Dodecaproths - Page 2

Kosmaj · 2006-01-14, 17:13

Quote:

I haven't written that program between 14 Jan 06 03:39 PM and 03:51 PM.

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

Found first DodecaProth for n=57:
87653084113035 57

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

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:

Originally Posted by Kosmaj

Yes, I guess you began after writing message #259?

Yes.

Kosmaj · 2006-01-15, 00:58

Congrats to tcadigan for a new DodecaProth! I found 3 for n=62:

99828673281855 62
286846836764775 62
1692654062704395 62

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

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.

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.

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 magic_constant now set to 32000. Can you have a look and tell us how to avoid this kind of problems. Can you possibly set magic_constant 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:

Originally Posted by 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.

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.

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

All right, thanks.

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

Note that k 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.

Kosmaj · 2006-01-15, 13:29

All right, thanks.

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

Note that k 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.

R. Gerbicz · 2006-01-15, 13:44

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: http://www.robertgerbicz.tar.hu/dodeca_2_0.exe

Or see the attachment for the c code.

2006-01-14, 17:30	#13
Kosmaj Nov 2003 3622₁₀ Posts	n=57 Found first DodecaProth for n=57: 87653084113035 57 And imagine, for such a small k<100T. Has one extra leg to the left, none to the right.

2006-01-14, 18:15	#14
R. Gerbicz "Robert Gerbicz" Oct 2005 Hungary 2·7·103 Posts	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. Last fiddled with by R. Gerbicz on 2006-01-14 at 18:17

2006-01-15, 10:23	#18
Kosmaj Nov 2003 7046₈ Posts	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. 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. 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 magic_constant now set to 32000. Can you have a look and tell us how to avoid this kind of problems. Can you possibly set magic_constant 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. Last fiddled with by Kosmaj on 2006-01-15 at 10:26

2006-01-15, 13:29	#21
Kosmaj Nov 2003 2×1,811 Posts	All right, thanks. BTW, I just ran into the first DodecaProth for n=70: 14494401979227555 70 [2E16] Note that k 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.

2006-01-14, 18:15	#15
tcadigan Sep 2004 UVic 2×5×7 Posts	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.

2006-01-15, 00:58	#17
Kosmaj Nov 2003 111000100110₂ Posts	Congrats to tcadigan for a new DodecaProth! I found 3 for n=62: 99828673281855 62 286846836764775 62 1692654062704395 62 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).