3 ms·

Okay ... wow ... how big do the numbers need to get to bog down Mathematica?

• Pyxl101 11y ago
  The numbers that we're talking about are not big. The number you specified: 641071800653367850802176606120792275422168080497001121 OK, so take a 64 bit integer. That's the typical size of an integer in a modern programming language. A signed integer can represent 2^63-1 which is 9223372036854775807. Imagine a "big integer" which is a composite of multiple 64-bit integers. With a big integer made up of two regular integers, you can represent the value 170141183460469231731687303715884105727. With three, you get to 3138550867693340381917894711603833208051177722232017256447 if I'm doing the math right. That's already in the ballpark of the number you mentioned - just three regular integers together. Granted, I'm not talking about how difficult the factoring is, but it's worth noting that the size of the numbers are pretty small to a computer. Modern computers are really fast and can brute force a large number of computations. Mathematica probably has a fairly optimized general purpose factoring algorithm as well. A number like this might be more difficult to factor: 16158503035655503650357438344334975980222051334857 74201606517271376232756943394544659860070576145673 18443589804609490097470597795752454605475440761932 24141560315438683650498045875098875194826053398028 81919203378413839610932130987808091904716923808523 52908229260181525214437879457705329043037761995619 65192760957166694834171210342487393282284747428088 01766316102903890282966551309635423015707512929643 20885583629718018592309286787991755761508229522018 48806616643615613562842355410104862578550863465661 73483927129032834896752299863417649931910776258319 47186677718010677166148023226592393024760740967779 26805529798115327