20200513, 10:04  #1 
Nov 2016
4320_{8} Posts 
Dozenal near and quasi repunit primes
Are there any searching for near and quasi repunit primes (primes of the form aaa...aaab, abbb...bbb, aaa...aaabc, abbb...bbbc, abccc...ccc, see thread https://mersenneforum.org/showthread.php?t=19717) in dozenal (duodecimal)?
There are a lot of such searching in decimal (https://stdkmd.net/nrr/#factortables_nr and https://stdkmd.net/nrr/prime/primedifficulty.txt), and I finished this searching in dozenal up to n=1000 (decimal 1728) 
20200513, 10:16  #2  
Nov 2016
8D0_{16} Posts 
Quote:
Code:
label expression {1}55 (10^n+3E7)/E {2}97 (2*10^n+695)/E {8}77 (8*10^n107)/E {E}9E 10^n21 20{E} 21*10^n1 22{E} 23*10^n1 34{1} (309*10^n1)/E 53{E} 54*10^n1 89{1} (804*10^n1)/E 99{1} (8E4*10^n1)/E 10^n21, 21*10^n1, (309*10^n1)/E, 54*10^n1, (804*10^n1)/E even n: algebra factors (difference of two squares) odd n: factor of 11 23*10^n1 even n: factor of 11 odd n: algebra factors (difference of two squares) (8E4*10^n1)/E covering set {5, 11, 25} also note that the form 1{5}1, which is (14*10^n41)/E, can be prime only for n=1 because even n: algebra factors (difference of two squares) odd n: factor of 11 (and this number for n=1 is exactly 11) Can someone found a prime of the form {1}55 (111...11155), {2}97 (222...22297), {8}77 (888...88877) in dozenal? 

20200513, 18:13  #3 
Nov 2016
4320_{8} Posts 
I use srsieve to sieve all {a}b and a{b} forms, and type "srsieve m 429981696 n 1729 N 248832 p 13 P 429981696 k.txt" and "srfile G srsieve.out", however, the result text files are now apply to pfgw, these are the programs and the result text files (unfortunately, the folder is too large (>4 MB), even zipped, so I separate it to 3 zip files), can someone help me how to use srsieve to sieve them and make a file that is apply to pfgw?
Last fiddled with by sweety439 on 20200513 at 18:15 
20200515, 08:06  #4  
"Sam"
Nov 2016
311 Posts 
Quote:
srfile a "t16_b12.txt" "t17_b12.txt" "t19_b12.txt" which I then ran on pfgw for a few minutes without finding anything. If you need to anything, you could always switch back between g, a, or G switches. Replacing the files with * symbol srfile a "t*_b12.txt" could save you some time. BTW you should really check PRPtop before sieving sequences. Last fiddled with by carpetpool on 20200515 at 08:06 

20200517, 01:05  #5  
Nov 2016
2^{4}×3×47 Posts 
Quote:
However, when I do the pfgw.exe for this abcd file, it tested all numbers of the form 1*12^n11 (numbers of the form {E}1 in dozenal) first, I want to test the numbers sorted by exponent (i.e. test n=1729 of all forms in the sieve file, then n=1730 of all forms in the sieve file, then n=1731 of all forms in the sieve file, etc.), how to do? 

20200517, 06:55  #6 
"Sam"
Nov 2016
311 Posts 
I don't know of any utility that does this but srfile:
Code:
>>> srfile help srfile 0.6.17  A file utility for srsieve. Usage: srfile [OPTION ...] <INFILE ...> o output FILE Write sieve to FILE instead of srsieve.out. k knownfactors FILE Remove factors in FILE from the sieve. d delete SEQ Delete sequence SEQ from the sieve e.g. d "254*5^n1" g newpgen Write sieve to NewPGen format files t*_b*_k*.npg. G prp Write sieve to PRP (sorted by n) files t*_b*.prp. w pfgw Write sieve to pfgw (sorted by n) file sr_b.pfgw. a abcd Write sieve to abcd format file sr_b.abcd. Q subseqs X Print base b^Q subsequence stats for all Q dividing X. c congruence X Print congruence (mod X) information for sequences. p pfactor X Print Prime95 worktodo.ini entries for P1 factoring. X is number of PRP tests saved by finding a factor. v verbose Be verbose. q quiet Be quiet. h help Print this help. INFILE ... Read sieve from INFILE. 
20200517, 10:11  #7 
Mar 2006
Germany
2·1,423 Posts 
srfile "w" option sorts by n!
When running pfgw also use an expression like "{number_primes,$a,1}" in the header, see the documentation there. 
20200517, 15:21  #8 
Nov 2016
8D0_{16} Posts 
Do you know what I tell? The cmd.exe prints:
Code:
Recognized ABCD Sieve file: ABCD File 1*12^173511 is composite: RES64: [6BDE769573E9DD87] (0.0390s+0.0017s) 1*12^174111 is composite: RES64: [B58118C70216C647] (0.0347s+0.0015s) 1*12^174411 is composite: RES64: [142A82E3727A17D2] (0.0367s+0.0012s) 1*12^174611 is composite: RES64: [7E35AA5FEEC6F6FD] (0.0380s+0.0014s) 1*12^174911 is composite: RES64: [97163264F74252C8] (0.0412s+0.0018s) 1*12^175011 is composite: RES64: [E83850812A9BEBC8] (0.0401s+0.0014s) 1*12^175311 is composite: RES64: [1DB9B8478E2FA7C6] (0.0399s+0.0016s) 1*12^175811 is composite: RES64: [5EAE71FA1429FD5D] (0.0392s+0.0034s) 1*12^176211 is composite: RES64: [511A3C0E8959CE0E] (0.0395s+0.0013s) 1*12^176711 is composite: RES64: [59E005357B6740DD] (0.0445s+0.0014s) 1*12^177311 is composite: RES64: [AE3F4045D68FB340] (0.0692s+0.0014s) 1*12^177511 is composite: RES64: [2E6AE6083215A94F] (0.0453s+0.0018s) 1*12^178011 is composite: RES64: [98D5BD70E37258CC] (0.0377s+0.0015s) 1*12^178311 is composite: RES64: [A3923A1E6AA77841] (0.0427s+0.0013s) 1*12^178511 is composite: RES64: [9F1B420E350BFFCC] (0.0430s+0.0013s) 1*12^179311 is composite: RES64: [DCCA9D5E4B98EB44] (0.0459s+0.0012s) 1*12^180611 is composite: RES64: [EE0AD2158FEEFCDC] (0.0386s+0.0039s) 1*12^181011 is composite: RES64: [398A1BC7C63F2956] (0.0475s+0.0014s) 1*12^181311 is composite: RES64: [03761C9BFB3ABD46] (0.0486s+0.0014s) 1*12^183511 is composite: RES64: [F6E11B4B32134874] (0.0378s+0.0014s) 1*12^184011 is composite: RES64: [BCFE8C1BAF1D26B2] (0.0553s+0.0016s) 1*12^186911 is composite: RES64: [0569E7AD2978EC5C] (0.0560s+0.0042s) 1*12^187011 is composite: RES64: [F41DB45A4575B26D] (0.0551s+0.0010s) 1*12^187311 is composite: RES64: [E43D492C726AB3C8] (0.0492s+0.0014s) 1*12^188111 is composite: RES64: [EC7DB6D650DCAAA8] (0.0504s+0.0014s) 1*12^189511 is composite: RES64: [A1168D47291AFB92] (0.0551s+0.0012s) 1*12^189611 is composite: RES64: [A91D2899F9E80912] (0.0500s+0.0015s) 1*12^190111 is composite: RES64: [3AE6E7644F645918] (0.0537s+0.0014s) 1*12^190511 is composite: RES64: [B883EE2E70080C73] (0.0512s+0.0014s) 1*12^190811 is composite: RES64: [60959CD3DBDB153E] (0.0496s+0.0013s) 1*12^191111 is composite: RES64: [4B58FDB27213AB3B] (0.0497s+0.0011s) 1*12^192111 is composite: RES64: [37CEC4EB70D1574A] (0.0483s+0.0014s) 1*12^192611 is composite: RES64: [FCB2F1D40487D934] (0.0581s+0.0013s) Code:
1*12^1729+43 1*12^1729+65 1*12^1729+109 2*12^172913 2*12^1729+31 2*12^1729+53 2*12^1729+97 3*12^172925 3*12^1729+19 3*12^1729+41 3*12^1729+85 4*12^172937 4*12^1729+7 4*12^1729+29 4*12^1729+73 5*12^172949 5*12^1729+17 5*12^1729+61 6*12^172961 6*12^172917 6*12^1729+5 6*12^1729+49 7*12^172973 7*12^172929 7*12^1729+37 8*12^172985 8*12^172941 8*12^172919 8*12^1729+25 9*12^172997 9*12^172953 9*12^172931 9*12^1729+13 10*12^1729109 10*12^172943 10*12^1729+1 1*12^172911 1*12^17297 1*12^17295 16*12^17295 18*12^17297 2*12^17291 23*12^17291 27*12^17295 29*12^17297 3*12^17291 34*12^17291 38*12^17295 40*12^17297 4*12^17291 45*12^17291 49*12^17295 51*12^17297 5*12^17291 56*12^17291 62*12^17297 6*12^17291 67*12^17291 71*12^17295 73*12^17297 7*12^17291 78*12^17291 82*12^17295 8*12^17291 89*12^17291 93*12^17295 95*12^17297 9*12^17291 100*12^17291 104*12^17295 106*12^17297 10*12^17291 111*12^17291 117*12^17297 11*12^17291 122*12^17291 126*12^17295 128*12^17297 1*12^1730+43 1*12^1730+65 1*12^1730+109 2*12^173013 2*12^1730+31 2*12^1730+53 2*12^1730+97 3*12^173025 3*12^1730+19 3*12^1730+41 3*12^1730+85 4*12^173037 4*12^1730+7 4*12^1730+29 4*12^1730+73 5*12^173049 5*12^1730+17 5*12^1730+61 6*12^173061 6*12^173017 6*12^1730+5 6*12^1730+49 7*12^173073 7*12^173029 7*12^1730+37 8*12^173085 8*12^173041 8*12^173019 8*12^1730+25 9*12^173097 9*12^173053 9*12^173031 9*12^1730+13 10*12^1730109 10*12^173043 10*12^1730+1 1*12^173011 1*12^17307 1*12^17305 16*12^17305 18*12^17307 2*12^17301 23*12^17301 27*12^17305 29*12^17307 3*12^17301 34*12^17301 38*12^17305 40*12^17307 4*12^17301 45*12^17301 49*12^17305 51*12^17307 5*12^17301 56*12^17301 62*12^17307 6*12^17301 67*12^17301 71*12^17305 73*12^17307 7*12^17301 78*12^17301 82*12^17305 8*12^17301 89*12^17301 93*12^17305 95*12^17307 9*12^17301 100*12^17301 104*12^17305 106*12^17307 10*12^17301 111*12^17301 117*12^17307 11*12^17301 122*12^17301 126*12^17305 128*12^17307 1*12^1731+43 1*12^1731+65 1*12^1731+109 2*12^173113 2*12^1731+31 2*12^1731+53 2*12^1731+97 3*12^173125 3*12^1731+19 3*12^1731+41 3*12^1731+85 4*12^173137 4*12^1731+7 4*12^1731+29 4*12^1731+73 5*12^173149 5*12^1731+17 5*12^1731+61 6*12^173161 6*12^173117 6*12^1731+5 6*12^1731+49 7*12^173173 7*12^173129 7*12^1731+37 8*12^173185 8*12^173141 8*12^173119 8*12^1731+25 9*12^173197 9*12^173153 9*12^173131 9*12^1731+13 10*12^1731109 10*12^173143 10*12^1731+1 1*12^173111 1*12^17317 1*12^17315 16*12^17315 18*12^17317 2*12^17311 23*12^17311 27*12^17315 29*12^17317 3*12^17311 34*12^17311 38*12^17315 40*12^17317 4*12^17311 45*12^17311 49*12^17315 51*12^17317 5*12^17311 56*12^17311 62*12^17317 6*12^17311 67*12^17311 71*12^17315 73*12^17317 7*12^17311 78*12^17311 82*12^17315 8*12^17311 89*12^17311 93*12^17315 95*12^17317 9*12^17311 100*12^17311 104*12^17315 106*12^17317 10*12^17311 111*12^17311 117*12^17317 11*12^17311 122*12^17311 126*12^17315 128*12^17317 Last fiddled with by sweety439 on 20200517 at 15:22 
20200517, 15:30  #9 
Nov 2016
2^{4}·3·47 Posts 
Also, the abcd file has the number 1*12^n+43, 1*12^65, 1*12^109, etc. instead of (1*12^n+43)/11, (1*12^n+65)/11, (1*12^n+109)/11, etc. however, I want to test the primility for the (1*12^n+43)/11, (1*12^n+65)/11, (1*12^n+109)/11, etc. how to change the numbers in the abcd file? For text file (for the prp file), I know how to do, like my reserving for extended SR46 and SR58: (For every base (b) for the forms (k*b^n+1)/gcd(k+1,b1) and (k*b^n1)/gcd(k1,b1), there exists a unique value of k for each form that has been conjectured to be the lowest 'Sierpinski value' (+1 form) or 'Riesel value' (1 form) that is composite for all values of n >= 1. k's make a full covering set with all or partial algebraic factors (e.g. (4*19^n1)/3, 4*24^n1, (4*25^n1)/3, 9*4^n1, (9*25^n1)/8, 9*36^n1) are not considered)

20200517, 15:48  #10 
Nov 2016
2^{4}·3·47 Posts 
Besides, I use srsieve to sieve them, but srsieve can only sieve a*b^n+c with a>=1, b>=2, c != 0, gcd(a,c)=1, gcd(b,c)=1, it cannot sieve the general case (a*b^n+c)/d (like many cases of dozenal nearrepunits:
Code:
{1}5 (12^n+43)/11 {1}7 (12^n+65)/11 {1}E (12^n+109)/11 2{1} (23*12^n1)/11 3{1} (34*12^n1)/11 4{1} (45*12^n1)/11 
20200517, 19:26  #11  
"Sam"
Nov 2016
311 Posts 
Quote:


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