ecm [options] B1 [B2min-B2max | B2]
B1 is the step 1 bound. It is a mandatory parameter. It can be given either in integer format (for example 3000000) or in floating-point format (3000000.0 or 3e6). The largest possible B1 value is 9007199254740996 for P-1, and ULONG_MAX or 9007199254740996 (whichever is smaller) for ECM and P+1. All primes 2 <= p <= B1 are processed in step 1.B2
B2 is the step 2 bound. It is optional: if omitted, a default value is computed from B1, which should be close to optimal. Like B1, it can be given either in integer or in floating-point format. The largest possible value of B2 is approximately 9e23, but depends on the number of blocks k if you specify the -k option. All primes B1 <= p <= B2 are processed in step 2. If B2 < B1, no step 2 is performed.B2min-B2max
alternatively one may use the B2min-B2max form, which means that all primes B2min <= p <= B2max should be processed. Thus specifying B2 only corresponds to B1-B2. The values of B2min and B2max may be arbitrarily large, but their difference must not exceed approximately 9e23, subject to the number of blocks k.
Perform P-1 instead of the default method (ECM).-pp1
Perform P+1 instead of the default method (ECM).
[ECM, P-1, P+1] Use x (arbitrary-precision integer or rational) as initial point. For example, -x0 1/3 is valid. If not given, x is generated from the sigma value for ECM, or at random for P-1 and P+1.-sigma s
[ECM] Use s (arbitrary-precision integer) as curve generator. If omitted, s is generated at random.-A a
[ECM] Use a (arbitrary-precision integer) as curve parameter. If omitted, is it generated from the sigma value.-go val
[ECM, P-1, P+1] Multiply the initial point by val, which can any valid expression, possibly containing the special character N as place holder for the current input number. Example:
ecm -pp1 -go "N^2-1" 1e6 < composite2000
[ECM, P-1, P+1] Perform k blocks in step 2. For a given B2 value, increasing k decreases the memory usage of step 2, at the expense of more cpu time.-treefile file
Stores some tables of data in disk files to reduce the amount of memory occupied in step 2, at the expense of disk I/O. Data will be written to files file.1, file.2 etc. Does not work with fast stage 2 for P+1 and P-1.-power n
[ECM, P-1] Use x^n for Brent-Suyama´s extension ( -power 1 disables Brent-Suyama´s extension). The default polynomial is chosen depending on the method and B2. For P-1 and P+1, disables the fast stage 2. For P-1, n must be even.-dickson n
[ECM, P-1] Use degree-n Dickson´s polynomial for Brent-Suyama´s extension. For P-1 and P+1, disables the fast stage 2. Like for -power, n must be even for P-1.-maxmem n
Use at most n megabytes of memory in stage 2.-ntt, -no-ntt
Enable or disable the Number-Theoretic Transform code for polynomial arithmetic in stage 2. With NTT, dF is chosen to be a power of 2, and is limited by the number suitable primes that fit in a machine word (which is a limitation only on 32 bit systems). The -no-ntt variant uses more memory, but is faster than NTT with large input numbers. By default, NTT is used for P-1, P+1 and for ECM on numbers of size at most 30 machine words.
Quiet mode. Found factorizations are printed on standard output, with factors separated by white spaces, one line per input number (if no factor was found, the input number is simply copied).-v
Verbose mode. More information is printed, more -v options increase verbosity. With one -v, the kind of modular multiplication used, initial x0 value, step 2 parameters and progress, and expected curves and time to find factors of different sizes for ECM are printed. With -v -v, the A value for ECM and residues at the end of step 1 and step 2 are printed. More -v print internal data for debugging.-timestamp
Print a time stamp whenever a new ECM curve or P+1 or P-1 run is processed.
Use GMP´s mpz_mod function (sub-quadratic for large inputs, but induces some overhead for small ones).-modmuln
Use Montgomery´s multiplication (quadratic version). Usually best method for small input.-redc
Use Montgomery´s multiplication (sub-quadratic version). Theoretically optimal for large input.-nobase2
Disable special base-2 code (which is used when the input number is a large factor of 2^n+1 or 2^n-1, see -v).-base2 n
Force use of special base-2 code, input number must divide 2^ n+1 if n > 0, or 2^| n|-1 if n < 0.
Take input from file file instead of from standard input.-save file
Save result of step 1 in file. If file exists, an error is raised. Example: to perform only step 1 with B1=1000000 on the composite number in the file "c155" and save its result in file "foo", use-savea file
ecm -save foo 1e6 1 < c155
Like -save, but appends to existing files.-resume file
Resume residues from file, reads from standard input if file is "-". Example: to perform step 2 following the above step 1 computation, use-chkpoint file
ecm -resume foo 1e6
Periodically write the current residue in stage 1 to file. In case of a power failure, etc., the computation can be continued with the -resume option.
ecm -chkpnt foo -pm1 1e10 < largenumber.txt
Perform n runs on each input number (default is one). This option is mainly useful for P+1 (for example with n=3) or for ECM, where n could be set to the expected number of curves to find a d-digit factor with a given step 1 bound. This option is incompatible with -resume, -sigma, -x0. Giving -c 0 produces an infinite loop until a factor is found.-one
In loop mode, stop when a factor is found; the default is to continue until the cofactor is prime or the specified number of runs are done.-b
Breadth-first processing: in loop mode, run one curve for each input number, then a second curve for each one, and so on. This is the default mode with -inp.-d
Depth-first processing: in loop mode, run n curves for the first number, then n curves for the second one and so on. This is the default mode with standard input.-I n
In loop mode, multiply B1 by a factor depending on n after each curve. Default is one which should be optimal on one machine, while -I 10 could be used when trying to factor the same number simultaneously on 10 identical machines.
Add n seconds to stage 1 time. This is useful to get correct expected time with -v if part of stage 1 was done in another run.-h, --help
Display a short description of ecm usage, parameters and command line options.-printconfig
Prints configuration parameters used for the compilation and exits.
0 if normal program termination, 1 if error occurredBit 1
0 if no proper factor was found, 1 otherwiseBit 2
0 if factor is composite, 1 if factor is a probable primeBit 3
0 if cofactor is composite, 1 if cofactor is a probable primeThus, the following exit status values may occur: 0
Normal program termination, no factor found1
Composite factor found, cofactor is composite6
Probable prime factor found, cofactor is composite8
Input number found10
Composite factor found, cofactor is a probable prime14
Probable prime factor found, cofactor is a probable prime