodecaProths FoundHere is the list of all DodecaProths found so far and the status of search. I found two more for n=62.
[CODE] 7946515823715 44 9604223498415 44 10872870991605 44 Robert [Done] 45 None [Done] 46 None [Done] 45960089776965 47 69283546229205 47 Robert [Done] 48 None [Done] 19000157002995 49 374180855930805 49 502414540060965 49 555428994253665 49 Robert [Done] 50 None [Done] 145174433549145 51 246834311745945 51 868049887559295 51 Kosmaj [Done] 2808528662035845 52 R.Gerbicz [Done] 243175720207035 53 2045619551693025 53 2104470659030355 53 2468433344406645 53 4167419818747185 53 5622222735873975 53 R.Gerbicz [Done] 54-55 [Not tested] 56 [1.2E15] 87653084113035 57 Kosmaj [2E15] 58 [2E15] 59 [2E15] 60 [2E15] 61 [2E15] 99828673281855 62 286846836764775 62 1692654062704395 62 3574476316006155 62 6553886937433395 62 Kosmaj [9E15] 63 [2E15] 64 [2E15] 65 [2E15] 229350894172785 66 tcadigan [1E15] 67 [3E15] 68 [3E15] 69 [3E15] 14494401979227555 70 Kosmaj [2E16] 71 [1E15] [/CODE] |

First DodecaProth n=56[B]4356015966090075 56 [/B] [5E15]
I'm now working on n=58 and n=71. BTW, it will be good to creata a separate thread for DodecaProths and move related posts there. Tell Citrix in his thread about it, and tell him that his thread will be soon deleted because at the time he wrote it we already discussed DodecaProths here but he never bother to have a look. |

OK, will do, will also create a separate reservation/results thread and grab the info from here.
OK: Reservations thread: [url]http://www.mersenneforum.org/showthread.php?t=5359[/url] Please post only reservations or results in that thread. Use this thread for discussions. Thanks for the help Kosmaj. |

Estimation of the number of dodecaproths for nAs I estimated the number of octoproths for a given n value, it is also possible to give an estimation for dodecaproths:
Let's define the "weight" for n: [CODE] w(n)=T=2048.0;forprime(p=3,10^4,l=listcreate(12);g=Mod(2,p)^n;h=1/g;a=[g,-g,h,-h,2*g,-2*g,h/2,-h/2,4*g,-4*g,h/4,-h/4];\ a=lift(a);for(i=1,12,listput(l,a[i],i));l=listsort(l,1);T*=(1-length(l)/p)/(1-1/p)^12);return(T)[/CODE] then by this we can estimate the number of dodecaproths for a given n by: [CODE] f(n)=round(w(n)*2^n/(n*log(2))^12*1/64)[/CODE] For example if n=53 then f(n)=4. The true number is 6. |

Can someone else check this one. The list above stated None for n=50.
But the PARI script (isddp.txt) run against all known Octoproth's gave this:- 717083008036395 50 is DodecaProth! ... Left_legs=1, Rigth_legs=0. Either there is a problem with dodeca_2_0.c or that PARI script:- $ ../dodeca20 50 7170000000000000 7200000000000000 You can also find the k n values in results_dodeca.txt file ( These are 3-probable primes ) n=50, kmin=7170000000000000, kmax=7200000000000000, version=2.0 Starting the sieve... Using the first 9 primes to reduce the size of the sieve array The sieving is complete. Number of Prp tests=1567 Time=22 sec. |

[QUOTE=Greenbank]Can someone else check this one. The list above stated None for n=50.
But the PARI script (isddp.txt) run against all known Octoproth's gave this:- 717083008036395 50 is DodecaProth! ... Left_legs=1, Rigth_legs=0. Either there is a problem with dodeca_2_0.c or that PARI script:- $ ../dodeca20 50 7170000000000000 7200000000000000 You can also find the k n values in results_dodeca.txt file ( These are 3-probable primes ) n=50, kmin=7170000000000000, kmax=7200000000000000, version=2.0 Starting the sieve... Using the first 9 primes to reduce the size of the sieve array The sieving is complete. Number of Prp tests=1567 Time=22 sec.[/QUOTE] That is a new dodecaproth! I think somebody made a mistake when he searched this n value ( for this he used your tables!). For my program: you have typed 10 times larger number than original!!! Try again. For me it is correctly found this number! |

Yup, just noticed that:-
$ ../dodeca20 50 717000000000000 720000000000000 You can also find the k n values in results_dodeca.txt file ( These are 3-probable primes ) n=50, kmin=717000000000000, kmax=720000000000000, version=2.0 Starting the sieve... Using the first 8 primes to reduce the size of the sieve array 717083008036395 50 The sieving is complete. Number of Prp tests=213 Time=6 sec. This proves that double checking is useful (and necessary!). Also got:- $ ../dodeca20 58 10000000000000000 100000000000000000 You can also find the k n values in results_dodeca.txt file ( These are 3-probable primes ) n=58, kmin=10000000000000000, kmax=100000000000000000, version=2.0 Starting the sieve... Using the first 11 primes to reduce the size of the sieve array 74362823389729875 58 Status: 6.0 percentage of the project is complete. Time thusfar: 990 sec. Yes, that's in the range 10000T (1E16) to 100000T (1E17). [B]Sorry Kosmaj, this was in your reserved range, I was supposed to be testing n=55. Should teach me to check things more closely.[/B] |

49 and 50By the way, my first effort looked at the first 65000 octoproths, due to limiations of file handling in MS Excel, and therefore 49 was incomplete. It needs to be run with Robert's program.
Regards Robert Smith |

[QUOTE=robert44444uk]By the way, my first effort looked at the first 65000 octoproths, due to limiations of file handling in MS Excel, and therefore 49 was incomplete. It needs to be run with Robert's program.
Regards Robert Smith[/QUOTE] I took my octo_complete.txt file and ran it through (a slightly modified) "isddp.txt" in PARI. That's how I found the missing n=50 one. I've done this for all n in that file (up to and including n=54) and everything else is correct. (Will double double check that though ;-) ). |

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