# Speeding up integer factorization

FactorInteger[\
1753350708383031782588046639322910185667191775904884028394870335573708\
1329332754967408178320621636495008627555647919326124228527397903620225\
6803882958349216995208390375036531324697580818153748596792447979487742\
2054261515476192755340796353096012287087985683618499427644284167542022\
3341009458254842973728890139510342494364595312153299061940220948544576\
4544020947397606858624243134108441449730128905563781329638553432164246\
8438470088716821201658597409344994423773317917197480372998204052203537\
3757592439886428035375387505362186166756730538800714557760401940990990\
72133536402769493358477702660834983272717873544265749, 2]


After 15 min, a factor is computed as 773618132427345151923061. During this time, total CPU utilization is about 15%. Is there a way to speed up the computation by forcing more CPU utilization? I'm using Mathematica 9.0, but I can upgrade if this functionality is built into later versions.

• FactorInteger is essentially a black box, so I don't think this is possible. If it's implemented in such a way as to run on a single core, we cannot change that. Unless of course there are some undocumented options I'm not aware of. As a first step I would look for purpose-made tools for integer factorization in the hope that something faster turns up ... – Szabolcs Jul 15 '16 at 10:22
• Also note that this is not really an issue if you have multiple integers to work with. If you absolutely need multi-core scalability for factorization of single integers, it's probably best to look for specialized tools... – kirma Jul 15 '16 at 15:39
• I guess you've a multiprocessor machine. The FactorInteger is running on only one. Therefore your total cpu util. – yarchik Jul 15 '16 at 19:35