...snip...
In terms of Gapcoin's results ("the list of prime gaps as a usable dataset"), we can see that certain shifts have been mined much more extensively than others. See Help (tab) > Record prime gaps in the v0.9.4 release, for example.
This is due to the original and established
efficient 'default' settings for the built-in CPU (and GPU) miners ... namely ...
Shifts 20, 25, 32, 64, 512, 896, 1024 ...
Ignoring the coin part of Gapcoin and just looking at the gap records, the shift determines the size of the primes examined. Shift 25 is finding gaps in the 5k-6k range, which Gapcoin has done a lot of work in. Shift 512 in the 12k-17k range. Shift 896 18k-24k. Shift 1024 20k-28k. Ranges very approximate.
The higher gap lengths have lower merits, making records easier to find, but take longer to calculate and find. Other shift amounts, especially larger than 25, are more likely to find new records since the threshold is lower. Presumably one doesn't want to do this at the expense of coin return however (there are tools that are much better than Gapcoin at finding records, but they don't have coins).
Generally, less blocks will be mined at the higher shifts.
Whilst the network difficulty is comparatively low and we work towards new mining software it may be interesting to set proof of work at a variety of slightly lower shifts ... herewith some examples for single core (or more) CPU systems ...
Note
optimal 'default': Header shift 25 , Sieve size: 33554432 , Primes in sieve: 900000
>
setgenerate true 1 1048576 900000 20 low gapsperday
>
setgenerate true 1 2097152 900000 21 low gapsperday
>
setgenerate true 1 4194304 900000 22>
setgenerate true 1 8388608 900000 23>
setgenerate true 1 16777216 900000 24> setgenerate true 1 33554432 900000 25
>
setgenerate true 1 67108864 900000 26>
setgenerate true 1 134217728 900000 27etc.,
...
Higher shifts are best with the ctr, as per Jonnie Frey's original documentation / recommended sets ...
:: Mining with the Chinese Remainder Theorem
fig. 1
:: The ctr algorithm is divided into 2 parts. The first part,
:: is a simple greedy algorithm which ties to find offsets
:: for each involved prime, so that the desired number range
:: has at least prime candidates as possible.
::
:: The second part is an evolutionary algorithm, which tries to improve the
:: results form the greedy algorithm. Therefor the greedy algorithm
:: will be executed several times with slightly different parameters, to produce
:: ctrs which differs in quality, which than can be used by the evolutionary algorithm.
::
:: The output is a text file which can be used by gapminer as an input for ctr sieving.
::
:: Parameter description:
::
::
:: --calc-ctr Indicates that we want to calculate a ctr file.
::
:: --ctr-strength This is used to variate the computing time spend
:: within the greedy algorithm. Higher strength
:: can yield better results.
::
:: --ctr-primes The number of primes to use in the ctr file. The more
:: primes the better the ctr result, but the shift
:: also increases. Minimum shift can be calculated as
:: the binary logarithm of the product of all primes:
:: log2(p1 * p2 * ... *pn).
::
:: --ctr-evolution Whether to use the evolutionary algorithm or not.
::
:: --ctr-fixed This number indicates the number of starting primes
:: which wound get touched by the evolutionary algorithm
:: the offsets for the primes 2,3,5,7,11... are mostly
:: perfect computed by the greedy algorithm, and changing
:: them only declines the result.
::
:: --ctr-ivs The number of individuals used in the evolutionary algorithm.
:: More increases computing time but mostly also the
:: result quality.
::
:: --ctr-range Percent deviation from the number of primes.
:: Useful if you don't want to look for a specific number
:: of primes.
::
:: --ctr-bits -256 The shift value you later use for sieving has to be greater
:: than log2(p1*p2*..*pn). With this flag you can fine tune a specific
:: shift by setting this to shift - log2(p1*p2*..*pn).
::
:: --ctr-merit The target merit (while testing the ctr it seamed that
:: sieving for target-merit - 1 yields the best results)
::
:: --ctr-file The target ctr output file. You can open this with a
:: text editor. Look for the n_candidates value, the smaller
:: it is the better the ctr file.
::
::
:: Example settings which were used to calculate the current ctr files:
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 8 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 10 --ctr-primes 14 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 8 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 13 --ctr-primes 19 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 10 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 13 --ctr-primes 24 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 10 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 12 --ctr-primes 29 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 11 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 9 --ctr-primes 34 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 11 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 12 --ctr-primes 38 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 11 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 14 --ctr-primes 42 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 11 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 15 --ctr-primes 46 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 12 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 16 --ctr-primes 50 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 12 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 9 --ctr-primes 55 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 12 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 16 --ctr-primes 58 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 12 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 16 --ctr-primes 62 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 12 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 15 --ctr-primes 66 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 12 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 13 --ctr-primes 70 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 13 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 11 --ctr-primes 74 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 13 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 9 --ctr-primes 78 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 13 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 15 --ctr-primes 81 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 13 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 12 --ctr-primes 85 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 13 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 17 --ctr-primes 88 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 13 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 14 --ctr-primes 92 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 14 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 10 --ctr-primes 96 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 14 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 15 --ctr-primes 99 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 14 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 10 --ctr-primes 103 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 14 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 15 --ctr-primes 106 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 14 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 10 --ctr-primes 110 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 14 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 14 --ctr-primes 113 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 14 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 9 --ctr-primes 117 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 15 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 13 --ctr-primes 120 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 15 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 17 --ctr-primes 122 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 15 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 11 --ctr-primes 127 -t 4 --ctr-file my-ctr-file.txt
:: gapminer-cpu.exe --calc-ctr --ctr-evolution --ctr-fixed 15 --ctr-strength 150000 --ctr-merit 22 --ctr-ivs 1000 --ctr-range 0 --ctr-bits 15 --ctr-primes 130 -t 4 --ctr-file my-ctr-file.txt
fig. 2
:::::::::::::::::::::::::::::::::::::::
:: choose your preferred mining method:
::
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:: Mining with the Chinese Remainder Theorem (solo mining examles)
::
:: Shift 64
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 64 --crt crt/crt-22m-64s.txt --threads 4 --fermat-threads 1 --sieve-primes 50000
::
:: Shift 96
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 96 --crt crt/crt-22m-96s.txt --threads 4 --fermat-threads 1 --sieve-primes 50000
::
:: Shift 128
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 128 --crt crt/crt-22m-128s.txt --threads 4 --fermat-threads 1 --sieve-primes 50000
::
:: Shift 160
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 160 --crt crt/crt-22m-160s.txt --threads 4 --fermat-threads 1 --sieve-primes 100000
::
:: Shift 192
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 192 --crt crt/crt-22m-192s.txt --threads 4 --fermat-threads 1 --sieve-primes 100000
::
:: Shift 224
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 224 --crt crt/crt-22m-224s.txt --threads 4 --fermat-threads 1 --sieve-primes 100000
::
:: Shift 256
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 256 --crt crt/crt-22m-256s.txt --threads 4 --fermat-threads 1 --sieve-primes 100000
::
:: Shift 288
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 288 --crt crt/crt-22m-288s.txt --threads 4 --fermat-threads 1 --sieve-primes 300000
::
:: Shift 320
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 320 --crt crt/crt-22m-320s.txt --threads 4 --fermat-threads 1 --sieve-primes 300000
::
:: Shift 352
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 352 --crt crt/crt-22m-352s.txt --threads 4 --fermat-threads 1 --sieve-primes 300000
::
:: Shift 384
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 384 --crt crt/crt-22m-384s.txt --threads 4 --fermat-threads 1 --sieve-primes 500000
::
:: Shift 416
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 416 --crt crt/crt-22m-416s.txt --threads 4 --fermat-threads 1 --sieve-primes 500000
::
:: Shift 448
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 448 --crt crt/crt-22m-448s.txt --threads 4 --fermat-threads 1 --sieve-primes 500000
::
:: Shift 480
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 480 --crt crt/crt-22m-480s.txt --threads 4 --fermat-threads 1 --sieve-primes 500000
::
:: Shift 512
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 512 --crt crt/crt-22m-512s.txt --threads 4 --fermat-threads 1
::
:: Shift 544
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 544 --crt crt/crt-22m-544s.txt --threads 4 --fermat-threads 1
::
:: Shift 576
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 576 --crt crt/crt-22m-576s.txt --threads 4 --fermat-threads 1
::
:: Shift 608
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 608 --crt crt/crt-22m-608s.txt --threads 4 --fermat-threads 1
::
:: Shift 640
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 640 --crt crt/crt-22m-640s.txt --threads 4 --fermat-threads 1
::
:: Shift 672
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 672 --crt crt/crt-22m-672s.txt --threads 4 --fermat-threads 1
::
:: Shift 704
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 704 --crt crt/crt-22m-704s.txt --threads 4 --fermat-threads 1
::
:: Shift 736
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 736 --crt crt/crt-22m-736s.txt --threads 4 --fermat-threads 1
::
:: Shift 768
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 768 --crt crt/crt-22m-768s.txt --threads 4 --fermat-threads 1
::
:: Shift 800
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 800 --crt crt/crt-22m-800s.txt --threads 4 --fermat-threads 1
::
:: Shift 832
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 832 --crt crt/crt-22m-832s.txt --threads 4 --fermat-threads 1
::
:: Shift 864
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 864 --crt crt/crt-22m-864s.txt --threads 4 --fermat-threads 1
::
:: Shift 896
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 896 --crt crt/crt-22m-896s.txt --threads 4 --fermat-threads 1
::
:: Shift 928
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 928 --crt crt/crt-22m-928s.txt --threads 4 --fermat-threads 1
::
:: Shift 992
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 992 --crt crt/crt-22m-992s.txt --threads 4 --fermat-threads 1
::
:: Shift 1024
:: gapminer-cpu.exe localhost -p 31397 -u <rpc-user> -x <rpc-password> --shift 1024 --crt crt/crt-22m-1024s.txt --threads 4 --fermat-threads 1
::
::
:::::::::::::::::::::::::::::::::::::::::::::::
:: Mining without the Chinese Remainder Theorem
::
:: stratum (recommend)
:: gapminer-cpu.exe -o your-pool . club -p 3385 -u user.worker -x password -t 4 --stratum
::
:: getwork
:: gapminer-cpu.exe -o http:// your-pool . club -p 4200 -u user.worker -x password -t 4
::
:: solo mining
:: gapminer-cpu.exe -o 127.0.0.1 -p 31397 -u <rpc user> -x <rpc password> -t 4
...
More on this soon ...
...
If we don't see additional community interest and an increase in hashing power in 2021 and beyond then it maybe prudent to create a mining consortium to see what additional prime gap records Gapcoin will acheive.
If this is going to be a Prime Gap of maximum known merit vs an Economic
Tragedy of the commons type of affair, then so
BTCe it! ...
-
https://en.wikipedia.org/wiki/Prime_gap#Numerical_results-
https://en.wikipedia.org/wiki/Tragedy_of_the_commons...snip...
