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

Kosmaj 2006-01-14 17:13

[QUOTE]I haven't written that program between 14 Jan 06 03:39 PM and 03:51 PM.[/QUOTE] Yes, I guess you began after writing message #259? As for limits I'm using kmin=15 and kmax between 1E15 and 1E16 (for the time being).

Kosmaj 2006-01-14 17:30

n=57
 
Found first DodecaProth for n=57:
[B]87653084113035 57[/B]

And imagine, for such a small k<100T.
Has one extra leg to the left, none to the right.

R. Gerbicz 2006-01-14 18:15

No more dodecaproth for n=52
 
I've searched the full range for n=52 to find all dodecaproth.
Here is the full report: on Pentium4 Celeron 1.7 GHz:
C:\>dodeca_1_0 52 1 4503599627370495
You can also find the k n values in results_dodeca.txt file ( These are 3-probable primes )
n=52, kmin=1, kmax=4503599627370495, version=1.0
Starting the sieve...
Using the first 10 primes to reduce the size of the sieve array
2808528662035845 52
The sieving is complete.
Number of Prp tests=613089
Time=8917 sec.

Ps. I've verified all 12 numbers are primes.

tcadigan 2006-01-14 18:15

I don't get all the other stuff with legs and everything. just ran the program (dodeca_1_0.exe) here's what I got:

n=66, kmin=1, kmax=1000000000000000, version=1.0
Starting the sieve...
Using the first 10 primes to reduce the size of the sieve array
229350894172785 66
The sieving is complete.
Number of Prp tests=138495
Time=2992 sec.

R. Gerbicz 2006-01-14 18:36

Probably we can start a new thread for reservation for dodecaproth search, to avoid the duplication.

[QUOTE=Kosmaj]Yes, I guess you began after writing message #259?[/QUOTE]

Yes.

Kosmaj 2006-01-15 00:58

Congrats to [B]tcadigan[/B] for a new DodecaProth! I found 3 for n=62:

[B]99828673281855 62
286846836764775 62
1692654062704395 62[/B]

BTW, I checked n=56 to 1200T (1.2E15) and n=57-62 to 2000T (2E15) but besides the one for n=57 I found none. I'm proceeding with n=63-70 to 2000T (will skip n=66).

Kosmaj 2006-01-15 10:23

R. Gerbicz
 
I noticed a large slow-down of dodeca.exe ver. 1.0 on a large range. Have a look. Case 1:
[CODE]
n=70, kmin=15, kmax=3000000000000000, version=1.0
Using the first 10 primes to reduce the size of the sieve array
Time=1968 sec.[/CODE]
Case 2:
[CODE]n=70, kmin=3000000000000000, kmax=10000000000000000, version=1.0
Using the first 11 primes to reduce the size of the sieve array
Status: 0.3 percentage of the project is complete. Time thusfar: 69 sec.[/CODE] I stopped the second instance but 0.3% in 69 sec means 23000 sec for the range 7000T wide, while less than 2000sec were needed for a range 3000T wide. The only difference is the number of primes used (10 -> 11) so I guess it's related to [I]magic_constant[/I] now set to 32000. Can you have a look and tell us how to avoid this kind of problems. Can you possibly set [I]magic_constant[/I] dynamically based on input parameters (kmin and kmax) or enable "-x" on the cmd-line as you mentioned before for octo.exe. Thanks.

BTW, I checked all n=67-70 to 3000T but found no new DodecaProths.

R. Gerbicz 2006-01-15 12:05

[QUOTE=Kosmaj]I noticed a large slow-down of dodeca.exe ver. 1.0 on a large range. Have a look. Case 1:
[CODE]
n=70, kmin=15, kmax=3000000000000000, version=1.0
Using the first 10 primes to reduce the size of the sieve array
Time=1968 sec.[/CODE]
Case 2:
[CODE]n=70, kmin=3000000000000000, kmax=10000000000000000, version=1.0
Using the first 11 primes to reduce the size of the sieve array
Status: 0.3 percentage of the project is complete. Time thusfar: 69 sec.[/CODE][/QUOTE]

OK
I'll see it. Yesterday I have not calculated this, but I thought that there will be such a problem using many primes in the sieving area ( first 11 primes means we are using primes up to 31 ). Probably this occured because we are sieving more numbers ( 12 numbers ).

Kosmaj 2006-01-15 13:24

1 Attachment(s)
All right, thanks.

BTW, I just ran into the first DodecaProth for n=70:
[B]14494401979227555 70[/B] [2E16]

Note that [I]k[/I] has 17 digits. k*2^n+/-1 members have 38, while 2^n+/-k have 22 digits. One leg on the left and one on the right.

I'm also enclosing a Pari script I use to verify DodecaProths and count legs. To use it start Pari from the folder where you saved the file, then type:
[CODE]
gp> read("isddp.txt")
gp> isddp(14494401979227555,70)
14494401979227555 70 is DodecaProth! ... Left_legs=1, Rigth_legs=1.
[/CODE]

Kosmaj 2006-01-15 13:29

All right, thanks.

BTW, I just ran into the first DodecaProth for n=70:
[B]14494401979227555 70[/B] [2E16]

Note that [I]k[/I] has 17 digits. k*2^n+/-1 members have 38, while 2^n+/-k have 22 digits. One leg on the left and one on the right.

I'm also enclosing a Pari script I use to verify DodecaProths and count legs. To use it start Pari from the folder where you saved the file, then type:
[CODE]
gp> read("isddp.txt")
gp> isddp(14494401979227555,70)
14494401979227555 70 is DodecaProth! ... Left_legs=1, Rigth_legs=1.
[/CODE]

R. Gerbicz 2006-01-15 13:44

New dodeca program version 2.0
 
1 Attachment(s)
This is faster than dodeca 1.0, but the speed up is very very different for different n values and ranges.

To obtain this I've eliminated almost all modular multiplications ( in the part when we see if "g" is good or not ). Now magic_constant=32000 is good for this version. I'll think what would be a good "default" value. But note that we are sieving also up to 32000 and one block length is also 32000.

Kosmaj can you test this version, I've checked only for n=44,47. And test your previous case 1 and case 2.

You can download exe for windows from: [URL="http://www.robertgerbicz.tar.hu/dodeca_2_0.exe"]http://www.robertgerbicz.tar.hu/dodeca_2_0.exe[/URL]

Or see the attachment for the c code.


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