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Old 2015-06-29, 21:40   #1
storflyt32
 
Feb 2013

2×229 Posts
Default Question regarding basic routines being used in Yafu.

This question regarding Yafu.

Try factoring this number using Yafu.


44096960194782291366479454359491906344841565340583527174583102754161753989731256661629217599721831954204869680333042143
92214394159744837682107086978499602473447767242334353357941451979895362618476983333841414747101359369233055182503304999
79630603297611718752853982675644541515500831575276458831578538124258307250764447789152171010322588749838165142649629175
84020806958703


Please be patient, it may take a little while.

Using the factor command on this number, I get this output.

>> factor(4409696019478229136647945435949190634484156534058352717458310275416175
39897312566616292175997218319542048696803330421439221439415974483768210708697849
96024734477672423343533579414519798953626184769833338414147471013593692330551825
03304999796306032976117187528539826756445415155008315752764588315785381242583072
5076444778915217101032258874983816514264962917584020806958703)

fac: factoring 44096960194782291366479454359491906344841565340583527174583102754
16175398973125666162921759972183195420486968033304214392214394159744837682107086
97849960247344776724233435335794145197989536261847698333384141474710135936923305
51825033049997963060329761171875285398267564454151550083157527645883157853812425
830725076444778915217101032258874983816514264962917584020806958703
fac: using pretesting plan: normal
fac: no tune info: using qs/gnfs crossover of 95 digits
div: primes less than 10000
fmt: 1000000 iterations
rho: x^2 + 3, starting 1000 iterations on C369
rho: x^2 + 2, starting 1000 iterations on C369
rho: x^2 + 1, starting 1000 iterations on C369
pm1: starting B1 = 150K, B2 = gmp-ecm default on C369


Here it stops, or hangs, because rather of thinking of this number as being composite, which in fact it is, is stumbles on the main factor of this number which is a P361. Assumedly this P361 is being found by means of ecm and not a similar or corresponding LLR-based routine or algorithm.

The result output ends with the following output next without any blank line in between.

Total factoring time = 19.1111 seconds


***factors found***

P3 = 379
P8 = 96666203
P361 = 1203634929737438335454617351130401638793869985654394037649782756926640918
64337211050484230494473111973859423993046930339321279582615743723570549962425283
85445649393860054641940943188043553546342404127976000800327689307296589399840051
89497823085695969506760933090568262914697592455268323932217950828957481983060180
118711976610859253926447485955538315068488175719

ans = 1

Probably the second time I factored this number, so therefore please disregard "Total factoring time".

Please see http://factordb.com/index.php?id=1100000000788098520 for the complete factorization.

My question is then which implementation, or rather software routine is being used in order to get either to or possibly past the pm1: line at the bottom, but before starting the ecm which in fact is not present at all in the output following next.

Not necessarily about the time it takes to factorize it.

For an example of this, a different number has to be located.

Found an example of the use of the ecm command using another number.


ans = 63060329761171875285398267564454151550083157527645883157853812425830725076
444778915217101032258874983816514264962917584020806958703

>> factor(6306032976117187528539826756445415155008315752764588315785381242583072
5076444778915217101032258874983816514264962917584020806958703)

fac: factoring 63060329761171875285398267564454151550083157527645883157853812425
830725076444778915217101032258874983816514264962917584020806958703
fac: using pretesting plan: normal
fac: no tune info: using qs/gnfs crossover of 95 digits
div: primes less than 10000
fmt: 1000000 iterations
rho: x^2 + 3, starting 1000 iterations on C124
rho: x^2 + 2, starting 1000 iterations on C124
rho: x^2 + 1, starting 1000 iterations on C124
pm1: starting B1 = 150K, B2 = gmp-ecm default on C124
ecm: 30/30 curves on C115, B1=2K, B2=gmp-ecm default
ecm: 74/74 curves on C115, B1=11K, B2=gmp-ecm default
ecm: 3/214 curves on C115, B1=50K, B2=gmp-ecm default, ETA: 54 sec
Total factoring time = 6.1694 seconds


***factors found***

P2 = 61
P3 = 211
P4 = 3191
P10 = 1140339157
P22 = 1189210668498443467117
P94 = 11322030199047430621404385799783580279923302675789483337124140301905739746
04891546909031182367

ans = 1


Is a number perhaps considered being prime before a subsequent or following use of the ecm command is determining that this number rather is composite?

For this number it apparently does not bother too much about the small factors also being part of this number,

Last fiddled with by storflyt32 on 2015-06-29 at 21:51
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Old 2015-06-29, 22:34   #2
bsquared
 
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"Ben"
Feb 2007

1101111110112 Posts
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It is pretty straight forward. Every time a factor is found the cofactor is checked for primitude. APRCL is used for the proof, which takes several seconds for a 361 digit number.
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Old 2015-06-29, 23:25   #3
storflyt32
 
Feb 2013

2·229 Posts
Default

https://en.wikipedia.org/wiki/Adlema...primality_test

Found this web-page for the given answer.

Thanks anyway.
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